Abstract:
A microphone apparatus for processing and outputting an output signal of a microphone array including at least nine microphones includes a directivity function processing circuit that converts the output signal of the microphone array into a unidirectional signal and that outputs the unidirectional signal. The directivity function processing circuit expands a directivity function whose variable is an incident angle of an acoustic wave into a Fourier series up to at least third order. The variable in the expanded expression is produced from output signals of the microphones forming the microphone array.

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
     The present invention contains subject matter related to Japanese Patent Application JP 2005-048542 filed in the Japanese Patent Office on Feb. 24, 2005, the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a microphone apparatus. 
     2. Description of the Related Art 
     In a videoconference, for example, generally, speech of speakers is picked up by a microphone on a table. The microphone may also pick up ambient noise, and an unclear speech signal may be output from the microphone. There are methods for picking up speech of speakers by using a microphone in order to obtain a clear speech signal. 
     A first method is to use a directional microphone and to give emphasis on speech while suppressing noise when the speech is input to the microphone. A second method is to adaptively process a speech signal output from a microphone to reduce noise components. The first and second methods relatively reduce the level of the noise components included in the speech signal, thereby obtaining a clear speech signal. 
     A microphone apparatus employing the first method includes six microphones disposed around a reference microphone (microphone unit), in which the outputs of the microphones are combined using a Fourier transform so that the overall microphone apparatus provides unidirectional performance. 
     This microphone apparatus is disclosed in Japanese Unexamined Patent Application Publication No. 2002-271885. 
     SUMMARY OF THE INVENTION 
     The above-described microphone apparatus combines the outputs of the microphones by determining the value of the first-order approximation term in the Fourier transform under the assumption of a single sound source and by deriving the value of the third-order approximation term from the first-order approximation term. Although the microphone apparatus provides unidirectional performance, the directional range (i.e., angular range in which gain can be obtained) is as wide as about ±60° off the main axis. 
     However, such a wide directional range makes it difficult to achieve the desired effects of a directional microphone in an environment where a plurality of sound sources or a noise source exists. 
     It is therefore desirable to provide a unidirectional microphone apparatus with a narrow directional range in which the direction of the directivity is electrically variable. 
     According to an embodiment of the present invention, a microphone apparatus for processing and outputting an output signal of a microphone array including at least nine microphones includes a directivity function processing circuit that converts the output signal of the microphone array into a unidirectional signal and that outputs the unidirectional signal, wherein the directivity function processing circuit expands a directivity function whose variable is an incident angle of an acoustic wave into a Fourier series up to at least third order, and the variable in the expanded expression is produced from output signals of the microphones forming the microphone array. 
     Therefore, the microphone apparatus has sharp unidirectional characteristics, and the directional direction of the microphone apparatus can be varied. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram showing a directivity function of a microphone; 
         FIGS. 2A and 2B  are characteristic diagrams showing the directivities of microphones; 
         FIG. 3  is a characteristic diagram for analyzing the directivity of a unidirectional microphone; 
         FIG. 4  is a diagram showing an analysis result of the directivity of the unidirectional microphone; 
         FIGS. 5A to 5C  are characteristic diagrams showing the directivity of the unidirectional microphone; 
         FIG. 6  is a layout diagram of a microphone array according to an embodiment of the present invention; 
         FIG. 7  is a diagram showing a directivity function of the unidirectional microphone using an approximation expression; 
         FIG. 8  is a diagram showing a portion of the directivity function; 
         FIG. 9  is a diagram showing a portion of the directivity function; 
         FIG. 10  is a diagram showing a portion of the directivity function; 
         FIG. 11  is a diagram showing a portion of the directivity function; 
         FIG. 12  is a diagram showing a portion of the directivity function; 
         FIG. 13  is a diagram showing a portion of the directivity function; 
         FIG. 14  is a diagram showing a directivity function according to an embodiment of the present invention; 
         FIG. 15  is a block diagram of a microphone apparatus according to an embodiment of the present invention; 
         FIGS. 16A and 16B  are characteristic diagrams of the microphone apparatus according to the embodiment of the present invention and a microphone apparatus of the related art; 
         FIGS. 17A and 17B  are characteristic diagrams of the microphone apparatus according to the embodiment of the present invention and a microphone apparatus of the related art; 
         FIG. 18  is a flowchart showing an exemplary routine for obtaining the directivity function shown in  FIG. 14 ; 
         FIG. 19  is a diagram showing a portion of the directivity function; and 
         FIG. 20  is a diagram showing a portion of the directivity function. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Directivity Function 
     A microphone is a converter for converting an acoustic wave output from a sound source into a speech signal (audio signal), and has a predetermined transfer characteristic with respect to the direction, frequency, etc., of the input acoustic wave. 
