Abstract:
A first-order signal generator ( 135 ). The generator comprises a shift register ( 210 ′) having a number N of bit positions. Each bit position is operable to store a binary value, the shift register operable to shift the binary value at each of the bit positions. The generator also comprises circuitry for tapping selected ones of the bit positions and circuitry for applying a function ( 220 ′) to each binary value in the selected ones of the bit positions to provide a function output. The generator also comprises circuitry for coupling the function output as an input to one of the bit positions. Lastly, the generator also comprises circuitry ( 230 ′) for outputting a first-order noise signal by coupling, as a twos complement number, each binary value in a plurality of the bit positions

Description:
CROSS-REFERENCES TO RELATED APPLICATION  
       [0001]     Not Applicable.  
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT  
       [0002]     Not Applicable.  
       BACKGROUND OF THE INVENTION  
       [0003]     The present embodiments relate to digital circuits and are more specifically directed to a first-order noise generator.  
         [0004]     Noise generator output signals are used in various electronic device applications. As one application and detailed later, such a generator may provide a noise signal having a desired frequency profile (i.e., shaped noise) for use in an electronic device, such as in a sigma-delta converter. In this and other applications, various design criteria are often established in connection with implementing the noise generator, and indeed these criteria often apply to other circuitry associated with the application. For example, one criterion is to minimize the amount of power consumed by a device. As other examples, device size, complexity, and cost all should be minimized. As still another example with respect to the various signal generators, a certain frequency response is desired. Particularly in the present context of a first-order noise signal generator, preferably the response curve, over a desired range of frequencies, is such that the response curve changes by 10 dB per every order of magnitude of frequency of interest, where each order of frequency is sometimes referred to as a “decade;” thus, the goal is a frequency response change of 10 dB/decade for a first-order response. The preceding goals have been met to a certain extent in the prior art by implementing a first-order decay signal generator using a number of linear feedback shift registers (“LFSRs”) in a single implementation, as further detailed below.  
         [0005]     By way of background first to an individual LFSR,  FIG. 1  illustrates a single LFSR designated generally at  10 . LFSR  10  has N bit positions B 0  through B N-1 , each for storing a binary value of 0 or 1. As a shift register, the device operates in a cycle, typically in response to a clock (not shown), to shift the content of each bit position in a same direction and into a respective adjacent bit position, where the content in one end (e.g., at B N-1 ) is shifted out of the register and the content at the other end (e.g., B 0 ) receives a new input value. Thus, in this example and for sake of uniform discussion in this document, a shift is shown to be from left to right, although the opposite case most certainly may be alternatively implemented by one skilled in the art. In an LFSR, the bit content at selected bit positions (“SBPs”) of the register are combined into a function, shown as function f{SBPs} and designated at  20  in  FIG. 1 . The output of function f{SBPs} is also input into the register&#39;s input bit, which in the present example is bit position B 0 . Thus, in a given cycle, function f{SBPs} is determined, and while each of bit positions B 0  through B N-2  shifts its content rightward to the next adjacent bit and B N-1  shifts its content out of register  10 , the result of function f{SBPs} is provided as an input to bit position B 0 . This determination of function f{SBPs} and its provision as an input is the feedback function of the LFSR. Note that the function f{SBPs} may be determined in various forms, and typically it is implemented as a logical XOR of the SBPs, which are also sometimes referred to as taps, in a given order. The particular positions chosen as the SBPs as well as the exact choice of function f{SBPs} vary and may be determined by one skilled in the art from various known or ascertainable resources. Two uses of the contents of LFSR  10  of  FIG. 1  are noted with respect to the prior art, as separately described below.  
