Patent Publication Number: US-10312837-B2

Title: Information processing apparatus, and recording medium storing computer program

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an information processing apparatus and a recording medium storing a computer program for processing a signal acquired by measuring a moving object. 
     Description of the Related Art 
     Generally, an optical rotary encoder is widely used to detect a movement amount, an angle, a position, and/or the like of a moving object, such as a motor. The optical rotary encoder irradiates a rotational signal plate where a pattern required to detect a signal is formed, with uniform light from a light-emitting diode (LED) or the like. Then, the optical rotary encoder detects transmitted light delivered through the pattern or reflected light returned from the signal plate by a light-sensitive element, such as a photodiode or a phototransistor. The optical rotary encoder generates an electric signal pattern from a result of the detection. Then, the optical rotary encoder generates an encoder output signal based on this electric signal pattern. As functional categorization of the encoder output signal, there are known an incremental type, which is output as a relative position, and an absolute type, which is output as an absolute position. The following paragraphs will be described, focusing on the incremental type. 
     Regarding the incremental type, there is known a technique for realizing highly accurate detection of the position by interpolation processing. This technique works, as a precondition therefor, assuming that amplitude and offset values of the encoder signals are consistent and two-phase analog sinusoidal signals out of phase with each other by 90 degrees are output. 
     As specific methods for the interpolation processing, there are known a method based on resistor division and a method based on an arctangent (arctan) calculation. 
     As a method for carrying out the arctangent calculation, there is known a method that performs rotational calculation processing on coordinate data, which is called a “COordinate Rotation DIgital Computer (CORDIC) algorithm”. First, CORDIC handles an input signal as two-dimensional coordinate data. Then, CORDIC allows the arctangent calculation to be realized only by repeating a simple calculation constituted by a bit shift and an addition/subtraction for a rotation of coordinates in this two-dimensional coordinate data. 
     However, the actual encoder output signal contains a harmonic component therein, and is not an ideal sinusoidal signal. Therefore, even correcting errors of the amplitude, the offset, and the phase with respect to the encoder output signal has been unable to achieve a precise sinusoidal signal, resulting in occurrence of a detection error when the interpolation processing has been performed. 
     To correct such a detection error, a technique discussed in Japanese Patent Application Laid-Open No. 2009-303358 generates such a correction value that a value acquired by differentiating a detected displacement amount (detected angle) of the encoder, i.e., a displacement speed is kept constant. This technique sets the generated correction value for each detected position in advance, thereby correcting the detected position. Further, a technique discussed in Japanese Patent Application Laid-Open No. 2006-170837 utilizes the fact that the detection error transitions periodically and approximates a sine wave by this detection error amount, thereby sequentially calculating the detection error amount and correcting the detected position. 
     SUMMARY OF THE INVENTION 
     The related art suffers from a number of problems. For example, the method discussed in Japanese Patent Application Laid-Open No. 2009-303358 requires preparations of correction values as many as a resolution of the detected position. Therefore, this method results in an undesirable enormous increase in a memory area storing the correction values according to an increase in the resolution of the detected position. On the other hand, the method discussed in Japanese Patent Application Laid-Open No. 2006-170837, as a first disadvantage thereof, requires a calculation time period for generating the correction value. Further, even when the transition of the detection error can approximate the ideal sine wave, positional information (a reference position) used to calculate the detection error is the detected position including the error, so that this method results in an undesirable reduction in accuracy with which the detection error is calculated due to its principle itself. 
     Various aspects of the present invention include, among other things, methods and apparatuses capable of processing the encoder signal of the moving object with high accuracy while saving a capacity of the memory spent for the correction of the detection error. 
     To ameliorate the above-described problems, according to an aspect of the present invention, an information processing apparatus includes an acquisition unit configured to acquire a first phase signal and a second phase signal that are acquired by measuring a rotation of a moving object, and a calculation unit configured to calculate a rotational angle by an iterative calculation so as to satisfy a relational expression bearing an arctangent. The relational expression bearing the arctangent uses a first cosine wave and a second cosine wave at a higher harmonic of the first cosine wave for the first phase signal, and a first sine wave and a second sine wave at a higher harmonic of the first sine wave for the second phase signal. 
     Further features of the present invention will become apparent from the following description of example embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a control block diagram illustrating a motor control apparatus according to a first example embodiment. 
         FIG. 2  is a block diagram illustrating a configuration of a displacement detection unit according to the first example embodiment. 
         FIG. 3  is a block diagram illustrating a configuration of an interpolation processing unit according to the first example embodiment. 
         FIG. 4  is a block diagram illustrating a configuration of an arctangent calculation unit according to the first example embodiment. 
         FIG. 5  is a block diagram illustrating a configuration of an arctangent calculation unit according to a second example embodiment. 
         FIG. 6  is a block diagram illustrating a configuration of an arctangent calculation unit according to a third example embodiment. 
         FIG. 7  is a block diagram illustrating a configuration of an arctangent calculation unit according to a fourth example embodiment. 
         FIG. 8  is a block diagram illustrating a configuration of a displacement detection unit according to a fifth example embodiment. 
         FIG. 9  is a block diagram illustrating a configuration of a harmonic component removal filter unit according to the fifth example embodiment. 
         FIGS. 10A and 10B  schematically illustrate the motor control apparatus. 
         FIG. 11  illustrates two-phase encoder output signals. 
         FIG. 12  illustrates an ideal waveform (sine wave) of the encoder signal and an actual waveform of the encoder signal. 
         FIG. 13  illustrates a detected displacement amount and a detection error with respect to an actual displacement of the motor. 
         FIG. 14  illustrates a waveform of an encoder signal including a harmonic distortion according to the first example embodiment, the second example embodiment, and the fifth example embodiment. 
         FIG. 15  illustrates a calculation result according to the first example embodiment. 
         FIG. 16  illustrates a calculation result according to the second example embodiment. 
         FIG. 17  illustrates a calculation result in a case where no correction is made in the third example embodiment. 
         FIG. 18  illustrates a waveform of an encoder signal including a harmonic distortion according to the third example embodiment. 
         FIG. 19  illustrates a calculation result according to the third example embodiment. 
         FIG. 20  illustrates a calculation result according to the fifth example embodiment. 
         FIG. 21  illustrates output signals having two phases that are output by an optical encoder. 
         FIG. 22  illustrates an operation of a vectoring mode of a COordinate Rotation DIgital Computer (CORDIC). 
         FIG. 23  illustrates how a vector mode function is realized by rotating a reference vector. 
         FIGS. 24A and 24B  each illustrate an example of a configuration of a CORDIC according to a sixth example embodiment. 
         FIGS. 25A and 25B  each illustrate an example of a configuration of a CORDIC according to a seventh example embodiment. 
         FIGS. 26A and 26B  each illustrate an example of a configuration of a CORDIC according to an eighth example embodiment. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     In the following description, example embodiments of the present invention will be described in detail with reference to the drawings. 
     An information processing apparatus mounted on a motor control apparatus and capable of removing a harmonic distortion superposed on an encoder signal will be described as a first example embodiment of an information processing apparatus according to a first example embodiment of the present invention. 
     &lt;Configuration of Motor Control Apparatus&gt; 
       FIGS. 10A and 10B  schematically illustrate a motor control apparatus according to the present example embodiment.  FIG. 10A  is an overall view of a motor control apparatus  1000 , and  FIG. 10B  is a schematic plan view of an encoder scale  1002 . Further, the motor control apparatus  1000  detects a rotational angle (displacement amount) of a motor shaft of a rotational motor  1001 . 
     The rotational angle is detected by the encoder scale  1002  including a rotational slip disk and a fixed slit disk, and a sensor unit  1003  including a light-emitting element (light-emitting diode) and a light-sensitive element (photodiode). The rotational slit disk is mounted on the motor shaft of the rotational motor  1001 , and rotates together with the motor shaft. On the other hand, the fixed slit disk and the sensor unit  1003  are fixed on a substrate. The encoder is configured in such a manner that the rotational slit disk and the fixed slit disk are positioned between the light-emitting element and the light-sensitive element. 
     A plurality of slits  1005  is provided on the encoder scale  1002 . The encoder scale  1002  rotates around the motor shaft as a center of a rotational axis thereof according to a rotational displacement of the motor shaft of the rotational motor  1001 . The rotation of the rotational slit disk leads to either permitting or prohibiting light of the light-emitting element to be transmitted or from being transmitted therethrough. Further, the fixed slit disk includes two slits so that signals output from the encoder have two phases. 
     Two light-sensitive elements are provided to the sensor unit  1003 , and these light-sensitive elements form electric signal patterns having two phases by detecting the light transmitted through the slits  1005  and further divided into two types of patterns, i.e., an A-phase pattern and a B-phase pattern due to the fixed slits, respectively. 
       FIG. 11  illustrates the two-phase encoder output signals. As illustrated in  FIG. 11 , an A-phase signal and a B-phase signal out of phase with each other by 90 degrees are generated in the optical encoder. The encoder is configured in this manner in a case where the encoder acquires the two-phase encoder signals, but the encoder includes a plurality of fixed slits and a plurality of light-sensitive elements in a case where the encoder acquires encoder signals having a plurality of phases. The detection principle of the encoder is not limited to the optical method (the method using the transmitted light), and the encoder can also employ another method, such as an optical method using reflected light, an electrostatic method, and a magnetic method. Further, the rotational slit disk may be mounted on a driving target body to be driven by the motor control apparatus  1000  instead of being mounted on the motor shaft, and the encoder may be configured to detect a movement amount of the driving target body. 
     A motor controller  1004  controls rotational driving of the rotational motor  1001 . The motor controller  1004  includes a driving unit that drives the rotational motor  1001 , and a control unit that controls this driving unit. The motor controller  1004  compares a motor rotational angle (target displacement amount), which is a target value, and a motor detected angle (detected displacement amount), which is an actually measured value. Then, the motor controller  1004  performs feedback control so that the actually measured value matches the target value. This is a motor control method called a closed loop, but the motor controller  1004  can employ even an open loop control method that drives the motor while acquiring the motor detected angle (detected displacement amount) but not comparing it with the target value. 
       FIG. 1  is a control block diagram of the motor control apparatus  1000  according to the present example embodiment. A driving unit  101  feeds a predetermined driving signal  1  to the rotational motor  1001  based on an output signal from the motor controller  1004 , which is a superior control unit. The motor shaft, which is a movable portion  102  (measurement target object), is displaced by a predetermined rotational angle by the input of the driving signal  1  thereto. A displacement detection unit  103  detects a displacement amount (positional displacement amount) of the rotational angle of the movable portion  102  and outputs a result of the detection. 
       FIG. 2  illustrates a configuration of the displacement detection unit  103  according to the present example embodiment. An encoder  201  movable according to the movement of the movable portion  102  generates the encoder signals that are sinusoidal two-phase signals out of phase with each other by 90 degrees like the examples illustrated in  FIG. 11  according to the displacement amount, and outputs the generated signals to an interpolation processing unit  202 . These encoder signals are not ideal sine waves and generally each contain a harmonic component therein as indicated by an actual encoder signal illustrated in  FIG. 12  (only one phase is illustrated). Optical phenomena, such as occurrence of a light intensity distribution of the light-emitting element and a diffraction phenomenon due to the fixed slit and the rotational slit, are complicatedly intertwined with each other, by which this harmonic component occurs. Now, for example, the optical encoder is used as the encoder  201 . However, the phenomenon in which the harmonic component occurs and is superposed is known to also occur in a magnetic encoder due to a distortion of a magnetic field distribution, a distortion of a magnetic resistance, and/or the like, and is not limited to the optical encoder. 
       FIG. 3  illustrates a configuration of the interpolation processing unit  202 . An analog/digital (A/D) convertor  301  is used to convert an analog A-phase signal  4  and an analog B-phase signal  5 , which are analog wavelike signals, into digital signals (digital A-phase signal  6  and digital B-phase signal  7 ). A filter circuit and/or a noise removal circuit are/is mounted on the interpolation processing unit  202  to remove a noise component contained in the encoder signals that occurs between before and after the A/D conversion. Known configurations can be used as configurations of these filter circuit and noise removal circuit, and therefore detailed descriptions thereof will be omitted herein. 
     An offset and phase difference correction unit  302  performs offset processing on each of the digital A-phase signal  6  and the digital B-phase signal  7  with respect to a reference value of each of them. By this offset processing, the A-phase and B-phase encoder signals are turned into such signals that change toward a negative side and a positive side across zero. 
     Further, in a phase difference correction, the offset and phase difference correction unit  302  performs correction processing so that the phase difference between the A phase and the B phase matches 90 degrees. Examples of a method for this processing for correcting the phase difference include a method that performs rotational calculation processing on one of the encoder signals only by an amount corresponding to a deviation of the phase difference from 90 degrees, and a method that sets a sum of the A phase and the B phase and a difference between the A phase and the B phase as new two-phase signals, thereby guaranteeing that the phase difference matches 90 degrees regarding the new two-phase signals. In this manner, an adjusted digital A-phase signal  8  and an adjusted digital B-phase signal  9  offset and corrected in terms of the phase difference are acquired. 
     A region determination unit  303  determines a Lissajous quadrant (region) generated from the adjusted digital A-phase signal  8  and the adjusted digital B-phase signal  9 . Assume that the Lissajous quadrant is a first quadrant if both the A-phase signal and the B-phase signal are positive, a second quadrant if the A-phase signal is negative and the B-phase signal is positive, a third quadrant if both the A-phase signal and the B-phase signal are negative, and a fourth quadrant if the A-phase signal is positive and the B-phase signal is negative. Positional information of the encoder is incremented or decremented according to a change in the quadrant at this time, by which rough positional information is acquired. This positional information allows the position to be acquired 90-degrees by 90-degrees, for example, if an encoder slit interval is determined to be 360 degrees. A sum of this rough positional information and an interpolated position, which will be described below, is determined to be the detected displacement amount, but this rough positional information will not be described in the following paragraphs because the present description will focus only on the interpolation processing (interpolated position). 
     Further, the region determination unit  303  outputs A-phase data X  10 , which is an absolute value of the adjusted digital A-phase signal  8 , and B-phase data Y  11 , which is an absolute value of the adjusted B-phase signal  9 , so as to allow calculation processing subsequent to the region determination unit  303  to be performed with use of only positive values. 
     An arctangent calculation unit  304  calculates the interpolated position by calculating an arctangent value (arctan) based on the A-phase data X  10  and the B-phase data Y  11 , and outputs an interpolated position  12  in a range of 0 degrees to 90 degrees, i.e., in the first quadrant. 
     An angle conversion unit  305  corrects the interpolated position  12  in the range of 0 degrees to 90 degrees that is calculated by the arctangent calculation unit  304  according to the quadrant information (division into the four quadrants) determined by the region determination unit  303 . More specifically, the interpolated position  12  is directly set as the detected displacement amount if the quadrant information indicates the first quadrant or the third quadrant, and “90 degrees—the interpolated position  12 ” is set as the detected displacement amount if the quadrant information indicates the second quadrant or the fourth quadrant (the rough positional information is added at this time in a case where the rough positional information is taken into consideration). In this manner, the displacement detection unit  103  sequentially calculates a highly accurate angular value subjected to the interpolation processing from the encoder signal. However, a calculation error undesirably occurs if the calculation is carried out for the angular calculation by the arctangent calculation unit  304  assuming that the encoder signal is the ideal sine wave, like the conventional technique. A cause thereof is the harmonic component contained in the encoder signal, and the detection error occurs in this case. 
       FIG. 12  illustrates the ideal waveform (sine wave) of the encoder signal and the actual waveform of the encoder signal. Further,  FIG. 13  illustrates the detected displacement amount and the detection error when the actual waveform of the encoder signal illustrated in  FIG. 14  is input. The detection error refers to a difference between an actual displacement amount and the detected displacement amount of the driven motor. 
     As illustrated in  FIG. 13 , the detected displacement amount is not linear with respect to the actual displacement amount due to an influence of the detection error. In other words, the detected displacement amount draws a curve on the graph. When the encoder signal is the ideal sine wave, the displacement detection error does not occur and the actual displacement amount and the detected displacement amount are linear with respect to each other. In other words, the detected displacement amount draws a straight line on the graph. 
     Further, as understood from a change in the detection error illustrated in  FIG. 13 , the detection error periodically changes with respect to the actual displacement amount, i.e., depends on a generation amount of the harmonic component of the encoder signal, and changes so as to have four cycles in one encoder slit interval (360 degrees). Then, the error occurs by approximately ±5 degrees. However, this is an example of a characteristic when the encoder signal is the encoder waveform illustrated in  FIG. 14 , and the detection error is not limited thereto. Further, the above-described tendency also appears in a cosine wave. 
     In the above-described manner, the harmonic component occurs in the encoder signal, and carrying out the calculation without taking the harmonic component into consideration undesirably causes the detection error. The present example embodiment carries out an arctangent calculation in consideration of the harmonic component contained in the encoder signal (harmonic distortion correction CORDIC rotational calculation method) to improve detection accuracy of the displacement detection unit  103 . In the following description, details thereof will be described. 
     &lt;Configuration of Arctangent Calculation Unit in Consideration of Harmonic Component&gt; 
       FIG. 4  illustrates a configuration of the arctangent calculation unit  304  using the CORDIC rotational calculation that can correct the harmonic distortion according to the present example embodiment. In the present example embodiment, the configuration using the CORDIC calculation will be described, but the rotational angle may be acquired by being converged with use of an iterative calculation, such as a binary search. An A-phase input signal X (A-phase data X  10 ) and a B-phase input signal Y (B-phase data Y  11 ) assumed to be used in the first example embodiment are each expressed by an expression (1). However, as already described above, the A-phase data X  10  and the B-phase data Y  11  are input as the absolute values, and therefore are assumed to have only positive values actually.
 