     The characteristic of the microphone is given by Eq. (1) shown in  FIG. 1 . The transfer characteristic D(θ, ω) is a function that varies depending on the direction θ and the angular frequency ω of the input acoustic wave, and represents the directivity of the microphone. The transfer characteristic D(θ, ω) is generally referred to as a “directivity function”. Thus, the directivity function represents the directivity of the microphone. 
     For example, a non-directional (omnidirectional) microphone has a directivity pattern shown in  FIG. 2A , and the directivity function is given as follows:
 
 D (θ, ω)=1
 
     A bidirectional microphone has a directivity pattern shown in  FIG. 2B , and the directivity function is given as follows:
 
 D (θ, ω)=cos θ
 
     Eq. (1) is satisfied when a single sound source exists. When N sound sources exist, Eq. (1) is satisfied for each of the sound sources, and the characteristic of the microphone is therefore given by Eq. (2) shown in  FIG. 1 . 
     Analysis of Unidirectional Microphone 
       FIG. 3  shows an ideal directivity function (directivity) of a unidirectional microphone. The following definitions are used: 
     θ: direction (angle) of sound source with respect to microphone 
     θ c : directional direction (direction of directional microphone) 
     θ w : directional range (angular range in which predetermined gain can be obtained). 
     The illustrated characteristic is regarded as a directivity function with respect to the variable θ, and can be written in terms of a Fourier series as given by Eq. (3) shown in  FIG. 4 . Expanding Eq. (3), using the approximation expression up to n=3, leads to Eq. (4) shown in  FIG. 4 . 
     In Eq. (4) , by setting, for example, θ w =60° and changing the directional direction θ c , directional characteristics shown in  FIGS. 5A to 5C  are obtained. A microphone with a directivity function satisfying Eq. (4) provides relatively sharp directivity as shown in  FIGS. 5A to 5C , and the directional direction θ c  can be arbitrarily varied. 
     Creation of Directivity Function 
     Referring to  FIG. 6 , nine microphones (microphone units) M 0  to M 8  are arranged in an array of three rows and three columns on the same plane to form a microphone array  10 . The microphones M 0  to M 8  are non-directional. The microphones M 0  to M 8  are equally spaced in both the row and column directions with a distance d therebetween. The microphone M 4  disposed at the center is the reference microphone. For example, the microphones M 0  to M 8  are pressure-type electret condenser microphones, and the distance d is 21 mm. 
     A sound source (not shown) is located in a plane including the microphone array  10 . The distance between the sound source and the reference microphone M 4  is represented by R, and the incident angle of the acoustic wave with respect to the microphones M 0  to M 8 , or the directional direction, is represented by θ. The distance R is greater than the distance d between the microphones M 0  to M 8 . The incident angle θ has any value. In  FIG. 6 , the incident angle θ is zero in the row direction of the microphones M 0  to M 8 . 
     The acoustic wave output from the sound source is given by Eq. (5) shown in  FIG. 7 . The output signal of the microphone Mi (i=0 to 8) is represented by x Mi (t). 
     In the microphone array  10 , Eq. (1) is applied to the reference microphone M 4 . By substituting Eq. (3) in Eq. (1) and modifying the equation, Eq. (6) shown in  FIG. 7  is obtained. As in Eq. (4), Eq. (6) is written by using the approximation up to n=3. 
     According to Eq. (6), the microphone array  10  has directivity, for example, as shown in  FIGS. 5A to 5C , if cos θ, cos 2θ, cos 3θ, sin θ, sin 2θ, and sin 3θ are determined. By changing the Fourier coefficients a 0  to a 3  and b 1  to b 3  depending on the values θ c  and θ w , the directional direction can be varied in the manner shown in  FIGS. 5A to 5C . 