         [0006]     In a first prior art use of LFSR  10 , the entire sequence of bits, B 0  through B N-1  (which may be designated as [B 0 :B N-1 ]) may be used as a pseudorandom code generator. Such an application is desirable in telecommunication applications, or elsewhere, where a code is desired that has good auto and cross-correlation properties. When such an application is implemented, the sequence of [B 0 :B N-1 ] as it changes for each cycle of operation provides in effect a white or nearly-white noise signal. To illustrate this aspect,  FIG. 2  depicts a plot of the FFT of such a sequence over time, for an example of N=16 and for use of the SBPs of bit positions B 3 , B 8 , B 14 , and B 15 , and at a clocking rate of 40 MHz of LFSR  10 . As can be readily appreciated, across the depicted frequency spectrum there is a 0 dB response, demonstrating therefore the above-described white noise signal.  
         [0007]     A second prior art use of LFSR  10  is now described with reference to  FIG. 3 .  FIG. 3  illustrates a first-order noise generator  30 , that is, one that produces an output signal having a decay on the order of 10 dB/decade. Generator  30  includes a number M of LFSRs, each of the general form of LFSR  10  in  FIG. 1  and, thus, for sake of reference, shown in  FIG. 3  as LFSR  10   0 ,  10   1 , and so forth through  10   M-1 . While not explicitly shown, note also that each different LFSR x  in  FIG. 3  may use different taps as compared to the other LFSRs in generator  30 . The output of a same bit position of each LFSR is concatenated into an M-bit register  40 , thereby providing a value with bits V 0  through V M-1 ; for sake of example, that same bit position in  FIG. 3  is shown as the rightmost position (corresponding to position B N-1 ) in  FIG. 1 . Value [V 0 :V M-1 ] is connected as an input to a first order high pass filter  45 , which in response provides an output to a twos complement analyzer  50 , the output of which provides a first-order noise signal, FON. The operation of each LFSR  10   x  in generator  30  is as described in connection with  FIG. 1 , operating therefore in parallel and in a single cycle to each provide a respective value bit, V x , to register  40 . In response, twos complement analyzer  50  interprets the output of first order high pass filter  45  as a twos complement number, and thereby outputs its equivalent such as a signed number as FON. Thus, value [V 0 :V M-1 ] changes for each cycle of operation of the LFSRs  10   0  through  10   M-1 . With this operation and the successive changes in value [V 0 :V M-1 ] as well as the corresponding changes in FON, a first-order response is generated, that is, the changes in FON provide a 10 dB/decade decay if examined in the frequency domain.  
         [0008]     While the preceding applications have proven useful in various implementations, recall that design criteria seek to reduce device size, complexity, power consumption, and cost. Given these goals as well as others that may be ascertained by one skilled in the art, there arises a need to improve upon the prior art, as is achieved by the preferred embodiments described below.  
       BRIEF SUMMARY OF THE INVENTION  
       [0009]     In one preferred embodiment, there is a first-order signal generator. The generator comprises a shift register having a number N of bit positions. Each bit position is operable to store a binary value, and the shift register is operable to shift the binary value at each of the bit positions. The generator also comprises circuitry for tapping selected ones of the bit positions and circuitry for applying a function to each binary value in the selected ones of the bit positions to provide a function output. The generator also comprises circuitry for coupling the function output as an input to one of the bit positions. Lastly, the generator also comprises circuitry for outputting a first-order noise signal by coupling, as a twos complement number, each binary value in a plurality of the bit positions.  
         [0010]     Other aspects are also disclosed and claimed.  
     
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING  
       [0011]      FIG. 1  illustrates a linear feedback shift register (“LFSR”) according to the prior art.  
         [0012]      FIG. 2  illustrates a frequency response of the entirety of the bits in prior art LFSR of  FIG. 1 .  
         [0013]      FIG. 3  illustrates an M-bit value generator that provides a first-order decay signal by using M LFSRs according to the prior art.  
         [0014]      FIG. 4  illustrates a modulator system into which the preferred embodiments may be implemented.  
         [0015]      FIG. 5   a  illustrates the output components of the  FIG. 4  system when no dither signal is provided.  
         [0016]      FIG. 5   b  illustrates the output components of the  FIG. 4  system when a white noise dither signal is provided.  
         [0017]      FIG. 5   c  illustrates the output components of the  FIG. 4  system when a first-order noise dither signal is provided.  
