Abstract:
A noise shaping system including an inner loop and outer noise shaping loops. The inner noise shaping loop includes an inner loop filter and a quantizer for quantizing an output of the inner loop filter. The outer noise shaping loop includes an outer loop filter having an input receiving feedback from the quantizer of the inner noise shaping loop and an output driving an input of the inner loop filter of the inner noise shaping loop.

Description:
FIELD OF INVENTION 
   The present invention relates in general to digital filtering and noise shaping and in particular to noise-shapers and filters with noise shaping quantizers and systems and methods using the same. 
   BACKGROUND OF INVENTION 
   The Super Audio Compact Disk (SACD) system records audio data on an optical disk as a single-bit digital stream at a high oversampling rate. This high oversampling rate advantageously extends the signal bandwidth well beyond the range of human audibility and reduces the need for significant anti-aliasing filtering. Consequently, audible time-domain effects, which normally result when steep low-pass anti-aliasing filters are used in traditional digital audio systems, are typically no longer a significant problem in SACD systems. 
   The advantages provided by the high oversampling rate of the SACD bit stream are countered to a certain degree by the significant disadvantages of the one-bit data format. For example, to maintain a large dynamic range in the audio band using one-bit data, the noise must be shifted out of the audio band with a noise transfer function having a relatively steep passband edge. Delta-sigma modulators are commonly utilized in SACD systems to generate such a noise transfer function, although conventional delta-sigma modulators are normally insufficient for some advanced audio applications. 
   Increasingly, SACD systems are being integrated into audio systems, such as those found in home theater systems, which utilize a set of main speakers without an extended bass response and a subwoofer which provides the remaining low frequency bass output. The task of splitting and directing the bass and higher frequency responses to the appropriate speakers in such a system is difficult when highly oversampled data, such as SACD data, is being processed. Ideally, the crossover and mixing required to make the frequency split would be done at the full SACD oversampling rate to realize the advantages of highly oversampled data discussed above. Filtering highly oversampled data however normally requires performing highly accurate multiplications on digital data words of significantly long length. 
   Hence, some new techniques are required for processing highly oversampled audio data, such as SACD data, which support applications such as home theater audio while at the same time being relatively simple and inexpensive to implement. 
   SUMMARY OF INVENTION 
   The principles of the present invention are generally embodied in filters and noise shaping systems that include a noise shaping quantizer at the output. According to one particular embodiment, a noise shaping system includes an inner noise and outer noise shaping loops. The inner noise shaping loop includes an inner loop filter and a quantizer for quantizing an output of the inner loop filter. The outer noise shaping loop includes an outer loop filter having an input receiving feedback from the quantizer of the inner noise shaping loop and an output driving an input of the inner loop filter. 
   In delta-sigma modulator applications, a noise shaping quantizer at the output allows out-of-band quantization noise to be shifted further out-of-band. Additionally, by noise shaping the quantizer output, the number of bits in the delta-sigma feedback loop is also advantageously reduced. In filter applications, such as IIR filters, a noise shaping quantizer is used according to the inventive principles to minimize the coefficient multiplier circuits. Consequently, both lowpass and highpass filters, suitable for applications such as audio crossover filters, may be constructed relatively simply and inexpensively. In sum, the principles of the present invention are useful when digital filters are required to operate on highly oversampled data with a sampling rate of approximately eight (8) or more times the signal bandwidth. 