 X=a   1  cos θ− a   3  cos 3θ
 
 Y=a   1  sin θ− a   3  sin 3θ  (1)
 
     The first example embodiment takes the harmonic component into consideration as far as a third harmonic component as indicated in the expression (1). Further, a 1  and a 3  in the expression (1) represent a coefficient (intensity) of a fundamental frequency component and a coefficient (an intensity) of the third harmonic component, respectively, and the first example embodiment is designed for a case where each of them is the same between the A phase and the B phase. At this time, the arctangent calculation is carried out. More specifically, in the present example embodiment, a rotational angle θ satisfying a relational expression indicated by an expression (2) acquired from the expression (1) is acquired by the CORDIC rotational calculation method. 
     
       
         
           
             
               
                 
                   
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                         ⁢ 
                         
                             
                         
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     Intensity information  41  (a 1  and a 3 ) is input from the superior control unit to a rotational direction determination unit  401  as known information. This intensity information  41  can be acquired by, for example, a method that analyzes a frequency of the encoder signal by fast Fourier transform (FFT) in advance, and extracts intensity components of the fundamental frequency and the third harmonic. However, the information input here does not necessary have to be the intensity component, and such an arbitrary value that can reduce detection error may be selected as a value corresponding to the intensity information  41 . 
     &lt;θ Rotational Calculation&gt; 
     In a θ rotational calculation, a rotational calculation is carried out based on a basic rotational angle θ, and this is rotational calculation processing for acquiring coordinate data corresponding to the fundamental frequency component. A selection unit  402  forming the θ rotational calculation selects a fixed value (1, 0) that is reference coordinate data  42  at the first rotational calculation in a series of CORDIC calculations, and selects θ rotated coordinate data  48 , which is a result of the CORDIC rotational calculation, at the second and subsequent rotational calculations, which is carried out as an iterative calculation. The A-phase data X  10  and the B-phase data Y  11  are updated, and the above-described iterative calculation is cleared when a new arctangent calculation is carried out. Then, this leads to a start of a new CORDIC calculation, in which the reference coordinate data  42  (1, 0) is recursively selected as the first rotational calculation and the rotated coordinate data  48  is selected after that. 
     A θ i  rotation unit  404  is a rotational calculation circuit that rotates θ rotation selected coordinate data  44  by a rotational angle of θ i  in a direction indicated by a rotational direction δ i    47 . This rotational calculation has a characteristic of the CORDIC rotational calculation, and a rotational calculation expressed by an expression (3) is carried out with respect to a number of iterative rotational calculation times i. 
     
       
         
           
             
               
                 
                   
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     In this expression (3), (X i-1 , Y i-1 ) is coordinate data input to the θ i  rotation unit  404 , and (X i , Y i ) indicates coordinate data output from the θ i  rotation unit  404 . Further, the number of the iterative rotational calculation times i has values from 0 to m−1, as m represents a final number of the iterative rotational calculation times. Further, in the expression (3), when the number of the iterative rotational calculation times i is zero, (X −1 , Y −1 ) becomes coordinate data on a right-hand side, and this corresponds to the reference coordinate data  42  (1, 0) selected by the selection unit  402  as the first rotational calculation. Further, the rotational direction δ i    47  is fixed to 1 (positive rotation (i.e., rotation in leftward direction)) when the number of the iterative rotational calculation times i is zero, and 1 or −1 (negative rotation (rotation in rightward direction)) is selected according to a result of the determination made by the rotational direction determination unit  401  after that. Further, the actual rotational angle θ i  of the rotational calculation with respect to the number of the rotational calculation times i, which is indicated in the expression (3), is expressed by an expression (4).
 
θ i =tan −1 (2 −1 )  (4)
 
     A 2θ rotational correction unit  406  is a correction circuit that corrects a difference in the absolute value due to a difference between the number of the rotational calculation times carried out by the θ i  rotation unit  404  and the number of the rotational calculation times carried out by a 3θ i  rotation unit  405 , which will be described below. More specifically, the 2θ rotational correction unit  406  carries out a calculation expressed by an expression (5). 
     
       
         
           
             
               
                 
                   
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     In the expression (5), (X in , Y in ) on a right-hand side is rotated coordinate data  46  before the correction that is the output of the θ i  rotation unit  404 , and (X out , Y out ) on a left-hand side is rotated coordinate data  48  (COS θ, SIN θ) corrected (updated) by the 2θ rotational correction unit  406 . 
     However, this calculation does not necessarily have to be carried out by this rotational correction unit  406 , and a calculation unit capable of realizing a similar function may be disposed in the rotational direction determination unit  401 , which will be described below. 
     The above-described series of operations corresponds to one iterative rotational calculation in the basic CORDIC calculation (θ rotational calculation). In the present example embodiment, a 3θ rotational calculation illustrated in  FIG. 4  is also carried out at the same time as this basic CORDIC calculation (θ rotational calculation). 
     &lt;3θ Rotational Calculation&gt; 
     In the 3θ rotational calculation, the rotational calculation is carried out based on a rotational angle 3θ, and this is rotational calculation processing for acquiring coordinate data corresponding to the third harmonic component. A selection unit  403  forming the 3θ rotational calculation selects reference coordinate data  43  (1, 0) at the first rotational calculation in a series of CORDIC calculations (3θ), and selects 3θ rotated coordinate data  49 , which is a result of the CORDIC rotational calculation, at the second and subsequent rotational calculations, which is carried out as an iterative calculation. The A-phase data X  10  and the B-phase data Y  11  are updated, and the above-described iterative calculation is cleared when a new arctangent calculation is carried out. Then, this leads to a start of a new CORDIC calculation, in which the reference coordinate data  43  (1, 0) is selected again as the first rotational calculation, and the rotated coordinate data  49  is selected after that. 
     The 3θ i  rotation unit  405  rotates 3θ rotation selected coordinate data  45  by the rotational angle of 3θ i  in the direction indicated by the rotational direction δ i    47 . This rotational calculation has the characteristic of the CORDIC rotational calculation, and a rotational calculation expressed by an expression (6) is carried out with respect to the number of the iterative rotational calculation times i. 
     