         [0018]      FIG. 6   a  illustrates a generator of an 8-bit value indicating a first-order noise signal according to the preferred embodiments.  
         [0019]      FIG. 6   b  illustrates a generator of an N-bit value indicating a first-order noise signal according to the preferred embodiments.  
         [0020]      FIG. 7  illustrates a frequency response of the N-bit value in the preferred embodiment LFSR of  FIGS. 6   a  and  6   b.    
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0021]     The preferred embodiments are described as implemented into a dither circuit and with a modulator system utilizing that dither circuit. However, it is contemplated that this invention may have benefit in applications other than the specific implementation described in this specification. Accordingly, it is to be understood that the following description is provided by way of example only and is not intended to limit the true scope of this invention as claimed. Additionally,  FIGS. 1, 2 , and  3  are described in the earlier Background Of This Invention section of this document and the reader is assumed familiar with the principles of that discussion.  
         [0022]      FIG. 4  illustrates a functional block diagram of a single-stage modulator system  100  into which the preferred embodiments may be implemented. In general, system  100  has various aspects known in the art and such a modulator may be implemented in various forms, such as by including it in a digital signal processor (“DSP”) or by embodying each functional block in one of various circuits that are implemented by either hardware, software, or a combination thereof. Further, the overall operation of system  100  may be improved by inclusion of a linear feedback shift register first-order noise generator, consistent with the preferred embodiments as detailed later. Before reaching that discussion, however, system  100  in general is described. By way of introduction, system  100  may have many uses. As examples, modulator system  100  may be implemented as a sigma-delta converter, which can be used in an analog-to-digital converter, a digital-to-analog converter, or a fractional-N frequency synthesizer as well as in other quantizing tasks, and often these tasks and hence these devices are included in various electronic products. Sigma-delta converters compare favorably with other data converter technologies in that typically, in the former, a considerable percentage of the transistors are non-critical digital transistors that may be reduced in size, with only a relatively small number of analog transistors. Thus, converters are low cost, and they also provide high dynamic range and flexibility in converting low bandwidth input signals.  
         [0023]     Looking now to  FIG. 4  in detail, it may be implemented as either an analog or digital system  100  and, thus, is shown and described in general terms to apply to both systems. Thus, system  100  includes an input  100   IN  for receiving an input signal, x(k). Input  100   IN  is connected to a sigma-delta module  110 . The output of sigma-delta module  110  is connected as an input to a transfer function block  120 , having a transfer function, G(z). Block  120  may be implemented as an accumulator, integrator, or other device with its particular transfer function G(z) depending on the order of the modulator. The output of block  120  is connected as an input to a summing node  130 , which also receives as another input a dithering function, d(k) that is provided from a noise generator  135 . The output of summing node  130  is connected as an input to a quantizer  140 , which in the illustrated instance is shown for sake of a simpler example as a two-level quantizer implemented as a comparator; hence, this comparator has a second input connected to a reference level, V ref , which may be ground or some other potential. The output of quantizer  140  provides for system  100  the output  100   OUT  and a corresponding signal, y(k), which may be connected to other circuitry, such as a digital filter (not shown) so as to remove noise outside the band of interest. In addition, output  100   OUT  is also fed back as an input to a transfer function block  150 , having a transfer function F(z). Block  150  may be implemented as a digital-to-analog converter (“DAC”) or digital filter with its particular transfer function F(z) depending on factors such as the order of the modulator. As further appreciated below, the output of block  150  is connected to sigma-delta module  110 , whereby it is subtracted by sigma-delta module  110  from the signal x(k) provided at input  100   IN . Indeed, this operation provides the “sigma” and “delta” aspects, thereby giving rise to the sigma-delta name for system  100 .  