     Method for Determining cos θ, cos 2θ, cos 3θ, sin θ, sin 2θ, and sin 3θ 
     The values of cos θ, cos 2θ, cos 3θ, sin θ, sin 2θ, and sin 3θ that are needed in Eq. (6) are determined from the output signals of the microphones M 0  to M 3  and M 5  to M 8 , which will be described in detail below. 
     Case of cos θ 
     As shown in  FIG. 8 , when the acoustic wave output from the sound source is input to the microphones M 3 , M 4 , and M 5  in the middle row of the microphone array  10 , if the acoustic wave output from the sound source is given by Eq. (5) shown in  FIG. 7 , path length differences shown in  FIG. 8  occur between the sound source and the microphones M 3  to M 5 . The output signals of the microphones M 3  to M 5  are given by Eq. (7) shown in  FIG. 8 . In Eq. (7), the path length differences are based on the distance R between the sound source and the reference microphone M 4 . 
     The difference between the output signal of the microphone M 3  and the output signal of the microphone M 5  is given by Eq. (8) shown in  FIG. 8 . When the relation of the approximation expression sin α=α is applied to Eq. (8), Eq. (8) can be changed to Eq. (9) shown in  FIG. 8 , and Eq. (9) is modified into Eq. (10). According to Eq. (10), the value of cos θ is obtained by performing arithmetic processing on the output signals of the microphones M 3  and M 5 . 
     If the microphone M 4  is assumed to be located at the center between the microphones M 3  and M 5 , it is understood according to Eq. (10) that the output signal of the microphone M 4  can be generated from the output signals of the microphones M 3  and M 5 . Furthermore, Eq. (10) shows that the bidirectional characteristic shown in  FIG. 2B  is obtained by performing arithmetic processing on the output signals of the microphones M 3  and M 5 . 
     Case of sin θ 
     As shown in  FIG. 9 , when the acoustic wave output from the sound source is input to the microphones M 1 , M 4 , and M 7  in the middle column of the microphone array  10 , path length differences shown in  FIG. 9  occur between the sound source and the microphones M 1 , M 4 , and M 7 . The output signals of the microphones M 1 , M 4 , and M 7  are given by Eq. (11) shown in  FIG. 9 . In Eq. (11), the path length differences are based on the distance R between the sound source and the reference microphone M 4 . 
     The difference between the output signal of the microphone M 1  and the output signal of the microphone M 7  is given by Eq. (12) shown in  FIG. 9 . When the relation of the approximation expression sin α=α is applied to Eq. (12), Eq. (12) can be changed to Eq. (13) shown in  FIG. 9 , and Eq. (13) is modified into Eq. (14). 
     According to Eq. (14), the value of sin θ is obtained by performing arithmetic processing on the output signals of the microphones M 1  and M 7 . Furthermore, Eq. (14) shows that the bidirectional characteristic in which the bidirectional characteristic shown in  FIG. 2B  is shifted by 90° is obtained by performing arithmetic processing on the output signals of the microphones M 1  and M 7 . 
     Case of cos 2θ 
     Eq. (10) also shows that the output signal of the microphone M 3  and the output signal of the microphone M 5  are used to determine the output signal of the microphone M 4  at the center therebetween. 
     As shown in  FIG. 10 , a virtual microphone V 3  is provided at the center between the microphones M 3  and M 4  and a virtual microphone V 5  is provided at the center between the microphones M 4  and M 5 . 
     The output signals of the virtual microphones V 3  and V 5  are given by Eqs. (15) and (16) shown in  FIG. 10  by a similar procedure of deriving Eq. (10), respectively. The difference between Eqs. (15) and (16) is given by Eq. (17) shown in  FIG. 10 . Eq. (18) shown in  FIG. 10  is derived from Eq. (17) using a similar procedure of deriving Eq. (10) from Eq. (8). 