       
         
           
             
               
                 
                   
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                   6 
                   ) 
                 
               
             
           
         
       
     
     In this expression (6), (X i-1 ′, Y i-1 ′) is coordinate data input to the 3θ i  rotation unit  405 , and (X i ′, Y i ′) indicates coordinate data (rotated coordinate data  49  (COS 3θ, SIN 3θ)) output from the 3θ i  rotation unit  405 . Further, in the expression (6), when the number of the iterative rotational calculation times i is zero, (X −1 ′, Y −1 ′) becomes coordinate data on a right-hand side, and this corresponds to the reference coordinate data  43  (1, 0) selected by the selection unit  403  as the first rotational calculation. Further, the actual rotational angle 3θ i  of the rotational calculation with respect to the number of the rotational calculation times i, which is indicated in the expression (6), is expressed by an expression (7).
 
3θ i =3·tan −1 (2 −i )  (7)
 
     The above-described series of operations corresponds to one iterative rotational calculation in the CORDIC calculation (3θ rotational calculation), which is one of characteristics of the present example embodiment. The rotated coordinate data  49  (COS 3θ, SIN 3θ) acquired at this time corresponds to the third harmonic component contained in the encoder signal. 
     In the above-described manner, the rotated coordinate data  48  (COS θ, SIN θ) and the rotated coordinate data  49  (COS 3θ, SIN 3θ) are acquired by the θ rotational calculation and the 3θ rotational calculation. However, actually, the absolute value increases every time the rotational calculation is carried out due to the characteristic of the CORDIC rotational calculation, and therefore the rotated coordinate data  48  and the rotated coordinate data  49  are multiplied by certain coefficients. However, the rotated coordinate data  48  and the rotated coordinate data  49  are brought into a state in which the coefficients of the coordinate data  48  and the coordinate data  49  match each other with the aid of the already described 2θ rotational correction unit  406 . Therefore, the coefficients do not directly affect the result of the calculation by the rotational direction determination unit  401 , which will be described below, whereby notations of these coefficients are omitted below. In the above description, the reference coordinate data  42  and the reference coordinate data  43  are assumed to be (1, 0), but they may be any coordinate data as long as the sine component is zero and the cosine components are the same in both of them. For example, they may be (2, 0) or may be (0.5, 0). 
     &lt;Determination of Rotational Direction&gt; 
     The following data is input to the rotational direction determination unit  401 . The rotated coordinate data  48  (COS θ, SIN θ) and the rotated coordinate data  49  (COS 3θ, SIN 3θ) respectively acquired from the θ rotational calculation and the 3θ rotational calculation are input to the rotational direction determination unit  401 . Further, the intensity information (a 1  and a 3 ), which is provided from the superior control unit, and the A-phase data X  10  and the B-phase data Y  11 , which are the encoder signal inputs, are also input. The direction determination unit  401  determines the rotational direction δ i    47  of the next iterative rotational calculation by using a calculation expression for determining the direction (discriminant). The expression used as the criterion is indicated by an expression (8) 
     
       
         
           
             
               
                 
                   
                     
                       Y 
                       X 
                     
                     - 
                     
                       
                         
                           
                             a 
                             1 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                         + 
                         
                           
                             a 
                             3 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                       
                       
                         
                           
                             a 
                             1 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                         - 
                         
                           
                             a 
                             3 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                           ⁢ 
                           θ 
                         
                       
                     
                   
                   ≥ 
                   0 
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     When the expression (8) is true, the rotational direction is determined to be the positive rotation (rotation in leftward direction), and δ i  has a value 1. When the expression (8) is false, the rotational direction is determined to be the negative rotation (rotation in rightward direction), and δ i  has a value −1. However, because the expression (8) can be mathematically derived, the discriminant is not limited to the expression (8). For example, a discriminant in which the fractions are cleared and the divisions are omitted as indicated in an expression (9) may be used. All of expressions derivable while maintaining the mathematical meaning of the expression (8) may be employed in the present example embodiment.
 
 Ya   1  cos θ− Ya   3  cos 3θ− Xa   1  sin θ− Xa   3  sin 3θ≥0  (9)
 
     In this manner, (COS 3θ, SIN 3θ), which is the third harmonic component, is contained in the discriminant, and this achieves an effect of correcting the third harmonic. The rotational direction δ i    47  is determined in this manner, which allows execution of the next iterative rotational calculation. 
     &lt;Calculation of Interpolated Position&gt; 
     The rotated coordinate data  48  and the rotated coordinate data  49  satisfying the expression (2), and a δ i  data row (data history), which serves as rotational angle information, can be acquired by carrying out the above-described θ rotational calculation, 3θ rotational calculation, and determination of the rotational direction, respectively, as many times as the final number of the iterative calculation times m. An argument calculation unit  407  carries out a calculation expressed by an expression (10) on the δ i  data row as the last calculation process, by which an argument θ formed by the rotated coordinate data  48 , i.e., the interpolated position  12  (θ) with the harmonic component removed therefrom is acquired.
 
θ=Σ i=0   m-1 δ i  tan −1 (2 −i )  (10)
 
     In the above-described manner, according to the present example embodiment, the argument can be calculated (arctangent calculation) while the harmonic component contained in the encoder output signal is removed as far as the third harmonic. As a result, the detected position can be acquired with high accuracy in which the detection error due to the third harmonic component is removed (corrected).  FIG. 15  illustrates the result of the calculation according to the present example embodiment when the encoder signal illustrated in  FIG. 13  is input. This result of the calculation is a result when the intensity a 1  of the fundamental frequency component is 1 and the intensity a 3  of the third harmonic component is −0.094. As illustrated in  FIG. 15 , the detection error is approximately ±0.15 degrees, and thus considerably reduces compared to the detection error when no correction is made. As a result, the detected displacement amount also almost matches the ideal displacement amount (they appear to overlap on the graph). 
     In the above-described manner, the calculation of the third harmonic component (3θ rotational calculation) is carried out at the same time as the conventional CORDIC calculation (corresponding to the θ rotational calculation). Then, the determination of the direction is also the improved determination using the discriminant in which the third harmonic component is added to the one in the conventional CORDIC calculation, and a calculation processing speed is not inferior compared to the conventional CORDIC calculation (in the case where only the θ rotational calculation is carried out). Further, the present example embodiment can also prevent or cut down the increase in the detection error correction memory. The present example embodiment can also be applied to another embodiment. For example, in the above description, the rotational motor is used as the movable portion  102 , but a linearly moving mechanism may be used instead thereof. Further, the movable portion  102  may be driven by an actuator such as a motor and a piezo actuator as the driving unit. 
     In a second example embodiment, another configuration of the arctangent calculation unit  304  will be described. More specifically, the second example embodiment is configured in consideration of harmonic components as far as a fifth harmonic component, and a  58  rotational calculation is added therein. Further, an expression used to determine the direction is different. In the following description, mainly, differences from the first example embodiment will be described. 
     &lt;Configuration of Arctangent Calculation Unit in Consideration of Harmonic Component&gt; 
       FIG. 5  illustrates a configuration of the arctangent calculation unit  304  using a CORDIC rotational calculation capable of correcting harmonic distortions as far as a fifth harmonic distortion according to the present example embodiment. The A-phase data X  10  and the B-phase data Y  11  assumed to be used in the second example embodiment are each expressed by an expression (11). However, as already described above, the A-phase data X  10  and the B-phase data Y  11  are input as the absolute values, and therefore are assumed to have only positive values actually.
 
 X=a   1  cos θ− a   3  cos 3θ+ a   5  cos 5θ
 
 Y=a   1  sin θ+ a   3  sin 3θ− a   5  sin 5θ  (11)
 
     The present example embodiment takes the harmonic components into consideration as far as the fifth harmonic component as indicated in the expression (11). Further, a 1 , a 3 , and a 5  in the expression (11) represent the intensity of the fundamental frequency component, the intensity of the third harmonic component, and an intensity of the fifth harmonic component, respectively, and the present example embodiment takes a case where each of them is the same between the A phase and the B phase. At this time, the arctangent calculation is carried out. More specifically, in the present example embodiment, θ satisfying a relational expression indicated by an expression (12) obtained from the expression (11) is obtained by the CORDIC rotational calculation method. 
     
       
         
           
             
               
                 
                   
                     Y 
                     X 
                   
                   = 
                   
                     
                       
                         
                           a 
                           1 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                       + 
                       
                         
                           a 
                           3 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                       - 
                       
                         
                           a 
                           5 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         5 
                         ⁢ 
                         θ 
                       
                     
                     
                       
                         
                           a 
                           1 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                       - 
                       
                         
                           a 
                           3 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         θ 
                       
                       + 
                       
                         
                           a 
                           5 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         5 
                         ⁢ 
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Intensity information  51  (a 1 , a 3 , and a 5 ) is input from the superior control unit to a rotational direction determination unit  501  as known information. This intensity information  51  can be acquired by, for example, a method that analyzes the frequency of the encoder signal by FFT in advance, and extracts the intensity components of the fundamental frequency, the third harmonic, and the fifth harmonic. 
     &lt;θ Rotational Calculation&gt; 
     A basic operation is similar to that of the first example embodiment, but a 4θ rotational correction unit  504  is different from that of the first example embodiment. 
     The 4θ rotational correction unit  504  corrects a difference in the absolute value due to a difference between the number of times that the rotational calculation is carried out by the θ i  rotation unit  404  and the number of times that the rotational calculation is carried out by a 5θ i  rotation unit  503 , which will be described below. More specifically, the 4θ rotational correction unit  504  carries out a calculation expressed by an expression (13). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             x 
                             out 
                           
                         
                       
                       
                         
                           
                             y 
                             out 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           1 
                           + 
                           
                             2 
                             
                               
                                 - 
                                 2 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               i 
                             
                           
                         
                         ) 
                       
                       2 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               x 
                               in 
                             
                           
                         
                         
                           
                             
                               y 
                               in 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     In the expression (13), (X in , Y in ) on a right-hand side is the rotated coordinate data  46  before the correction that is the output of the θ i  rotation unit  404 , and (X out , Y out ) on a left-hand side is the rotated coordinate data  48  (COS θ, SIN θ) corrected (updated) by the 4θ rotational correction unit  504 . 
     &lt;3θ Rotational Calculation&gt; 
     A basic operation is similar to that of the first example embodiment, but a 2θ rotational correction unit  505  is added thereto. 
     The 2θ rotational correction unit  505  corrects a difference in the absolute value due to a difference between the number of times that the rotational calculation is carried out by the 3θ i  rotation unit  405  and the number of times that the rotational calculation is carried out by the 5θ i  rotation unit  503 , which will be described below. More specifically, the 2θ rotational correction unit  505  carries out a calculation expressed by an expression (14). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             x 
                             out 
                           
                         
                       
                       
                         
                           
                             y 
                             out 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       ( 
                       
                         1 
                         + 
                         
                           2 
                           
                             
                               - 
                               2 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             i 
                           
                         
                       
                       ) 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               x 
                               in 
                             
                           
                         
                         
                           
                             
                               y 
                               in 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     In the expression (14), (X in , Y in ) on a right-hand side is rotated coordinate data  52  before the correction that is the output of the θ i  rotation unit  405 , and (X out , Y out ) on a left-hand side is the rotated coordinate data  49  (COS 3θ, SIN 3θ) corrected (updated) by the 2θ rotational correction unit  505 . 
     &lt;5θ Rotational Calculation&gt; 
     A selection unit  502  forming the 5θ rotational calculation selects reference coordinate data  53  (1, 0) at the first rotational calculation in a series of CORDIC calculations (5θ), and selects 5θ rotated coordinate data  55 , which is a result of the CORDIC rotational calculation, at the second and subsequent rotational calculations, which is carried out as an iterative calculation. The A-phase data X  10  and the B-phase data Y  11  are updated, and the above-described iterative calculation is cleared when a new arctangent calculation is carried out. Then, this leads to a start of a new CORDIC calculation, in which the reference coordinate data  53  (1, 0) is selected again as the first rotational calculation, and the rotated coordinate data  55  is selected after that. 
     The 5θ i  rotation unit  503  rotates 5θ rotation selected coordinate data  54  by a rotational angle of 5θ i  in the direction indicated by the rotational direction δ i    47 . This rotational calculation has the characteristic of the CORDIC rotational calculation, and a rotational calculation expressed by an expression (15) is carried out with respect to the number of times i that the rotational calculation is iteratively carried out. 
     