         [0024]     The operation of system  100  is now described. First, x(k) is provided to input  100   IN . During a first operational cycle, there is no value from the output of transfer function block  150 , so x(k) is output by sigma-delta module  110  to accumulator  120 . Transfer function block  120  operates based on the transfer function G(z), which in the example as an accumulator combines its input value to the value it accumulated in the preceding cycle; during a first operational cycle, there is no accumulated value and, thus, x(k) is coupled to summing node  130 , where it is combined with the dither signal d(k) provided by noise generator  135  as further detailed below, and that combined signal is coupled to quantizer  140 . Quantizer  140  compares its input to V ref , and if the input is larger than V ref , a digital  1  is output, and if the input is less than V ref , a digital  0  is output. This value is fed back to transfer function  150 , which responds according to F(z); for example, F(z) may represent a digital to analog conversion when system  100  is an analog input device, where the result is connected to sigma-delta module  110  and subtracted from the next value of x(k) coupled to input  100   IN . With the preceding discussion, the operation then continues, but starting with the next cycle, there are now two non-zero values input to sigma-delta module  110  so that it provides the difference thereof and further that value may be accumulated by transfer function block  120  with the value it determined from the preceding cycle. In general, therefore, and as known in the art, over time the loop of system  100  oscillates and the average of y(k) at the digital output  110   OUT  of quantizer  140 , providing the output of system  100  as signal y(k), is proportional to the input signal x(k).  
         [0025]     The operational effect with respect to system  100  of the dither signal d(k), as provided by noise generator  135 , is now further explored. In general, the dither signal d(k) is added to system  100  to reduce the effects of noise and undesirable tones. Specifically, the periodic pattern of operation of a sigma-delta modulator creates so-called spurs in the modulator output signal, which are signal-affecting single frequency tones. Dither is a random-generated noise signal that is added into the signal of system  100  so as to suppress these tones. To further appreciate this aspect, attention is now directed to  FIGS. 5   a  through  5   c , each of which depicts frequency along the horizontal axis and the system  100  output signal y(k) along its vertical axis.  
         [0026]     Looking first to  FIG. 5   a , it illustrates the output signal components y 1  and y 2  when no dither signal is provided, that is, when d(k) is zero. Component y 1  is typically bell-shaped and represents the primary data output and occurs in-band, that is, it falls within the band of interest for the system. In addition, however, component y 2  represents quantization noise that is caused by the operation of quantizer  140 , that is, it represents the error that necessarily arises when an input to quantizer  140  is not exactly equal to a threshold that corresponds to one of its digital outputs. Note that a majority of the noise in component y 2  is at frequencies out of the in-band interest frequencies, as is achieved by oversampling of system  100  at a frequency of f s , where f s /2 is also shown in each of  FIGS. 5   a  through  5   c . However, some of the noise from component y 2  is in the in-band region.  
         [0027]     Turning to  FIG. 5   b , it again illustrates the output signal components y 1  and y 2 , but it also depicts that an additional level of noise is included, as shown by component y 3 , when the dither signal d(k) is provided as white noise. As stated above, dither is desirable in that it suppresses spur tones, but as seen in  FIG. 5   b , when dither is provided as white noise, it also introduces additional noise both in-band as well as outside of the in-band frequency range.  
         [0028]     Turning to  FIG. 5   c , it once more illustrates the output signal components y 1  and y 2  of  FIGS. 5   a  and  5   b , but it now depicts the effect when the dither signal d(k) is provided as first-order noise, as shown by component y 4 . By comparing  FIG. 5   c  to  FIG. 5   b , note that outside the in-band frequency range, noise levels are comparable. However, note inside the in-band frequency range that the noise is reduced in  FIG. 5   c  as compared to  FIG. 5   b . Thus, the change from white noise dither ( FIG. 5   b ) to first-order noise dither ( FIG. 5   c ) reduces noise in the in-band region, which clearly is a desirable result. As detailed below, the preferred embodiments provide first-order noise dither, which therefore may be used in system  100  to achieve the  FIG. 5   c  benefit or in other applications where a first-order noise generator is beneficial.  