   
     BRIEF DESCRIPTION OF DRAWINGS 
     For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
       FIG. 1  is high level block diagram of an exemplary audio system suitable for practicing the present inventive principles; 
       FIG. 2A  is a block diagram of a generalized direct form infinite impulse response (IIR) filter; 
       FIG. 2B  is a block diagram of the transpose form of the IIR filter shown in  FIG. 2A ; 
       FIG. 2C  is a lowpass feedback filter with a noise shaping quantizer output stage according to the principles of the present invention and suitable for use in the digital audio processing block shown in  FIG. 1 ; 
       FIG. 3  is a block diagram of an exemplary embodiment of the noise shaping quantizer shown in  FIG. 2C ; 
       FIG. 4  illustrates a highpass feedback filter with a noise shaping quantizer output stage according to the principles of the present invention and suitable for use in the digital audio processing block shown in  FIG. 1 ; 
       FIG. 5  is a block diagram illustrating an exemplary delta-sigma data converter with telescoped quantizer according to the principles of the present invention and suitable for use in the digital to analog converter (DAC) subsystem of  FIG. 1 ; 
       FIG. 6  is a representative topology for the primary loop filter shown in  FIG. 5 ; and 
       FIG. 7  is an exemplary cascaded delta-sigma modulator topology with noise shaping quantizers according to the principles of the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The principles of the present invention and their advantages are best understood by referring to the illustrated embodiment depicted in  FIGS. 1–7  of the drawings, in which like numbers designate like parts. 
     FIG. 1  is a diagram of an exemplary digital audio system  100  according to the principles of the present invention. Advantageously, system  100  processes digital audio input data in the digital domain prior to conversion to analog form, as discussed in detail below. 
   Audio data are recovered from the associated digital audio storage media by a digital media drive  101 , such as a compact disk (CD) player, digital audio tape (DAT) player, or digital versatile disk (DVD) unit. In the illustrated embodiment, the recovered audio data are a one-bit data stream in the Sony/Philips Super Audio Compact Disk (SACD) format. In alternate embodiments, the audio data are in a multiple-bit format such as PCM. In addition to the audio data stream, media drive  101  also provides the corresponding SACD clocks and control signals. In particular, the audio data are input in response to the serial clock (SCLK) signal, which times the input of each data bit, a left-right clock (LRCK) signal, which times the input of samples of left and right channel stereo data, and a master clock (MCLK), which controls the overall audio processing timing. 
   The resulting recovered data undergoes digital processing, including digital filtering, in digital audio processing block  102 , prior to conversion to analog audio in digital to analog converter (DAC)  103 . Amplifier block  104  then drives a set of conventional main speakers  105   a  and  105   b , and a subwoofer  106 . 
   A conventional SACD system drives a pair of full range audio speakers. However, to extend SACD to applications, such as home theater systems, which typically utilize a set of main speakers without extended bass response and an associated subwoofer (e.g., main speakers  105   a  and  105   b , and subwoofer  106  of  FIG. 1 ), crossover filtering is required to direct the low frequency energy to the larger subwoofer (e.g., subwoofer  106  of  FIG. 1 ) and the higher frequency energy to the smaller main speakers (e.g., main speakers  105   a  and  105   b  of  FIG. 1 ). Telescopic filters embodying the present inventive principles advantageously allow for such crossover filtering to be performed efficiently at high oversampling rates (e.g., at eight (8) times oversampling and above). Typically, these systems run at 64–44100 Hz sampling rate, or about 2.8 MHz. 
   All infinite impulse response (IIR) digital filters can be implemented as transpose form filters. Transpose form filters are very similar to the delta-sigma modulators typically used in DACs. In particular, the truncation of the coefficient multiplications performed in IIR filters is mathematically equivalent to the quantization operations of a delta-sigma modulator; the truncation of the results of the multiplication operations performed in an IIR filter add white noise and gain to the output similar to the quantizer in a delta-sigma modulator. Therefore, an IIR filter can be designed in transpose form and the truncation of multiplication operations consolidated in a delta-sigma modulator quantizer such as the noise shaping quantizers discussed above. 
   In the case of a subwoofer (lowpass) crossover filter according to the inventive principles, a lowpass filter is designed in transpose form, the typical IIR delay elements are replaced with delaying integrators (e.g., having a transfer function of z^−1/(1−z^−1)) and the normal truncation operations are replaced with a simple delta-sigma modulator, such as a second order, five-bit delta-sigma modulator. This process is illustrated in  FIGS. 2A–2B . The replacement of delays by integrators affects a conformal mapping on the z-plane that further reduces the need for accurate coefficients and hence accurate multipliers. For a discussion of filter accuracy effects, see, for example, Roberts and Mullis,  Digital Signal Processing , Addison-Wesley Publishing Company, 1987. 