       
         
           
             
               
                 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 x 
                                 i 
                                 ″ 
                               
                             
                           
                           
                             
                               
                                 y 
                                 i 
                                 ″ 
                               
                             
                           
                         
                         ] 
                       
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 
                                   
                                     - 
                                     
                                       δ 
                                       i 
                                     
                                   
                                   ⁢ 
                                   
                                     2 
                                     
                                       - 
                                       i 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     δ 
                                     i 
                                   
                                   ⁢ 
                                   
                                     2 
                                     
                                       - 
                                       i 
                                     
                                   
                                 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                         · 
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 
                                   
                                     - 
                                     
                                       δ 
                                       i 
                                     
                                   
                                   ⁢ 
                                   
                                     2 
                                     
                                       - 
                                       i 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     δ 
                                     i 
                                   
                                   ⁢ 
                                   
                                     2 
                                     
                                       - 
                                       i 
                                     
                                   
                                 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                         · 
                         
                           [ 
                           
                             
                               
                                 1 
                               
                               
                                 
                                   
                                     - 
                                     
                                       δ 
                                       i 
                                     
                                   
                                   ⁢ 
                                   
                                     2 
                                     
                                       - 
                                       i 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     
                                       δ 
                                       i 
                                     
                                     ⁢ 
                                     
                                       2 
                                       
                                         - 
                                         i 
                                       
                                     
                                   
                                 
                               
                               
                                 1 
                               
                             
                           
                           ] 
                         
                         · 
                       
                     
                       
                   
                   ⁢ 
                   
                       
                     
                       
                         [ 
                         
                             
                         
                         ⁢ 
                         
                           
                             
                               1 
                             
                             
                               
                                 
                                   - 
                                   
                                     δ 
                                     i 
                                   
                                 
                                 ⁢ 
                                 
                                   2 
                                   
                                     - 
                                     i 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   δ 
                                   i 
                                 
                                 ⁢ 
                                 
                                   2 
                                   
                                     - 
                                     i 
                                   
                                 
                               
                             
                             
                               1 
                             
                           
                         
                         ] 
                       
                       · 
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               
                                 
                                   - 
                                   
                                     δ 
                                     i 
                                   
                                 
                                 ⁢ 
                                 
                                   2 
                                   
                                     - 
                                     i 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   δ 
                                   i 
                                 
                                 ⁢ 
                                 
                                   2 
                                   
                                     - 
                                     i 
                                   
                                 
                               
                             
                             
                               1 
                             
                           
                         
                         ] 
                       
                       · 
                       
                         [ 
                         
                           
                             
                               
                                 x 
                                 
                                   i 
                                   - 
                                   1 
                                 
                                 ″ 
                               
                             
                           
                           
                             
                               
                                 y 
                                 
                                   i 
                                   - 
                                   1 
                                 
                                 ″ 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     In this expression (15), (X i-1 ″, Y i-1 ″) is coordinate data input to the 5θ i  rotation unit  503 , and (X i ″, Y i ″) indicates coordinate data (rotated coordinate data  55  (COS 5θ, SIN 5θ)) output from the 5θ i  rotation unit  503 . Further, in the expression (15), when the number of the iterative rotational calculation times i is zero, (X −1 ″, Y −1 ″) becomes coordinate data on a right-hand side, and this corresponds to the reference coordinate data  53  (1, 0) selected by the selection unit  502  as the first rotational calculation. Further, the actual rotational angle 5θ i  in the rotational calculation with respect to the number of times i that the rotational calculation is carried out, which is indicated in the expression (15), is expressed by an expression (16).
 
5θ i =5·tan −1 (2 −i )  (16)
 
     The above-described series of operations corresponds to one iterative rotational calculation in the CORDIC calculation that is the 5θ rotational calculation according to the present example embodiment. Now, the acquired rotated coordinate data  55  (COS 5θ, SIN 5θ) corresponds to the fifth harmonic component contained in the encoder signal. 
     In the above-described manner, the rotated coordinate data  48  (COS θ, SIN θ), the rotated coordinate data  49  (COS 3θ, SIN 3θ), and the rotated coordinate data  55  (COS 5θ, SIN 5θ) are acquired by the θ rotational calculation, the 3θ rotational calculation, and the 5θ rotational calculation, respectively. However, actually, the absolute value increases every time the rotational calculation is carried out due to the characteristic of the CORDIC rotational calculation, and therefore the rotated coordinate data  48 , the rotated coordinate data  49 , and the rotated coordinate data  55  are multiplied by coefficients. However, the rotated coordinate data  48 , the rotated coordinate data  49 , and the rotated coordinate data  55  are brought into a state in which the coefficients of the coordinate data  48 , the coordinate data  49  and the coordinate data  55  match one another with the aid of the already described 4θ rotational correction unit  504  and  28  rotational correction unit  505 . Therefore, the coefficients do not directly affect the result of the calculation by the rotational direction determination unit  501 , which will be described below, whereby notations of these coefficients shall be omitted below. 
     &lt;Determination of Rotational Direction&gt; 
     The rotated coordinate data  48  (COS θ, SIN θ), the rotated coordinate data  49  (COS 3θ, SIN 3θ), and the rotated coordinate data  55  (COS 5θ, SIN 5θ) respectively obtained from the θ rotational calculation, the 3θ rotational calculation, and the 5θ rotational calculation are input to the rotational direction determination unit  501 . Further, the intensity information (a 1 , a 3 , and a 5 ), which is provided from the superior control unit, and the A-phase data X  10  and the B-phase data Y  11 , which are the encoder signal inputs, are also input. The direction determination unit  501  determines the rotational direction δ i    47  of the next iterative rotational calculation by a calculation expression for determining the direction. The expression used as the discriminant is indicated by an expression (17) 
     
       
         
           
             
               
                 
                   
                     
                       Y 
                       X 
                     
                     - 
                     
                       
                         
                           
                             a 
                             1 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                         + 
                         
                           
                             a 
                             3 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                         - 
                         
                           
                             a 
                             5 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                           ⁢ 
                           θ 
                         
                       
                       
                         
                           
                             a 
                             1 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                         - 
                         
                           
                             a 
                             3 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                           ⁢ 
                           θ 
                         
                         + 
                         
                           
                             a 
                             5 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                           ⁢ 
                           θ 
                         
                       
                     
                   
                   ≥ 
                   0 
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     When the expression (17) is true, the rotational direction is determined to be the positive rotation (rotation in the leftward direction), and δ i  has the value 1. When the expression (17) is false, the rotational direction is determined to be the negative rotation (rotation in the rightward direction), and δ i  has the value −1. However, because the expression (17) can be mathematically derived similarly to the first example embodiment, the discriminant is not limited to the expression (17). All of expressions derivable while maintaining the mathematical meaning of the expression (17) may be employed in the present example embodiment. 
     In this manner, the third harmonic component (COS 3θ, SIN 3θ) and the fifth harmonic component (COS 5θ, SIN 5θ) are contained in the discriminant, and this achieves an effect of correcting the harmonics as far as the fifth harmonic. 
     The rotational direction δ i    47  is determined in this manner, which allows execution of the next iterative rotational calculation. 
     &lt;Calculation of Interpolated Position&gt; 
     The rotated coordinate data  48 , the rotated coordinate data  49 , and the rotated coordinate data  55  satisfying the expression (12) can be acquired by carrying out the above-described θ rotational calculation, 3θ rotational calculation, 5θ rotational calculation, determination of the rotational direction as many times as the final number of times m that the calculation is iteratively carried out. The argument calculation unit  407  carries out the calculation expressed by the expression (10) as the final calculation process, by which the interpolated position  12  is obtained. 
     In the above-described manner, according to the second example embodiment, the arctangent calculation can be realized while the harmonic components contained in the encoder output signal are removed as far as the fifth harmonic. As a result, the detection error due to the third and fifth harmonic components is removed (corrected), and the detected position can be obtained with further higher accuracy than the first example embodiment. Similar to the first example embodiment, the calculation of the third harmonic component (3θ rotational calculation) and the calculation of the fifth harmonic component (5θ rotational calculation) are carried out at the same time as the conventional CORDIC calculation (corresponding to the θ rotational calculation). The determination of the direction is also the improved determination using the discriminant in which the third harmonic component and the fifth harmonic component are added to the one in the conventional CORDIC calculation, and the calculation processing speed is not inferior compared to the conventional CORDIC calculation (in the case where only the θ rotational calculation is carried out).  FIG. 16  illustrates the result of the calculation according to the second example embodiment when the encoder signal illustrated in  FIG. 13  is input. The result of the calculation is a result when the intensity a 1  of the fundamental frequency component is 1, the intensity a 3  of the third harmonic component is −0.094, and the intensity a 5  of the fifth harmonic component is −0.0023. The detection error is approximately ±0.02 degrees, and thus further reduces compared to that when the harmonic is corrected as far as the third harmonic according to the first example embodiment. 
     Further, in the second example embodiment, the method for correcting the harmonics as far as the fifth harmonic has been described, but harmonic components that are a cosine component COS (nθ) and a sine component (nθ) (n is a positive odd number) can be corrected by similarly implementing the configuration extension according to the second example embodiment from the first example embodiment. More specifically, these components can be corrected by adding θ rotational calculations as far as an nθ rotational calculation, adding the rotational correction unit that performs the correction regarding the number of times that the rotational calculation is carried out, and changing the discriminant in the rotational direction determination unit. In this manner, the present example embodiment can provide the arctangent calculation capable of easily removing a high harmonic component. 
     In a third example embodiment, another configuration of the arctangent calculation unit  304  will be described. A difference from the first example embodiment is to provide an arctangent calculation according to a case where the intensities of the fundamental frequency and the harmonic component are different between the A phase and B phase. In the first example embodiment, the intensity of the fundamental frequency component and the intensity of the harmonic component are the same between the A phase and the B phase as indicated in the expression (1). However, they may not be the same under influences of a characteristic of the encoder, the filter processing on the encoder signal, the processing for correcting the phase difference, and/or the like. Further, the accuracy with which the harmonic component is corrected also depends on accuracy of this intensity information, so that it is more convenient to allow the intensities to be set differently for the A phase and the B phase to provide the intensities with further high accuracy. Therefore, the present example embodiment provides an arctangent calculation according to a case where the intensities of the fundamental frequency and the harmonic component are different between the A phase and the B phase. In the following description, mainly, differences from the first embodiment will be described. 
     &lt;Configuration of Arctangent Calculation Unit in Consideration of Harmonic Component&gt; 
       FIG. 6  illustrates a configuration of the arctangent calculation unit  304  using a CORDIC rotational calculation capable of correcting the harmonic distortion as far as the third harmonic distortion according to the present example embodiment. The A-phase data X  10  and the B-phase data Y  11  assumed to be used in the third example embodiment are each expressed by an expression (17). However, as already described above, the A-phase data X  10  and the B-phase data Y  11  are input as the absolute values, and therefore are assumed to have only positive values actually.
 
 X=a   1  cos θ− a   3  cos 3θ
 
 Y=b   1  sin θ+ b   3  sin 3θ  (18)
 
     In the present example embodiment, the intensity of each of the components is different between the A phase and the B phase as illustrated in the expression (18). Therefore, in the present example embodiment, θ satisfying a relational expression indicated by an expression (1)9 obtained from the expression (18) is obtained by the CORDIC rotational calculation method (arctangent calculation is carried out). 
     
       
         
           
             
               
                 
                   
                     Y 
                     X 
                   
                   = 
                   
                     
                       
                         
                           b 
                           1 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                       + 
                       
                         
                           b 
                           3 
                         
                         ⁢ 
                         sin 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                     
                     
                       
                         
                           a 
                           1 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                       - 
                       
                         
                           a 
                           3 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         3 
                         ⁢ 
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     Intensity information  61  (a 1 , a 3 , b 1 , and b 3 ) is input from the superior control unit to a rotational direction determination unit  601  as known information. This intensity information  61  can be acquired by, for example, a method that analyzes the frequency of the encoder signal by FFT in advance, and extracts each of the intensity components. 
     &lt;θ Rotational Calculation&gt; 
     The θ rotational calculation and the 3θ rotational calculation are similar to those of the first example embodiment. 
     &lt;Determination of Rotational Direction&gt; 
     The rotated coordinate data  48  (COS θ, SIN θ) and the rotated coordinate data  49  (COS 3θ, SIN 3θ) respectively obtained from the θ rotational calculation and the 3θ rotational calculation are input to the rotational direction determination unit  601 . Further, the intensity information  61  (a 1 , a 3 , b 1 , and b 3 ), which is provided from the superior control unit, and the A-phase data X  10  and the B-phase data Y  11 , which are the encoder signal inputs, are also input to the rotational direction determination unit  601 . The direction determination unit  601  determines the rotational direction δ i    47  of the next iterative rotational calculation by a calculation expression for determining the direction. The expression used as the criterion is indicated by an expression (20). 
     