         [0029]      FIG. 6   a  illustrates noise generator  135  of  FIG. 4  in greater detail. Generator  135  includes a linear feedback shift register (“LFSR”)  210  that shares various attributes with LFSR  10  of  FIG. 1 ; thus, lesser detail is provided here with respect to the register and the reader is assumed familiar with the principles described earlier. Briefly, then, LFSR  210  has N=8 bit positions, B 0  through B 7 , each for storing a binary value of 0 or 1, and as a shift register, the device operates in each cycle to shift the content of each bit position [B 0 :B 6 ] in a same direction and, hence, into a respective adjacent bit position, while the content of position B 7  is shifted out of the register. Moreover, bit content at selected bit positions (“SBPs”) of the register are combined into a function, f{SBPs}, designated generally at  220 , and the output of function f{SBPs} is also input into the input bit of LFSR  210 , which in the present example is bit position B 0 . The function f{SBPs} may be determined in various forms, such as a logical XOR of the SBPs (or “taps”) in a particular sequence, where the particular positions chosen as the SBPs as well as the exact choice of function f{SBPs} may vary and may be determined by one skilled in the art from various known or ascertainable resources.  
         [0030]     Continuing in  FIG. 6   a  with respect to a preferred embodiment, LFSR  210  also includes a twos complement analysis  230 , where conductors or the like connect each bit B 0  through B N-1  of the sequence in LFSR  210  to twos complement analysis  230 . As its name suggests, analysis  230  is operable to treat its input as a twos complement number; thus, any input set of bits [B 0 :B 7 ] having a binary  1  in the most significant bit position (“MSB”), which in the present case is bit B 0 , is treated as a negative number and analysis  230  is operable to treat that number as a signed representation of the positive twos complement of the input value. Thus, analysis  230  is shown to provide an output first-order noise signal, FON, where that signal is intended to represent the bits [B 0 :B 7 ] when treated as a twos complement number. Accordingly, as known in the art, the positive counterpart value of a negative twos complement number (i.e., one with a  1  in its MSB) may be generated by taking the complement of each bit in the negative number, adding one to the result, and considering the binary result as a negative number. Thus, if a given binary number input to analysis  230  has a value of 0 in its MSB, then the number is unchanged and merely represents a positive binary value. Lastly, note therefore that analysis  230  is not necessarily manifested as an operational device but instead represents the function of treating the bits [B 0 :B 7 ] as a twos complement number, as further explored below.  
         [0031]     The operation of generator  135  is now described in connection with an example, as presented in the following Table 1.  
                                                                                             TABLE 1                       Row   B 0     B 1     B 2     B 3     B 4     B 5     B 6     B 7     FON, signed                                1   1   0   1   1   1   1   1   1   −65       2   0   1   0   1   1   1   1   1   95       3   1   0   1   0   1   1   1   1   −81       4   0   1   0   1   0   1   1   1   87                  
 
 Particularly, by way of presenting sequences to demonstrate an example although not representing an actual function f{SBPs}, each row of Table 1 illustrates the content of each bit position [B 0 :B 7 ] for LFSR  210 , as well as the twos complement value, FON, corresponding to each row. 
 
         [0032]     Looking now to the rows of Table 1 and starting with Row  1 , it depicts the values in LFSR  210  during a given time period, t 1 . During t 1 , the MSB of bits [B 0 :B 7 ] is a value of 1 and, thus, the function of analysis  230  implies that a twos complement treatment of those bits concludes that the number is a negative number. Moreover, one skilled in the art may readily confirm that, when treated as a negative number, those bits represent a value for FON of −65, as shown in the right column of Table 1. Accordingly and returning briefly to system  100  of  FIG. 4 , a representation of −65 is provided as the dither signal, d(k), to summing node  130 . After time t 1 , each bit in LFSR  210  shifts to the right, and the value of f{SBPs} is shifted into bit position B 0 , providing therefore the values shown in Row  2  of Table 2 at a time t 2 . As was the case during t 1 , during t 2 , again all of bits [B 0 :B 7 ] are treated, by the function depicted by analysis  230 , as a twos complement value; however, during t 2 , the MSB of bits [B 0 :B 7 ] is a value of 0 and, thus, the function of analysis  230  implies that a twos complement treatment of those bits concludes that the number is a positive number. Moreover, one skilled in the art may confirm that the positive number presented in Row  2  corresponds to a value of FON equal to 95, as shown in the right column of Table 1. In response, in system  100  of  FIG. 4 , a representation of  95  is provided as the dither signal, d(k), to summing node  130 . From these two examples, one skilled in the art will appreciate from Table 1 that this process continues, with a register right shift and a treatment of bits [B 0 :B 7 ] as the twos complement value equal to −81 during a time t 3  and provided as the dither signal, d(k), to summing node  130 , and with a register right shift and a twos complement value of 87 determined during a time t 4  and provided as the dither signal, d(k), to summing node  130 .  