     FIG. 2A  is a block diagram of a generalized direct form of an IIR filter  200 . Filter  200  is a second order IIR filter including a set of delays  201   a – 201   d  and a summer  202  which sums the output of each delay stage  201   a – 201   d  after multiplication by a corresponding coefficient a 0 –a 2  or b 1 –b 2 . A quantizer  206  reduces the number of bits generated by the multiplication operations applying coefficients a 1 –a 2  and b 1 –b 2  to the input data stream x(n). Filter  200  is shown in the equivalent transpose form in  FIG. 2B , in which filter stages  203   a – 203   b  implement the function h 1 =Z −1 . The coefficients in the transpose form become c 0 –c 1 , c 2  and d 1 ,-d 2 . The transpose form of filter  200  utilizes three summers  205   a – 205   c  and quantizer  206 . Conversion of a direct form IIR filter into transpose form is described in digital signal processing texts such as Proakis and Manolakis,  Digital Signal Processing Principles, Algorithms and Applications , Prentice-Hall, (1996). 
   As shown in  FIG. 2C , if stages  203   a  and  203   b  of the transpose form filter of  FIG. 2B , are replaced with respective delaying integrators  204   a  and  204   b  with a function Z −1 (1−Z −1 ), the coefficients c 0 , and c 1  are set to zero, and quantizer  206  is a noise shaping quantizer, as discussed below, then filter  200  takes on the topology shown in  FIG. 2C , which is essentially the topology of a feedback delta-sigma modulator. Specifically, filter  200  now includes a pair of delaying integrator stages  204   a  and  204   b  and associated input summers  205   b  and  205   c  which implement the feed forward coefficient c 2  and the feedback coefficients −d 2  and −d 1  in feedback path  207 . The truncation of the results of the multiplications by the digital stream by coefficients c 2 , −d 2  and d 1  is now performed in noise shaping quantizer  206 , which has a relatively flat signal-to-transfer function (STF) and a low order topology. Because noise shaping quantizer  206  noise shapes out-of-band noise to higher frequencies, the number of bits which must be fed-back to summers  205   b  and  205   c  can be advantageous and relatively small (e.g., 5–8 bits for audio systems, assuming 2 nd  order noise shaping). In turn, the multiplications by feedback coefficients −d 2  and −d 1  are relatively easy to implement in either hardware of software. the frequency response of this configuration of filter  200  is all-pole, which is appropriate for low pass filters. By selling the coefficients c 1  and c 2  of  FIG. 2B  to non-zero values, other filter configurations with noise shaping quantizers result. 
     FIG. 3  is a block diagram of an exemplary feedforward embodiment of noise shaping quantizer  206 . Generally, quantizer loop filter  301  has a constant signal transfer function (STF) of approximately 1 (i.e., a generally flat response across a wide frequency band) and a noise transfer function (NTF) selected to noise shape the quantization noise created by quantizer  305 . Quantizer  305  is normally a traditional numeric truncation quantizer, although further telescoping of noise shaping quantizers is possible. Optional dither source  306  guarantees that the quantization noise remains non-tonal. In the embodiment of noise shaping quantizer  206  shown in  FIG. 3 , the NTF is (1+Z −1 ) 2  which generates two co-located NTF zeros at the Nyquist frequency. In alternate embodiments, the NTF and the location of the NTF zeros may vary depending on the desired noise shaping. In the illustrated embodiment, the STF is identically 1. 