       
         
           
             
               
                 
                   
                     
                       Y 
                       X 
                     
                     - 
                     
                       
                         
                           
                             b 
                             1 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                         + 
                         
                           
                             b 
                             3 
                           
                           ⁢ 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                       
                       
                         
                           
                             a 
                             1 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                         - 
                         
                           
                             a 
                             3 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           3 
                           ⁢ 
                           θ 
                         
                       
                     
                   
                   ≥ 
                   0 
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     When the expression (20) is true, the rotational direction is determined to be the positive rotation (rotation in the leftward direction), and δ i  has the value 1. When the expression (20) is false, the rotational direction is determined to be the negative rotation (rotation in the rightward direction), and δ i  has the value −1. However, because the expression (20) can be mathematically derived similarly to the first example embodiment, the discriminant is not limited to the expression (20). All of expressions derivable while maintaining the mathematical meaning may be employed in the present example embodiment. In this manner, the iterative rotational calculation is sequentially carried out by the determination of the rotational direction δ i    47 . 
     In the above-described manner, according to the present example embodiment, the arctangent calculation can be provided while the third harmonic component is removed even when the intensities of the fundamental frequency and the harmonic component are different between the A phase and the B phase. 
       FIG. 17  illustrates the result of the calculation with no correction made and  FIG. 19  illustrates the result of the calculation according to the third example embodiment when an encoder signal illustrated in  FIG. 18  is input.  FIG. 19  illustrates a result of the calculation when the intensity a 1  of the fundamental frequency component of the A phase is 0.94, the intensity b i  of the fundamental frequency component of the B phase is 0.90, the intensity a 3  of the third harmonic component of the A phase is 0.055, the intensity b 3  of the third harmonic component of the B phase is 0.11. While the detection error is approximately ±8 degrees when no correction is made, the detection error considerably reduces to approximately ±0.2 degrees according to the third example embodiment. As a result, the detected displacement amount also almost matches the ideal displacement amount (they appear to overlap on the graph). 
     The present example embodiment changes the discriminant used by the rotational direction determination unit  601  according to an assumed theoretical formula of the encoder signal, thereby achieving flexible adaptability. Further, the present example embodiment can also be extended to a configuration capable of removing a high harmonic component similarly to the second example embodiment. This extension can be realized by the method described above in the description of the second example embodiment, and a description of the configuration for removing a high harmonic component with respect to the third example embodiment will be omitted herein. 
     In a fourth example embodiment, another configuration of the arctangent calculation unit  304  will be described. The arctangent calculation unit  304  according to the present example embodiment is configured for reducing a calculation load on the rotational direction determination unit. The process for determining the rotational direction based on the discriminant is a part of the CORDIC rotational calculation, and is iteratively performed. Therefore, it is possible to reduce the calculation load on this rotational direction determination unit, more specifically, perform this process only by an addition/subtraction, which allows the arctangent calculation to be carried out at an improved calculation speed as a result thereof. In the following description, mainly, differences from the first example embodiment and the third example embodiment will be described. 
     &lt;Configuration of Arctangent Calculation Unit in Consideration of Harmonic Component&gt; 
       FIG. 7  illustrates a configuration of the arctangent calculation unit  304  using a CORDIC rotational calculation capable of correcting the harmonic distortion as far as the third harmonic distortion according to the present example embodiment. The A-phase data X  10  and the B-phase data Y  11  assumed to be used in the fourth example embodiment are similar to those of the third example embodiment, and are expressed as indicated by the expression (17). Therefore, in the present example embodiment, the arctangent calculation unit  304  is configured to acquire θ satisfying the relational expression expressed by the expression (18) (carry out the arctangent calculation) by the CORDIC rotational calculation method similarly to the third example embodiment. 
     &lt;Generation of Initial Value of Rotational Calculation&gt; 
     An initial value generation unit  701  is configured significantly differently from that of the other example embodiments. The intensity information  61  (a 1 , a 3 , b 1 , and b 3 ), which is provided from the superior control unit, and the A-phase data X  10  and the B-phase data Y  11 , which are the encoder signal inputs, are fed to the initial value generation unit  701 . The initial value generation unit  701  generates four pieces of coordinate data based on these pieces of information, and feeds them to rotational calculations at stages subsequent thereto. More specifically, the initial value generation unit  701  generates and feeds initial coordinate data  71  (Ya 1 , 0), initial coordinate data  72  (Xb 1 , 0), initial coordinate data  73  (Ya 3 , 0), and initial coordinate data  74  (Xb 3 , 0). 
     &lt;θ Rotational Calculation&gt; 
     The θ rotational calculation includes two rotational calculations, i.e., a θ rotational calculation 1 and a θ rotational calculation 2, unlike the other example embodiments. A selection unit  702  forming the θ rotational calculation 1 selects the initial coordinate data  71  (Ya 1 , 0) at the first rotational calculation in the series of CORDIC calculations, and selects θ rotated coordinate data  81 , which is a result of the CORDIC rotational calculation, at the second and subsequent rotational calculations, which is carried out as an iterative calculation. The A-phase data X  10  and the B-phase data Y  11  are updated, and the above-described iterative calculation is cleared when a new arctangent calculation is carried out. Then, this leads to a start of a new CORDIC calculation, in which the updated initial coordinate data  71  (Ya 1 , 0) is selected again as the first rotational calculation, and the rotated coordinate data  81  is selected after that. The θ i  rotation unit  706  rotates θ rotation selected coordinate data  75  by the rotational angle of θ i  in the direction indicated by the rotational direction δ i    47 . This rotational calculation has the characteristic of the CORDIC rotational calculation, and the rotational calculation expressed by the expression (3) is carried out with respect to the number of the iterative rotational calculation times i. In this expression (3), (X i-1 , Y i-1 ) is coordinate data input to the θ i  rotation unit  706 , and (X i , Y i ) indicates coordinate data output from the θ i  rotation unit  706 . Further, the number of the iterative rotational calculation times i has the values from 0 to m−1, as m represents the final number of the iterative rotational calculation times. Further, in the expression (3), when the number of the iterative rotational calculation times i is zero, (X −1 , Y −1 ) becomes the coordinate data on the right-hand side, and this corresponds to the initial coordinate data  71  (Ya 1 , 0) selected by the selection unit  702  as the first rotational calculation. Further, when the number of the iterative rotational calculation times i is zero, the rotational direction δ i    47  is fixed to 1 (the positive rotation (the rotation in the leftward direction)), and 1 or −1 (negative rotation (rotation in the rightward direction)) is selected according to a result of a determination made by a rotational direction determination unit  712  after that. A 2θ rotational correction unit  710  corrects a difference in the absolute value due to a difference between the number of times that the rotational calculation is carried out by the θ i  rotation unit  706 , and the numbers of times that the rotational calculation is carried out by a 3θ i  rotation unit  708  and a 3θ i  rotation unit  709 , which will be described below. More specifically, the 2θ rotational correction unit  710  carries out the calculation expressed by the expression (5). 
     In the expression (5), (X in , Y in ) on the right-hand side is rotated coordinate data  79  before the correction that is the output of the θ i  rotation unit  706 , and (X out , Y out ) on the left-hand side is the rotated coordinate data  81  (Ya 1  COS θ, Ya 1  SIN θ) corrected (updated) by the 2θ rotational correction unit  710 . The above-described series of operations corresponds to one iterative rotational calculation in the θ rotational calculation 1 according to the present example embodiment. At this time, as a result of the input of the initial coordinate data  71  as the initial value, the rotated coordinate data  81  (Ya 1  COS θ, Ya 1  SIN θ) is obtained. The cosine component Ya i  COS θ therein serves as a calculation result corresponding to one of four terms in a discriminant used by the rotational direction determination unit  712 , which will be described below. The other rotational calculations (the θ rotational calculation 2, a 3θ rotational calculation 1, and a 3θ rotational calculation 2) are also carried out in a similar manner. Rotation selected coordinate data  76 , rotation selected coordinate data  77 , and rotation selected coordinate data  78  are selected by a selectin unit  703 , a selection unit  704 , and a selection unit  705 , respectively. Further, they are subjected to the rotational calculations by a θ i  rotation unit  707 , a 3θ i  rotation unit  708 , and a 3θ i  rotation unit  709 , respectively. Rotated coordinate data  80  before the correction that is subjected to the rotational calculation by the θ i  rotation unit  707  is corrected by a 2θ rotational correction unit  711 , by which rotated coordinate data  82  is obtained. In this manner, the rotated coordinate data  82  (Xb 1  COS θ, Xb 1  SIN θ), rotated coordinate data  83  (Ya 3  COS 3θ, Ya 3  SIN 3θ), and rotated coordinate data  84  (Xb 3  COS 3θ, Xb 3  SIN 3θ) are acquired, respectively. 
     &lt;Determination of Rotational Direction&gt; 
     The calculation expression for determining the direction by the rotational direction determination unit  712  according to the present example embodiment is indicated by an expression (21). This expression (21) is an expression in which the fractions are cleared and the divisions are omitted from the expression (20).
 
 Ya   1  cos θ− Ya   3  cos 3θ− Xb   1  sin θ− Xb   3  sin 3θ≥0  (21)
 