     Substituting Eq. (18) in Eq. (17) and rearranging the terms lead to Eq. (19). By applying a double-angle identity, which is given by Eq. (20) shown in  FIG. 10 , to Eq. (19), Eq. (21) shown in  FIG. 10  is obtained. Eq. (21) is modified into Eq. (22) shown in  FIG. 10 . 
     According to Eq. (22), the value of cos 2θ is obtained by performing arithmetic processing on the output signals of the microphones M 3  to M 5 . 
     Case of sin 2θ 
     A similar procedure of determining cos 2θ is used to determine sin 2θ. Specifically, as shown in  FIG. 11 , a virtual microphone V 3  is provided at the center between the microphones M 0  and M 6 , and a virtual microphone V 5  is provided at the center between the microphones M 2  and M 8 . 
     The output signals of the virtual microphones V 3  and V 5  are given by Eqs. (23) and (24) shown in  FIG. 11  by a similar procedure of deriving Eq. (14), respectively. The difference between Eqs. (23) and (24) is given by Eq. (25) shown in  FIG. 11 . Eq. (26) shown in  FIG. 11  is derived from Eq. (25) using a similar procedure of deriving Eq. (10) from Eq. (8). 
     Substituting Eq. (26) in Eq. (25) and rearranging the terms lead to Eq. (28). By applying a double-angle identity, which is given by Eq. (27) shown in  FIG. 11 , to Eq. (28), Eq. (29) shown in  FIG. 11  is obtained. 
     According to Eq. (29), the value of cos 2θ is obtained by performing arithmetic processing on the output signals of the microphones M 0 , M 2 , M 6 , and M 8 . 
     Case of cos 3θ 
     As shown in  FIG. 12 , a virtual microphone V 0  is provided at the center between the microphones M 0  and M 3 , a virtual microphone V 6  is provided at the center between the microphones M 3  and M 6 , and a virtual microphone V 3  is provided at the position of the microphone M 3 . Further, a virtual microphone V 2  is provided at the center between the microphones M 2  and M 5 , a virtual microphone V 8  is provided at the center between the microphones M 5  and M 8 , and a virtual microphone V 5  is provided at the position of the microphone M 5 . 
     The output signals of the virtual microphones V 0  and V 6  are given by Eqs. (30) and (31) shown in  FIG. 12  by a similar procedure of deriving Eq. (14), respectively. The difference between Eqs. (30) and (31) is given by Eq. (32) shown in  FIG. 12 . Eq. (33) shown in  FIG. 12  is derived from Eq. (32) using a similar procedure of deriving Eq. (10) from Eq. (8). Substituting Eq. (33) in Eq. (32) and rearranging the terms lead to Eq. (34). Likewise, Eq. (35) is obtained for the virtual microphones V 2 , V 8 , and V 5 . 
     A virtual microphone V 4  is provided at the position of the microphone M 4 , and the output signal of the virtual microphone V 4  is determined from Eqs. (34) and (35), thereby obtaining Eq. (36) shown in  FIG. 12 . Substituting Eqs. (36) and (10) in a triple-angle identity, which is given by Eq. (37) shown in  FIG. 12 , leads to Eq. (38) shown in  FIG. 12 . 
     According to Eq. (38), the value of cos 3θ is obtained by performing arithmetic processing on the output signals of the microphones M 0 , M 2 , M 3 , M 5 , M 6 , and M 8 . 
     Case of sin 3θ 
     As shown in  FIG. 13 , virtual microphones V 3 , V 4 , and V 5  are provided at the positions of the microphones M 3 , M 4 , and microphone M 5 , respectively. 
     The output signals of the virtual microphones V 3 , V 4 , and V 5  are given by Eqs. (39), (40), and (41) shown in  FIG. 13  by a similar procedure of deriving Eq. (10), respectively. 
     Further, a virtual microphone Va is provided at the center between the virtual microphones V 3  and V 4 , and a virtual microphone Vb is provided at the center between the virtual microphones V 4  and V 5 . The output signals of the virtual microphones Va and Vb are given by Eqs. (42) and (43) shown in  FIG. 13  by a similar procedure, respectively. The output signal of the virtual microphone V 4  is determined from the signals given by Eqs. (42) and (43), thereby obtaining Eq. (44) shown in  FIG. 13 . 