         [0033]      FIG. 6   b  illustrates  FIG. 6   a  illustrates noise generator  135  of  FIG. 6   a  in a more generalized form where an apostrophe is added to various reference numbers to provide a distinction for sake of contrast with  FIG. 6   a . Thus, in  FIG. 6   b , a noise generator  135 ′ is shown, and it includes an LFSR  210 ′ with selected taps connected to a function f{SBPs}  220 ′. Further, all N bits of LFSR  210 ′ are connected as inputs to a twos complement analysis  230 ′, and in response analysis  230 ′ provides a first-order noise signal, FON. Thus,  FIG. 6   b  further illustrates that contemplated within the inventive scope is that the number N of bit positions in may be altered by one skilled in the art to be one of many different number of bits, while still achieving the benefits of providing a first-order noise signal.  
         [0034]     With the operation described above of noise generator  135  or  135 ′, the sequence of output values of FON in the time domain may be analyzed in the frequency domain, with the result of an example of such an analysis shown in  FIG. 7 . Specifically,  FIG. 7  illustrates a plot of an FFT of the sequence of time domain outputs of noise generator  135  or  135 ′, as described above. Particularly, the plot of  FIG. 7  corresponds to an LFSR  210 ′ having sixteen bit positions (i.e., N=16), and in this example bit positions B 3 , B 8 , B 14 , and B 15  provide the taps to function f{SBPs} and at a sampling rate or 40 MHz. As can be seen by one skilled in the art, across the frequency range of interest, a first-order frequency response is provided. This response approaches the shape of component y 2  of  FIGS. 5   a  through  5   c , where as a result it also provides the low frequency suppression effect achieved and shown by component y 4  in  FIG. 5   c.    
         [0035]     From the above, it may be appreciated that the preferred embodiments provide a novel first-order noise generator, with various benefits over the prior art. For example, in comparing the prior art approach of  FIG. 3  with the inventive preferred embodiment of  FIGS. 6   a  and  6   b , one skilled in the art will appreciate that the preferred embodiment provides an M-bit first-order noise value, FON, that is generated using less than M LFSRs, whereas for the prior art wherein an M-bit first-order noise value was desired, a total of M LFSRs was required. This is achieved in the preferred embodiments by using more than one bit from an LFSR to generate the value of M, where in the illustrated preferred embodiment, all N bits of a single LFSR are used to correspond to the desired M-bit value used as the first-order noise signal. Thus, in a preferred embodiment, only one LFSR is needed regardless of the value of M. Accordingly, as M increases, a considerable and growing set of benefits are realized. As yet another benefit, the preferred embodiment approach does not require a high pass filter, as is required and shown by filter  45  in  FIG. 3  of the prior art. This set of benefits includes a reduction in power consumption, device size, complexity, and cost, as compared to the above-described prior art approach. As another benefit, the preferred embodiments permit a change in M with far less complexity in an overall change in design as would be required by an approach that requires a corresponding change in a number M of LFSRs. The preceding benefits are of considerable value, and one skilled in the art may ascertain still other benefits as well. Thus, the preferred embodiments include various aspects and advantages as compared to the prior art, and still others will be appreciated by one skilled in the art. Moreover, while the preferred embodiments have been shown by way of example, certain other alternatives have been provided and still others are contemplated. Thus, the preceding discussion and these examples should further demonstrate that while the present embodiments have been described in detail, various substitutions, modifications or alterations could be made to the descriptions set forth above without departing from the inventive scope which is defined by the following claims.