     Similarly to the other example embodiments, when the expression (21) is true, the rotational direction is determined to be the positive rotation (rotation in the leftward direction), and δ i  has the value 1. When the expression (21) is false, the rotational direction is determined to be the negative rotation (rotation in the rightward direction), and δ i  has the value −1. The present example embodiment is characterized in that the four terms on the left-hand side indicated in the expression (21) are contained in the respective results (rotated coordinate data  81 , the rotated coordinate data  82 , the rotated coordinate data  83 , and the rotated coordinate data  84 ) of the rotational calculations, which are the stages preceding thereto. Therefore, the rotational direction determination unit  712  can determine the rotational direction δ i    47  by carrying out only the addition/subtraction and referring to only the positive/negative determination thereof. This means that the CORDIC rotational processing unit for correcting the harmonic distortion is constructed without use of a multiplier. Therefore, this configuration leads to a speedup of the CORDIC rotational processing unit that carries out the iterative rotational calculation. 
     In the above-described manner, according to the present example embodiment, the CORDIC rotational calculation processing unit can be constructed without use of a multiplier. While realizing such a configuration, the present example embodiment allows the execution of the arctangent calculation that removes the harmonic component contained in the encoder output signal as far as the third harmonic, thereby succeeding in obtaining the highly accurate detected position in which the detection error due to the third harmonic component is removed (corrected) as a result thereof. The result of the calculation according to the present example embodiment is similar to that of the third example embodiment, and is acquired as illustrated in  FIG. 19 . Further, the present example embodiment can also be extended to a configuration capable of removing a high harmonic component similarly to the second example embodiment. This extension can be realized by the method described above in the description of the second example embodiment, and a description of the configuration for removing a high harmonic component with respect to the present example embodiment will be omitted herein. 
     A fifth example embodiment relates to an example application as a filter for removing the harmonic distortion in the CORDIC rotational calculation configured in consideration of the harmonic component that has been described in the other example embodiments, and the present example application will be described now. 
       FIG. 8  illustrates one example of a configuration of a displacement detection unit according to the fifth example embodiment. 
     An arctangent calculation unit  801  has the arctangent calculation function but does not have the function of removing the harmonic component, different from the configurations described in the descriptions of the other example embodiments. This is a configuration of the normal arctangent calculation using CORDIC. A large difference from the first example embodiment is that this arctangent calculation unit  801  includes a harmonic removal filter unit  802 . In the present example embodiment, because the arctangent calculation unit  801  does not calculate the harmonic component, the harmonic removal filter unit  802 , which is a stage preceding thereto, performs processing for removing the harmonic component. 
       FIG. 9  illustrates a configuration of the harmonic removal filter unit  802 . The harmonic removal filter unit  802  is configured approximately similarly to the arctangent calculation unit  304  according to the first example embodiment. A basic operation thereof is similar to the operation described in the description of the first example embodiment. A change therefrom is that the harmonic removal filter unit  802  is configured in such a manner that the argument calculation unit  407  is removed therefrom, and the rotated coordinate data  48  (COS θ, SIN θ), which is the calculation result of the θ rotational calculation, is output instead of the output of the rotational angle θ. The cosine component (COS θ) and the sine component (SIN θ) of the rotated coordinate data  48  correspond to harmonic component removed X data  14  and harmonic component removed Y data  16 , respectively. As a result of the series of iterative rotational calculations according to the present example embodiment, the rotated coordinate data  48  (COS θ, SIN θ), which is the fundamental frequency component, and the rotated coordinate data  49  (COS 3θ, SIN 3θ), which is the third harmonic component, can be acquired as an accompanying outcome. With use of this effect, the harmonic removal filter unit  802  is caused to function as a signal filter for extracting only the fundamental frequency component, i.e., removing the third harmonic component, which is a characteristic of the present example embodiment. 
     In the above-described manner, according to the present example embodiment, it is possible to provide an information processing apparatus of the encoder that has the filter function of removing the third harmonic component contained in each of the A-phase and B-phase signals.  FIG. 20  illustrates a result of performing the signal processing according to the fifth example embodiment on the encoder signal containing the harmonic component therein that is illustrated in  FIG. 14 . As illustrated in  FIG. 20 , it can be confirmed that the third harmonic component is removed and a highly accurate signal containing only the fundamental frequency component therein can be acquired. The present example embodiment can also be configured to employ the detailed configurations of the other example embodiments. More specifically, the present example embodiment can be configured to be able to remove a high harmonic component similarly to the second example embodiment, configured to work when the intensities of the fundamental frequency and the harmonic component are different between the A phase and the B phase similarly to the third example embodiment, and configured not to include the multiplier similarly to the fourth example embodiment. Theses configurations are arranged as described in the description of each of the example embodiments, and detailed descriptions thereof will be omitted herein. 
     Other Example Embodiments 
     The above-described example embodiments have been described as the example embodiments using the CORDIC calculation algorithm even for the calculation of the harmonic component, since the arctangent calculation is carried out based on the CORDIC calculation algorithm as a basic principle thereof. However, even use of another method for the calculation of the harmonic component is not a deviation from the spirit of the present invention. For example, the result of the basic rotational calculation acquired from the CORDIC rotational calculation (rotated coordinate data from the θ rotational calculation) can be converted into the rotated coordinate data subjected to the 3θ rotational calculation with use of a triple-angle formula of a trigonometric function. These pieces of rotated coordinate data may be input to the direction determination unit, and the direction determination unit may determine the direction of the next rotational calculation. 
     Further, the above-described example embodiments are configured as the recursive processing-type configuration that performs the operation of the iterative rotational calculation processing a plurality of times with use of the single rotation unit. However, the above-described example embodiments can also be realized even by a pipeline processing-type configuration that includes a plurality of stages of rotation units in the same rotational calculation unit, connects them in a pipeline manner, and performs the operation of the rotational calculation processing. The above-described motor control apparatus  1000  can be used for a pan head of, for example, a network camera and a stage of a manufacturing apparatus, and improve smoothness of an operation of the pan head. The network camera includes a central processing unit (CPU), a read only memory (ROM), a random access memory (RAM), an imaging unit, the pan head, and a network interface. 
     Further, the above-described example embodiments have been described assuming that the two-phase encoder signals for detecting the position, each of which contains the harmonic component therein. However, the applicability of the above-described example embodiments is not limited to the encoder signal, and the above-described example embodiments can also be applied to all kinds of two-phase signals containing the harmonic component therein. 
     For example, the two-phase signals corresponding to the motor rotational angle can be detected from a driving current when a three-phase brushless motor is driven. In other words, the motor rotational angle can be calculated by arctan (ATAN) processing from the detected two-phase signals. 
     It is known that the harmonic component is superposed on these two-phase signals. Therefore, applying the present example embodiment can eliminate the influence of the harmonic component in the two-phase signals, thereby allowing detection of a correct motor rotational angle. 
       FIG. 21  illustrates an A-phase signal and a B-phase signal having two phases that are output from an optical encoder mounted on a motor according to a sixth example embodiment of the present invention. The A-phase signal and the B-phase signal are a cosine wave and a sine wave out of phase with each other by 90 degrees. For example, the motor can measure a rotational position of the motor period by period in the sine wave by counting the sine-wave signal as a pulse. Further, the motor can detect what number period the position is in and how much degrees the phase of the position is, by detecting the phases of the sine wave and the cosine wave. The accuracy with which the motor rotational position is detected is determined according to accuracy with which the phase is detected, which raises a necessity of correctly detecting the phase. However, the actual signal output from the encoder contains the harmonic superposed thereon, and therefore cannot be the ideal sine wave and cosine wave. However, the waveform of the output signal can be regarded as an almost symmetric waveform in light of the mechanism according to which the output signal is generated. When the waveform of the output signal is the symmetric waveform, the superposed harmonic is limited to an odd harmonic. Further, as the order of the harmonic increases, power of the output signal drastically reduces. Therefore, the first priority is placed on the phase detection in consideration of the third harmonic, and then next priority is placed on the phase detection in consideration of the harmonics as far as the fifth harmonic. A configuration for them will be described now. 
       FIG. 22  illustrates an operation of a vectoring mode of a CORDIC. The CORDIC is an apparatus that carries out the rotational calculation of the coordinate data. The CORDIC calculates an argument of input two-dimensional vector data (X, Y) with use of the CORDIC rotational calculation in the vectoring mode. The CORDIC sequentially rotates the two-dimensional vector data (X, Y) toward an x axis according to a predetermined rotational angle sequence θ i =tan −1 (2 −i ) to allow the rotated vector to approximately coincide with the x axis in the end, and then determines that this cumulated rotational angle θ n  is the argument. Now, i is i=0, 1, 2, . . . . The cumulated rotational angle θ n  is a value acquired by cumulatively adding the rotational angle sequence θ i  while taking a rotational direction determined for each rotation into consideration, i.e., the cumulated rotational angle θ n  is calculated by θ n =Σsign(Y i )·θ i . In this expression, sign(Y i ) indicates, with ±1, a positive or negative sign of a y-axis component in the two-dimensional vector data when rotated by θ i , and the two-dimensional vector data is rotated in a rightward direction if sign(Y i ) is +1 and a leftward direction if sign(Y i ) is −1. 
       FIG. 23  illustrates how the vectoring mode function is realized by rotating a reference vector. In principle, the CORDIC can also acquire the argument as a rotational angle when the reference vector (1, 0) on the x axis is rotated toward the two-dimensional vector data (X, Y) by the CORDIC rotational calculation so that their orientations match each other, unlike the above-described vectoring mode. In other words, (cos θ, sin θ) is acquired as coordinates after this reference vector (1, 0) is rotated by θ in the leftward direction, and a discriminant for determining the next rotational direction is expressed as indicated by the following expression (22).
 
 Y/X ≥sin θ/cos θ  (22)
 
     The next rotational direction is determined to be the leftward direction if the discriminant (22) is true and the rightward direction if the discriminant (22) is false. However, generally, such an expression is not likely to be used in the calculation of the argument by the CORDIC. This is because the discriminant (22) requires a division, and undesirably leaves a multiplication even if the denominator in the discriminant (22) is transported, thereby being unable to be replaced with the simple calculation that is the characteristic of the CORDIC, i.e., a bit shift calculation and an addition/subtraction calculation. 
     However, in the present example embodiment, the discriminant (22) is highly useful. This is because the CORDIC according to the present example embodiment is characterized by extension of this discriminant (22) to the signal with the harmonic superposed thereon, and use of an expression acquired by transforming that into a discriminant for the vectoring mode. When the discriminant (22) is first transformed into the discriminant for the vectoring mode before being extended to the signal with the harmonic superposed thereon, the discriminant (22) is modified as indicated by the following expression (23).
 
− X  sin θ+ Y  cos θ≥0  (23)
 
     The discriminant (23) can be interpreted as an expression for determining whether or not the y-axis component is zero or larger when the vector (X, Y) is rotated by θ in the rightward direction, i.e., whether the rotated vector exceeds the x axis, as illustrated in  FIG. 22 . This discriminant (23) is a discriminant itself in the vectoring mode of the CORDIC. 
     Because the discriminant (23) is used to rotate the input two-dimensional vector (X, Y) while the discriminant (22) is used to rotate the reference vector (1, 0), the respective rotational directions are set to directions opposite from each other with the same result of the determination. In this manner, it can be understood that the discriminant (23) for the vectoring mode can be acquired from the discriminant (22) for the rotation of the reference vector. 
     Then, the discriminant (22) is extended to the signal with the third harmonic superposed thereon. Assuming that the amplitude values of the fundamental frequency and the third harmonic are known information a and β, respectively, a discriminant when the third harmonic is superposed on the fundamental frequency is expressed as indicated by the following expression (24).
 
 Y/X ≥(α sin θ+β sin 3θ)/(α cos θ−β cos 3θ)  (24)
 
     Numerators on both sides in the discriminant (24) correspond to a sine-wave phase component of the signal with the third harmonic superposed thereon, and denominators on the both sides in the discriminant (24) correspond to a cosine-wave phase component of the signal with the third harmonic superposed thereon. Then, θ when the right-hand side and the left-hand side are equal to each other in the expression (24) is the argument θ n  that should be acquired. A − sign is placed in front of β in the denominator on the right-hand side because the phase difference of the cosine wave is 90 degrees in the fundamental frequency but is turned into a phase difference of 270 degrees, i.e., a phase difference of −90 degrees in the third harmonic. For this reason, the apparent rotational direction of the third harmonic becomes opposite to the direction of the fundamental frequency. 
     The determination of the rotational direction according to the discriminant (24) proceeds in the following manner. If the discriminant (24) is true, the rotation is still insufficient, so that each of a fundamental frequency reference vector (α, 0) and a third harmonic reference vector (β, 0) is further rotated in an initial direction. On the other hand, if the discriminant (24) is false, the rotation is excessive, so that each of the fundamental frequency reference vector (α, 0) and the third harmonic reference vector (β, 0) is rotated in an opposite direction. Further, when the fundamental frequency reference vector (α, 0) is rotated according to the rotational angle sequence θ i , the third harmonic reference vector (β, 0) is rotated by 3θ i , which is three times as large as that. This is theoretical processing based on the discriminant (24), and, actually, the following processing is performed. 
     When the discriminant (24) is transformed into the discriminant for the vectoring mode similarly to the transform of the discriminant (22) into the discriminant (23) for the vectoring mode, the discriminant (24) is modified as indicated by the following expression (25).
 