     Substituting Eqs. (44) and (14) in a triple-angle identity, which is given by Eq. (45) shown in  FIG. 13 , leads to Eq. (46) shown in  FIG. 13 . 
     According to Eq. (46), the value of sin 3θ is obtained by performing arithmetic processing on the output signals of the microphones M 0  to M 3  and M 5  to M 8 . 
     Synthesis of Microphone Outputs 
     By replacing cos θ, cos 2θ, cos 3θ, sin θ, sin 2θ, and sin 3θ in Eq. (6) with Eqs. (10) , (22), (38), (14), (29), and (46), respectively, Eq. (47) shown in  FIG. 14  is obtained. According to Eq. (47), it is understood that the output signal of the reference microphone M 4  is combined with the output signals of the remaining microphones M 0  to M 3  and M 5  to M 8 , thereby achieving relatively sharp directivity (directivity function) as shown in  FIGS. 5A to 5C , and that the directional direction θ c  can be arbitrarily varied. 
     In Eq. (47), some terms are multiplied by 1/(jω). This arithmetic operation is carried out by performing a Fourier transform on the corresponding signals into the frequency domain. Specifically, the multiplication of 1/j means that the phase of the speech signal component at each frequency is advanced by 90°. In the actual arithmetic operation, the speech signal component in each band after the Fourier transform is processed so that the value of the imaginary part is replaced with the value of the real part and the value of the real part is replaced with the value of the imaginary part by inverting the sign of the real part. 
     The multiplication of 1/ω causes the amplitude (level) of the signal component to change depending on the frequency (ω/2π), and the amplitude is also compensated. 
     Embodiment 
       FIG. 15  shows a microphone apparatus according to an embodiment of the present invention. The microphone apparatus is configured such that the directional range θ w  is narrow and the directional direction θ c  is variable according to the concept described above. 
     The microphone apparatus includes a microphone array  10  having the structure shown in  FIG. 6 . The output signals of the microphones M 0  to M 8  are supplied to a nine-channel analog-to-digital (A/D) converter circuit  12  through a nine-channel microphone amplifier  11 , and are A/D converted into digital signals. The digital signals are supplied to a directional function processing circuit  13 , and the process given by Eq. (47) is performed to extract a signal y(t). The details of the processing method will be described below. 
     The output signal y(t) is supplied to a digital-to-analog (D/A) converter circuit  14 , and is D/A converted into an analog signal. The analog signal is transmitted to an output terminal  15  as a microphone output. 
     The directivity function processing circuit  13  is composed of, for example, a microcomputer, and is connected with an operation key  13 C. When the directional direction θ c  and the directional range θ w  are specified through the operation key  13 C, the Fourier coefficients a 0  to a 3  and b 1  to b 3  corresponding to the specified directional direction θ c  and directional range θ w  are generated and used in Eq. (47). In the processing circuit  13 , therefore, the output signals of the microphones M 0  to M 8  provide a characteristic corresponding to the specified directional direction θ c  and directional range θ w , and are combined into the signal given by Eq. (47). 
     The apparatus shown in  FIG. 15  is therefore a microphone apparatus whose directional range θ w  is narrow and whose directional direction θ c  is variable. Further, according to Eq. (47), the parameters needed for the computation are merely the output signals of the microphones M 0  to M 8  and the values for defining a directional characteristic (i.e., the values indicating the directional direction θ c  and the directional range θ w ). The directivity can be determined if the direction from which the acoustic wave arrives is unknown. 
       FIGS. 16A and 17A  show the simulation of the directivity of the microphone apparatus according to the embodiment of the present invention, and  FIGS. 16B and 17B  show the simulation of the directivity of the microphone apparatus of the related art disclosed in Japanese Unexamined Patent Application Publication No. 2002-271885 noted above. As is apparent from  FIGS. 16A and 16B , the frequency characteristics are substantially flat in the main frequency band. In  FIGS. 17A and 17B , patterns at an acoustic wave frequency of 1.5 kHz, by way of example, are illustrated. 