 Y (α cos θ−β cos 3θ)≥ X (α sin θ+β sin 3θ)
 
α Y  cos θ−β Y  cos 3θ≥α X  sin θ+β X  sin 3θ
 
(−α X  sin θ+α Y  cos θ)−(β X  sin 3θ+β Y  cos 3θ)≥0  (25)
 
     An expression in the left-side first parentheses and an expression in the second parentheses on a left-hand side in the discriminant (25) correspond to a rightward e rotation of the fundamental frequency component and a leftward 3θ rotation of the third harmonic component in the input two-dimensional vector data, respectively. The fundamental frequency component and the third harmonic component are mixed in each element in the input two-dimensional vector (X, Y), which means that the third harmonic component is mixed in the first parentheses and the fundamental frequency component is mixed in the second parentheses on the left-hand side in the discriminant (25). Theses mixed components are each an unnecessary component, but can be ignored because becoming zero by being canceled out at the time of the final stage of the rotation, i.e., when the input two-dimensional vector is rotated and coincides with the x axis at the destination of the rotation. It can be confirmed from a calculation that these mixed components are canceled out, but a description of this calculation will be omitted herein. This is because it can be said that the fact that the discriminant (25) can be acquired from the transform of the other discriminant guarantees that these unnecessary components are actually cancelled out. 
     The control of the rotational direction according to the discriminant (25) functions in the following manner. If the discriminant (25) is true, the rotation is still insufficient, so that the CORDIC further rotates each of fundamental frequency coordinates (αX, αY) and third harmonic coordinates (βX, βY) in the initial direction. On the other hand, if the discriminant (25) is false, the CORDIC rotates each of the fundamental frequency coordinates (αX, αY) and the third harmonic coordinates (βX, βY) in the opposite direction. The description so far has been focused on the principle of the CORDIC based on the discriminant (25). 
       FIG. 24A  is a block diagram illustrating an example of the configuration of the CORDIC according to the present example embodiment, and realizes the principle of the above-described CORDIC. The CORDIC is the apparatus that carries out the rotational calculation of the coordinate data, and includes a coordinate conversion generation unit  3001 , a rotational direction determination unit  3002 , a fundamental frequency CORDIC rotational calculation unit  3003 , a third harmonic CORDIC rotational calculation unit  3004 , a rotational angle cumulative calculation unit  3005 , and selectors  3101  and  3102 . The coordinate conversion generation unit  3001  inputs the input two-dimensional coordinate data (X, Y), the fundamental frequency amplitude α, and the third harmonic amplitude β, and generates the fundamental frequency coordinate data (αX, αY) to which the basic rotation is applied, and the third harmonic coordinate data (βX, βY) to which the threefold rotation is applied. The fundamental frequency CORDIC rotational calculation unit  3003  is a rotational calculation unit for the fundamental frequency, and causes the basic rotation of the fundamental frequency coordinate data. The third harmonic CORDIC rotational calculation unit  3004  is a rotational calculation unit for the third harmonic, and causes the threefold rotation of the third harmonic coordinate data. The rotational direction determination unit  3002  refers to pieces of data input to the two CORDIC rotational calculation units  3003  and  3004 , and determines the rotational direction of these pieces of input data based on the discriminant (25). The rotational angle cumulative calculation unit  3005  is a unit that cumulatively adds the rotational angle, and cumulatively adds the rotational angle in the fundamental frequency CORDIC rotational calculation unit  3003 . 
     Next, a method for carrying out the rotational calculation of the coordinate data by the CORDIC will be described. The coordinate conversion generation unit  3001  multiplies the input two-dimensional coordinate data (X, Y) by the fundamental frequency amplitude value α measured in advance, and outputs the fundamental frequency initial coordinate data (αX, αY) to the selector  3101 . Further, the coordinate conversion generation unit  3001  multiplies the input two-dimensional coordinate data (X, Y) by the third harmonic amplitude value β measured in advance, and outputs the third harmonic initial coordinate data (βX, βY) to the selector  3102 . The selector  3101  is a selector for the fundamental frequency, and selects the fundamental frequency initial coordinate data (αX, αY) and outputs this data to the fundamental frequency CORDIC rotational calculation unit  3003  at the first calculation (i=0). The selector  3102  is a selector for the third harmonic, and selects the third harmonic initial coordinate data (βX, βY) and outputs this data to the third harmonic CORDIC rotational calculation unit  3004  at the first calculation (i=0). Further, the selector  3101  selects fundamental frequency rotated coordinate data output from the fundamental frequency CORDIC rotational calculation unit  3003  and outputs this data to the fundamental frequency CORDIC rotational calculation unit  3003  at the second and subsequent calculations (i=1 or larger). The selector  3102  selects third harmonic rotated coordinate data output from the third harmonic CORDIC rotational calculation unit  3004  and outputs this data to the third harmonic CORDIC rotational calculation unit  3004  at the second and subsequent calculations (i=1 or larger). 
     The rotational direction determination unit  3002  is a rotational direction determination unit, and determines the rotational direction of the CORDIC rotational calculation units  3003  and  3004  with use of the discriminant (25) based on the pieces of coordinate data selected by the selectors  3101  and  3012 . The fundamental frequency CORDIC rotational calculation unit  3003  rotates the coordinate data output from the selector  3101  according to the rotational angle sequence θ i  in the rotational direction determined by the rotational direction determination unit  3002 , and outputs the fundamental frequency rotated coordinate data to the selector  3101 . More specifically, the fundamental frequency CORDIC rotational calculation unit  3003  rotates the coordinate data by the rotational angle of tan −1 (2 −i ) in an i-th cycle (i is zero or a larger integer). The third harmonic CORDIC rotational calculation unit  3004  rotates the coordinate data output from the selector  3102  in the rotational direction determined by the rotational direction determination unit  3002  by 3θ i , which is three times as large as the rotational angle sequence θ i , and outputs the third harmonic rotated coordinate data to the selector  3102 . More specifically, the third harmonic CORDIC rotational calculation unit  3004  rotates the coordinate data by the rotational angle of 3×tan −1 (2 −i ) in the i-th cycle. In other words, the third harmonic CORDIC rotational calculation unit  3004  rotates the coordinate data by a rotational angle that is acquired by multiplying the rotational angle used by the fundamental frequency CORDIC rotational calculation unit  3003  by the order of the harmonic (three). 
     As the CORDIC rotational calculation units  3003  and  3004  each iteratively carry out the rotational calculation, the rotated coordinate data output from each of the CORDIC rotational calculation units  3003  and  3004  eventually coincides approximately with the x axis. The remaining difference between the rotated coordinate data and the x axis depends on the number of times that the rotational calculation is iteratively carried out and the number of calculated bits, and reduces as the number of times that the rotational calculation is iteratively carried out and the number of calculated bits increases. The rotational angle cumulative calculation unit  3005  cumulatively adds the rotational angle by which the coordinate data is rotated by the CORDIC rotational calculation unit  3003  based on the rotational direction determined by the rotational direction determination unit  3002 , thereby converging the rotational angle to the argument θn of the vector of the fundamental frequency in the two-dimensional coordinate data. In this manner, the CORDIC inputs the two-dimensional coordinate data including the fundamental frequency and the third harmonic, and calculates the argument en of the vector of the fundamental frequency in the two-dimensional coordinate data. 
     Next, the determination of the rotational direction by the rotational direction determination unit  3002  will be described. Immediately before the CORDIC rotational calculation units  3003  and  3004  each carry out the first CORDIC rotational calculation according to the rotational angle sequence θ i , the rotational direction determination unit  3002  inputs the two pieces of y-axis component data αY and βY generated by the coordinate conversion generation unit  3001 , and calculates a difference αY−βY therebetween. Then, the rotational direction determination unit  3002  determines the rotational direction of the first rotation based on whether or not this difference αY−βY is zero or larger. The CORDIC rotational calculation units  3003  and  3004  rotate the pieces of coordinate data by θ i  (i=0) and 3θ i  (i=0) in the rotational direction determined by the rotational direction determination unit  3002 , respectively, and output the pieces of rotated coordinate data. The selectors  3101  and  3102  select the pieces of rotated coordinate data generated by the CORDIC rotational calculation units  3003  and  3004 , and output these pieces of data to the CORDIC rotational calculation units  3003  and  3004 , respectively. Next, the CORDIC rotational calculation units  3003  and  3004  each carry out the second rotation. The rotational direction determination unit  3002  determines the rotational direction of the second rotation according to whether or not a difference between y-axis components that is calculated by the following expression (26) is zero or larger. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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     Two rotational calculations on a left-hand side in the expression (26) are carried out by the CORDIC rotational calculation units  3003  and  3004 , respectively. A difference between y-axis components in results of two rotational calculations indicated on a right-hand side is equal to a difference on the left-hand side in the discriminant (25). By that, it is clarified that the configuration of the CORDIC illustrated in  FIG. 24A  corresponds to the discriminant (25). 
     Regarding the rotational direction of the third and subsequent rotational calculations, the rotational direction determination unit  3002  determines the rotational direction based on the discriminant (25) in a similar manner while replacing θ i  in the expression (26) with the cumulated rotational angle. 
     Next, a discriminant in a case where amplitudes of the sine wave and the cosine wave are different between the fundamental frequency and the third harmonic will be described. Assuming that α and α′ represent the amplitudes of the sine wave and the cosine wave of the fundamental frequency and β and β′ represent the amplitudes of the sine wave and the cosine wave of the third harmonic, the discriminants (24) and (25) are modified as indicated by the following expressions (27) and (28), respectively.
 
 Y/X ≥(α sin θ+β sin 3θ)/(α′ cos θ−β′ cos 3θ)  (27)
 
(−α X  sin θ+α′ Y  cos θ)−(β X  sin 3θ+β′ Y  cos 3θ)≥0  (28)
 
     The coordinate conversion generation unit  3001  inputs two-dimensional (α, α′) and (β, β′) instead of inputting one-dimensional α and β, and outputs two-dimensional coordinates (αX, α′Y) and (βX, β′Y). Processing after that is similar to the above-described processing. Therefore, it is understood that the present example embodiment can also be easily applied even when the amplitudes of the sine wave and the cosine wave are different between the fundamental frequency and the third harmonic, only by changing the coordinate conversion generation unit  3001  in the above-described manner. 
       FIG. 24B  illustrates an example of another configuration of the CORDIC according to the present example embodiment, and illustrates a configuration in which a scaling correction unit  3201  is added to the configuration of  FIG. 24A . The CORDIC rotational calculation units  3003  and  3004  each carry out the coordinate rotation only by the simple bit shift and addition/subtraction, and therefore an absolute value of the vector after the rotation slightly changes. The rotational angle is different between the fundamental frequency and the third harmonic, which leads to a difference between change rates of the absolute values of the vectors of them, undesirably making it impossible to simply add the pieces of coordinate data after they are rotated. Therefore, the absolute value(s) of both or one of them should be corrected to make the change rate of the absolute value consistent. 
     In the CORDIC illustrated in  FIG. 24A , if the coordinate data is multiplied by (1+2 −2i ) after the fundamental frequency is rotated by θ i , this can make the change rate of the absolute value consistent between the fundamental frequency and the third harmonic. This calculation can be carried out with use of only a bit shift and an addition. This is one possible method, and another method may also be employed. Such a calculation for correcting the absolute value of the vector is called a scaling correction. In  FIG. 24B , the scaling correction unit  3201  carries out the scaling correction to make the change rate of the absolute value consistent between the respective vectors of the fundamental frequency rotated coordinate data output from the CORDIC rotational calculation unit  3003  and the third harmonic rotated coordinate data output from the CORDIC rotational calculation unit  3004 . The scaling correction unit  3201  is a scaling correction unit for the fundamental frequency, and carries out the scaling correction using the bit shift and the addition. In the i-th cycle, the scaling correction unit  3201  multiplies the rotated coordinate data output from the CORDIC rotational calculation unit  3003  by (1+2 −2i ), and outputs a result of this multiplication to the selector  3101  as the fundamental frequency rotated coordinate data. When i is i=1 or larger, the selector  3101  selects the data output from the scaling correction unit  3201 , and outputs this data to the CORDIC rotational calculation unit  3003 . 
     Now, in the case of the CORDIC that rotates only the fundamental frequency with no harmonic superposed thereon, the scaling correction unit  3201  does not have to carry out the scaling correction for each rotational calculation, and can achieve the intended correction by collectively carrying out the scaling correction only once before or after all of the rotational calculations. Therefore, the scaling correction is often carried out together with another calculation carried out before or after the CORDIC calculation. In this case, the scaling correction unit  3201  is not explicitly indicated like the illustration in  FIG. 24A . Therefore, the CORDIC expressing an aspect of the present example embodiment is represented by the illustration in  FIG. 24A , in which the scaling correction unit  3201  is omitted. On the other hand, the CORDIC adapted to the actual processing is represented by the illustration in  FIG. 24B , in which the scaling correction unit  3201  is included. 
     In the sixth example embodiment, the superposed harmonic is only the third harmonic, but the fifth or higher harmonic is also superposed in the actual apparatus. However, the power of the harmonic drastically attenuates as the order of the harmonic increases, so that in some cases the fifth or higher harmonic may be able to be ignored. Conversely, in a case where highly accurate measurement is specified, a further high harmonic should also be processed without being ignored according to this accuracy. Then, in a seventh example embodiment of the present invention, a configuration that processes the harmonics as far as the fifth harmonic as the further high harmonic will be described. 
     First, the above-described discriminant (24) is extended to a discriminant including the fifth harmonic. Assuming that the amplitude of the fifth harmonic is γ, the discriminant (24) is modified as indicated by the following expression (29).
 
 Y/X ≥(α sin θ+β sin 3θ+γ sin 5θ)/(α cos θ−β cos 3θ+γ cos 5θ)   (29)
 
     Because the phase difference of 90 degrees in the fundamental frequency is turned into a phase difference of 450 degrees and becomes equivalent to the phase difference of 90 degrees in the fifth harmonic, a + sign is placed in front of γ in a denominator on a right-hand side. Then, the rotational direction of the fifth harmonic becomes the same as the direction of the fundamental frequency. 
     Next, when being transformed into a discriminant for the vectoring mode, the discriminant (29) is modified as indicated by the following expression (30).
 
 Y (α cos θ−β cos 3θ+γ cos 5θ)≥ X (α sin θ+β sin 3θ+γ sin 5θ)α Y  cos θ−β Y  cos 3θ+γ Y  cos 5θ≥α X  sin θ+β X  sin 3θ+γ X  sin 5θ(−α X  sin θ+α Y  cos θ)−(β X  sin 3θ+β Y  cos 3θ)+(−γ X  sin 5θ+γ Y  cos 5θ)≥0  (30)
 
     An expression in the third parentheses on a left-hand side in the discriminant 30 is a new term for rotating the fifth harmonic component in the rightward direction by 5θ. This new term is an unnecessary component for each of the first to third parentheses, but they are canceled out to become zero when the input two-dimensional vector is rotated and coincides with the x axis at the destination of the rotation. 
       FIG. 25A  illustrates an example of a configuration of the CORDIC according to the seventh example embodiment.  FIG. 25A  is a configuration in which a selector  4103  and a fifth harmonic CORDIC rotational calculation unit  4005  are added, and a coordinate conversion generation unit  4001  and a rotational direction determination unit  4002  are provided instead of the coordinate conversion generation unit  3001  and the rotational direction determination unit  3002 , respectively, compared to  FIG. 24A . The fifth harmonic CORDIC rotational calculation unit  4005  is a rotational calculation unit for the fifth harmonic. The CORDIC according to the present example embodiment performs processing based on the discriminant (30). In the following description, differences of the present example embodiment from the sixth example embodiment will be described. The coordinate conversion generation unit  4001  inputs the input two-dimensional coordinate data (X, Y), the fundamental frequency amplitude α, the third harmonic amplitude β, and the fifth harmonic amplitude γ, and outputs the fundamental frequency initial coordinate data (αX, αY), the third harmonic initial coordinate data (βX, βY), and fifth harmonic initial coordinate data (γX, γY). More specifically, the coordinate conversion generation unit  4001  multiplies the two-dimensional coordinate data (X, Y) by the fundamental frequency amplitude α, and outputs the fundamental frequency initial coordinate data (αX, αY) to the selector  3101 . Further, the coordinate conversion generation unit  4001  multiplies the two-dimensional coordinate data (X, Y) by the third harmonic amplitude β, and outputs the third harmonic initial coordinate data (βX, βY) to the selector  3102 . Further, the coordinate conversion generation unit  4001  multiplies the two-dimensional coordinate data (X, Y) by the fifth harmonic amplitude γ, and outputs the fifth harmonic initial coordinate data (γX, γY) to the selector  4103 . The selector  4103  is a selector for the fifth harmonic, and selects the fifth harmonic initial coordinate data (γX, γY) output from the coordinate conversion generation unit  4001  and outputs this data to the CORDIC rotational calculation unit  4005  at the first calculation (i=0). Further, the selector  4103  selects fifth harmonic rotated data output from the CORDIC rotational calculation unit  4005  and outputs this data to the CORDIC rotational calculation unit  4005  at the second and subsequent calculations (i=1 or larger). The rotational direction determination unit  4002  is a rotational direction determination unit, and determines the rotational direction with use of the discriminant (30) based on the pieces of coordinate data selected by the selectors  3101 ,  3102 , and  4103 . The CORDIC rotational calculation unit  4005  rotates the coordinate data selected by the selector  4103  in the rotational direction determined by the rotational direction determination unit  4002  by 5θ i , which is five times as large as the rotational angle sequence θ i , and outputs the fifth harmonic rotated coordinate data to the selector  4103 . In other words, the CORDIC rotational calculation unit  4005  rotates the coordinate data by the rotational angle of 5×tan −1 (2 −i ) in the i-th cycle. To improve the accuracy while dealing with a higher harmonic, this effect can be achieved by adding a CORDIC rotational calculation unit for a seventh harmonic and a ninth harmonic. 
       FIG. 25B  illustrates an example of another configuration of the CORDIC according to the present example embodiment, and is a configuration in which scaling correction units  4201  and  4202  are added to the configuration of  FIG. 25A . The scaling correction units  4201  and  4202  function to make the change rate of the input/output absolute value consistent among the plurality of CORDIC rotational calculation units  3003 ,  3004 , and  4005 , and, for this purpose, determine one of them as a reference and carries out the scaling correction on the other two outputs, similarly to  FIG. 24B . As one example thereof, the scaling correction unit  4201  is a scaling correction unit for the fundamental frequency. The scaling correction unit  4201  carries out the scaling correction on the data output from the fundamental frequency CORDIC rotational calculation unit  3003 , and the scaling correction unit  4202  carries out the scaling correction on the data output from the third harmonic CORDIC rotational calculation unit  3004 . 
     More specifically, in the i-th cycle, the scaling correction unit  4201  multiplies the data output from the fundamental frequency CORDIC rotational calculation unit  3003  by (1+2 −2i )×(1+2 −2i ), and outputs a result of this multiplication to the selector  3101  as the fundamental frequency rotated coordinate data. The scaling correction unit  4202  is a scaling correction unit for the third harmonic, and multiplies the data output from the third harmonic CORDIC rotational calculation unit  3004  by (1+2 −2i ) and outputs a result of this multiplication to the selector  3102  as the third harmonic rotated coordinate data in the i-th cycle. The scaling correction unit  4202  carries out the calculation constituted by the bit shift and the addition once, and the scaling correction unit  4201  carries out the calculation constituted by the bit shift and the addition twice. The selector  3101  selects the data output from the scaling correction unit  4201  and outputs this data to the CORDIC rotational calculation unit  3003  when i is i=1 or larger. The selector  3102  selects the data output from the scaling correction unit  4202  and outputs this data to the CORDIC rotational calculation unit  3004  when i is i=1 or larger. 
     In the sixth and seventh example embodiments, the case has been described where there is no difference between initial phases of the superposed harmonic and the fundamental frequency, and the initial phases of the harmonic and the fundamental frequency are in phase with each other. In the actual waveform, a phase difference from the fundamental frequency occurs for each harmonic due to the motor&#39;s structural factor. When the initial phase of the third harmonic with respect to the fundamental frequency is φ, the above-described discriminant (24) is modified as indicated by the following expressions (31) and (32).
 
 Y/X ≥(α sin θ+β sin(3θ+φ))/(α cos θ−β cos(3θ+φ))  (31)
 
(−α X  sin θ+α Y  cos θ)−(β X  sin(3θ+φ)+β Y  cos(3θ+φ))≥0   (32)
 
     This phase φ can be collected by subjecting the observed waveform to analysis processing, and is unchangeable as long as the structure of the motor is unchanged and therefore only has to be collected once basically. 
     The collected phase φ should be realized as processing for shifting the initial phase in the CORDIC calculation processing. 
     Therefore, as illustrated in  FIG. 26A , an eighth example embodiment includes a third harmonic coordinate rotation unit  6001  for rotating the initial coordinates (βX, βY) to be input to the selector  3102 , which is the stage preceding to the third harmonic CORDIC rotational calculation unit  3004 , by the phase φ. 
     This third harmonic coordinate rotation unit  6001  rotates the input coordinates (βX, βY), and outputs (βX cos φ−βY sin φ, βX sin φ+Y cos φ). After being rotated by the phase φ by this coordinate rotation unit  6001 , the signal processed as the third harmonic is rotated by 3θ by the third harmonic CORDIC rotational calculation unit  3004 , and therefore is rotated by 3θ+φ in total. Therefore, the present example embodiment makes a determination corresponding to the above-described discriminant (32). 
     Further, when the fifth harmonic is superposed and the initial phase thereof with respect to the fundamental frequency is φ, the above-described discriminant (30) is modified as indicated by the following expression (33).
 
(−α X  sin θ+α Y  cos θ)−(β X  sin(3θ+φ)+β Y  cos(3θ+φ))+(−γ X  sin(5θ+φ)+γ Y  cos(5θ+φ))≥0  (33)
 
     The configuration capable of making the above-described determination is realized by a configuration illustrated in  FIG. 26B , in which the configuration illustrated in  FIG. 25B  is additionally provided with the above-described third harmonic coordinate rotation unit  6001  that rotates the initial coordinates of the third harmonic and a fifth harmonic coordinate rotation unit  7001  that rotates the initial coordinates of the fifth harmonic at stages respectively preceding to the corresponding selectors  3102  and  4103 . 
     The third harmonic coordinate rotation unit  6001  operates in a similar manner to the unit  6001  illustrated in  FIG. 26A , and the fifth harmonic coordinate rotation unit  7001  rotates the input coordinates (γX, γY), and outputs (γX cos φ+Y sin φ, −γX sin φ+γY cos φ). Similarly to the third harmonic, after being rotated by the phase c by this coordinate rotation unit  7001 , the signal processed as the fifth harmonic is rotated by 5θ by the fifth harmonic CORDIC rotational calculation unit  4005 , and therefore is rotated by 5θ+φ in total. Therefore, the present example embodiment can make a determination corresponding to the above-described discriminant (33). 
     According to the sixth, seventh, and eighth example embodiments, from instantaneous values of the sine wave and the cosine wave with the harmonic superposed on each of them, the phase of the rotational angle of the fundamental frequency at this instantaneous moment can be detected with high accuracy, which eliminates the necessity for the calculation of the correction value and the correction value memory for correcting the harmonic distortion. Further, the sixth and seventh example embodiments do not require the calculation of the correction value, and therefore can detect the phase with low delay and thus detect the rotational position of the motor at a high speed, thereby facilitating the positional control of the motor or the like. 
     Other Embodiments 
     Embodiment(s) of the present invention can also be realized by a computer of a system or apparatus that reads out and executes computer executable instructions (e.g., one or more programs) recorded on a storage medium (which may also be referred to more fully as a ‘non-transitory computer-readable storage medium’) to perform the functions of one or more of the above-described embodiment(s) and/or that includes one or more circuits (e.g., application specific integrated circuit (ASIC)) for performing the functions of one or more of the above-described embodiment(s), and by a method performed by the computer of the system or apparatus by, for example, reading out and executing the computer executable instructions from the storage medium to perform the functions of one or more of the above-described embodiment(s) and/or controlling the one or more circuits to perform the functions of one or more of the above-described embodiment(s). The computer may comprise one or more processors (e.g., central processing unit (CPU), micro processing unit (MPU)) and may include a network of separate computers or separate processors to read out and execute the computer executable instructions. The computer executable instructions may be provided to the computer, for example, from a network or the storage medium. The storage medium may include, for example, one or more of a hard disk, a random-access memory (RAM), a read only memory (ROM), a storage of distributed computing systems, an optical disk (such as a compact disc (CD), digital versatile disc (DVD), or Blu-ray Disc (BD)™), a flash memory device, a memory card, and the like. 
     While the present invention has been described with reference to example embodiments, it is to be understood that the invention is not limited to the disclosed example embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Applications No. 2016-092383, filed May 2, 2016, No. 2016-092384, filed May 2, 2016, and No. 2016-118015, filed Jun. 14, 2016, which are hereby incorporated by reference herein in their entirety.