     As can be seen from  FIGS. 16A to 17B , the microphone apparatus according to the embodiment of the present invention (the characteristics shown in  FIGS. 16A and 17A ) provides better directivity as a unidirectional microphone than the microphone apparatus of the related art (the characteristics shown in  FIGS. 16B and 17B ). In particular, in the range of θ&lt;−60° or θ&gt;60°, acoustic waves from the corresponding directions are considerably suppressed. 
     Details of Operation of Directivity Function Processing Circuit 
     The directivity function processing circuit  13  executes a routine  100  shown in  FIG. 18  to perform the process given by Eq. (47). In this embodiment, one frame of speech signal includes 2048 samples. 
     The routine  100  starts from step  101 . In step  102 , the output signals of the microphones M 0  to M 8 , that is, the speech data output from the A/D converter circuit  12 , which correspond to nine-channel data for a sample, are input. In step  103 , the sums and differences in the bracketed expressions in Eq. (47) are calculated. For example, in the term in the third line of Eq. (47) (i.e., the term corresponding to Eq. (10)), the expression {x M3 (t)−x M5 (t)} is calculated. 
     In step  111 , it is determined whether or not the processing of steps  102  and  103  for the period of one frame has been performed, and, if not, the routine  100  returns to step  102 . 
     If the processing of steps  102  and  103  for the period of one frame has been performed, the routine  100  proceeds from step  111  to step  112 . In step  112 , the calculation results determined in step  103  are converted into frequency-domain data by performing a fast Fourier transform (FFT). In step  113 , coefficients of the bracketed expressions in Eq. (47) are phase-converted. For example, in the term in the third line of Eq. (47) (i.e., the term corresponding to Eq. (10)), the coefficient of the expression {x M3 (t)−x M5 (t)} is c/(2jωd), and the value c/(2ωd) is calculated, and is converted into the value of the imaginary part. 
     In step  114 , the Fourier coefficients a 0  to a 3  and b 1  to b 3  corresponding to the desired directivity are multiplied by the values determined in steps  103  and  113 , and the Fourier-series sum is calculated to determine the value given by Eq. (47). In step  115 , the determined value is subjected to inverse fast Fourier transform (IFFT) processing, and is converted into time-domain data. 
     In step  121 , the data converted in step  115  is supplied to the D/A converter circuit  14  for every period of one sample on a sample-by-sample basis. In step  122 , it is determined whether or not the processing of step  121  for the period of one frame has been performed, and, if not, the routine  100  returns to step  121 . 
     If the processing of step  121  for the period of one frame has been performed, the routine  100  proceeds from step  122  to step  123 . In step  123 , the process for the period of one frame ends. 
     According to the routine  100 , the process given by Eq. (47) is performed. In the routine  100 , the values in the bracketed expressions are calculated for each sample in step  103  before the FFT is performed in step  112 . The process can therefore be properly and smoothly carried out. 
     Another Method for Determining cos 2θ 
       FIGS. 19 to 20C  show another method for determining cos 2θ. Specifically, cos 2θ can be modified as given by Eq. (48) shown in  FIG. 19 . If the angles θ and φ satisfy the relation given by Eq. (49) shown in  FIG. 19 , Eq. (48) is equivalent to Eq. (50) shown in  FIG. 19 . 
     As shown in  FIGS. 20A and 20B , virtual microphones V 0 , V 2 , V 6 , and V 8  are provided at the positions where the microphones M 0 , M 2 , M 6 , and M 8  are rotated by 45° (=φ−θ) with respect to the reference microphone M 4  in the direction in which the incident angle θ decreases. In this case, the incident angle of the acoustic wave with respect to the virtual microphones V 0 , V 2 , V 6 , and V 8  is equal to the angle φ according to the relation given by Eq. (49). 
     The relationship between the acoustic wave with the incident angle φ and the output signals of the virtual microphones V 0 , V 2 , V 6 , and V 8  is equivalent to the relationship between the acoustic wave with the incident angle θ and the output signals of the microphones M 0 , M 2 , M 6 , and M 8 . Thus, the output signals of the virtual microphones V 0 , V 2 , V 6 , and V 8  are processed by a similar procedure to that of Eq. (29) (which is also shown in  FIG. 19 ) to yield the signal given by Eq. (51) shown in  FIG. 19 . 
     As shown in  FIG. 20C , the positions of the virtual microphones V 0 , V 2 , V 6 , and V 8  are shifted toward the reference microphone M 4  so as to be located at the positions of the microphones M 3 , M 1 , M 7 , and M 5 , respectively. In this case, the output signals of the virtual microphones V 0 , V 2 , V 6 , and V 8  are equivalent to the output signals of the microphones M 3 , M 1 , M 7 , and M 5 , respectively. The distance between the virtual microphones V 0 , V 2 , V 6 , and V 8  has a value of 2d in  FIG. 20B ; whereas, in  FIG. 20C , the difference has a value of √2·d. In the case of  FIG. 20C , therefore, Eq. (51) is changed to Eq. (52) shown in  FIG. 19 . 
     Substituting Eq. (50) in Eq. (52) leads to Eq. (53) shown in  FIG. 19 . It is therefore possible to calculate Eq. (47) using Eq. (53). 
     Other Embodiments 
     For example, in Eq. (10), the difference signal between the output signal of the microphone M 3  and the output signal of the microphone M 5  is obtained in the bracketed expression. When the distance d between the microphones M 0  to M 8  is small, if the frequency of the input acoustic wave is low, the difference between the acoustic wave input to the microphone M 3  and the acoustic wave input to the microphone M 5  is small and the level of the difference signal obtained in Eq. (10) becomes low. 
     When the distance d is large, if the frequency of the input acoustic wave is high, the path length difference between the acoustic wave input to the microphone M 3  and the acoustic wave input to the microphone M 5  is one wavelength or more, and the process given by Eq. (10) is not proper. 
     The same applies to the difference signal or sum signal of the output signals of the microphones M 0  to M 8 , resulting in low arithmetic precision in Eq. (47). It can therefore be difficult to obtain the desired directivity. 
     In such a case, two microphone arrays  10  are used. The distance d between microphones differs from one of the microphone arrays to the other, and the reference microphone disposed at the center is shared. The low-frequency component of the speech signal is extracted from the microphone array having a larger distance between the microphones, and the high-frequency component of the speech signal is extracted from the microphone array having a smaller distance. The signal obtained by summing the extracted components is subjected to the process given by Eq. (47), thereby achieving high directivity over a wide band. 
     In the above-described microphone apparatus, it is difficult to suppress noise arriving from the same direction as that of the target acoustic wave. In this case, for example, the output signal of the directivity function processing circuit  13  is adaptively processed to suppress the noise signal. In a case where noise is included in speech of speakers in a videoconference or the like, therefore, the noise can be suppressed to obtain a clear speech signal. 
     Further, first, the direction of a sound source can be detected, and, then, the directional direction θ c  and the directional range θ w  can be set again according to the detected direction, thereby emphasizing a target signal or suppressing an unnecessary signal. That is, the directivity function can be set so that sound in a specific direction can or cannot be picked up. Alternatively, a plurality of microphone arrays  10  may be arranged on the same plane so that the directional directions of the microphone arrays  10  are directed to a specific point, thereby emphasizing sound from a sound source located at the specific point. 
     Furthermore, it is possible to pick up clearer target sound by setting the directional direction to the target sound direction and the noise sound direction and subtracting the signal in the noise sound direction from the signal in the target sound direction. It is also possible to predict and remove acoustic waves input irrespective of the directional direction, such as noise from the vertical direction. 
     Moreover, a microphone array having a function, such as an echo canceller, may be used. In this case, impulse responses of the echo canceller are separately learned as information for the array outputs with individual directivities in, for example, 5°-step directional directions, thereby rapidly removing echo of the speech in the direction to which the microphone is directed. Alternatively, impulse responses of the echo canceller may be separately learned as information for, for example, eight directions, and the impulse response in a direction close to the direction to which the microphone is to be directed among the eight directions may be used as the initial value. In this case, the total amount of arithmetic operations can be reduced, and the residual echo can be reduced compared with the computation from the completely initial value. 
     It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and alterations may occur depending on design requirements and other factors insofar as they are within the scope of the appended claims or the equivalents thereof.