   Exemplary quantizer loop filter  301  includes a pair of integrator stages  302   a – 302   b , an input summer  303  and an output summer  304 . The direct input from filter stage  204   b  of  FIG. 2C , the output from first integrator stage  302   a  and the output from second integrator stage  302   b  are summed into the input of quantizer  305  by summer  304 . Quantizer  305  truncates the output from summer  304  and provides noise shaped feedback to noise shaping quantizer input summer  303  and feedback path  207  of  FIG. 2C . As a result of the noise shaping in quantizer loop filter  301 , the number of output bits from quantizer  305  is relatively small, around five (5) bits for audio applications. The topology of  FIG. 3  is telescoped by utilizing a noise shaping quantizer, including a loop filter and another quantizer, for the sub-topology of quantizer  305 . 
   Filter  200 , as ultimately depicted in  FIG. 2C , works very well in lowpass filter applications, such as a subwoofer crossover filter. However, application of the same principles to higher frequency filters, such as the highpass crossover filters necessary to filter low frequency energy from the inputs to main speakers  105   a  and  105   b  of  FIG. 1 , requires an additional modification.  FIG. 4  illustrates a high pass filter  400  suitable for such applications. In filter  400 , the primary input is set to a constant such as zero. The digital input signal X(n) is injected between the primary loop filter composed of delayed integrators  204   a  and  204   b  and noise shaping quantizer  206 . The input signal X(n) is shaped like noise (i.e., high passed) by the outer delta-sigma loop between the output of noise shaping quantizer  206  and the feedback inputs to summers  205   a  and  205   b . This filter has a double zero at dc, appropriate for many high-pass filters. While low-pass filter  200  will remove the high frequency out-of-band noise in the highly oversampled input signal (n), high-pass filter  400  will not remove this out-of-band noise present in the audio input signal, and therefore a lowpass filter could be required at the output of highpass filter  400 , such as a filter with a corner frequency of around 50 kHz. 
   The principles of the present invention can be extended to multiple telescoped filters and delta-sigma modulators. For example, the same process described above with respects to  FIGS. 2A–2C  may be used to characterize noise shaping quantizer  206  ( FIG. 2C ). In such a double-telescoped embodiment, the quantizer of noise shaping quantizer  206  includes a third noise shaping loop including a loop filter and truncator (quantizer). This process may be repeated to further telescope the output of the modulator or filter system to triple-telescoped embodiments and beyond. 
     FIG. 5  is a block diagram illustrating an exemplary delta-sigma data converter  500  suitable for use in DAC  103  shown in  FIG. 1 . According to the principles of the present invention, DAC  500  includes a telescoped delta-sigma modulator  510  with a primary loop filter  501  and a noise shaping quantizer  502 . Noise shaping quantizer  502  is generally a second delta-sigma modulator including a quantizer loop filter  503  and a quantizer  504 . Quantizer  504  in telescoped delta-sigma modulator  500  provides noise shaped feedback to both quantizer loop filter  503  through inner feedback loop  505  and to primary loop filter  501  through outer feedback loop  506 . Advantageously, since the feedback from quantizer  504  is noise shaped, the number of feedback bits to primary loop filter  501  and/or quantizer loop filter  503  can be significantly reduced while still maintaining sufficient attenuation in the data converter noise transfer function (NTF) baseband. Furthermore, telescoped modulator  500  can be further telescoped by utilizing a second noise shaping quantizer as quantizer  504  of noise shaping quantizer  502 . Representative topologies suitable for implementing telescoped delta-sigma modulator  500  is described further below in conjunction with  FIGS. 6 and 7 . 
   DAC subsystem  103  also includes dynamic element matching (DEM) logic  507 , which applies a re-routing algorithm to the output bits from puantizer  504  to account for mismatch errors between elements of following output DAC  508 . Output DAC  508  is preferably a conventional switched capacitor or current-steering DAC. 
     FIG. 6  depicts a representative topology for primary loop filter  501  of  FIG. 5 . In the embodiment shown in  FIG. 6 , primary loop filter  501  is a fourth (4 th ) order distributed feedback delta-sigma loop filter based on four (4) integrator stages  601   a – 601   d , including delaying integrators  601   a,    601   b,  and  601   d,  and non-delaying integrator  601   c,  and associated summers  602   a – 602   d.  The feedback coefficients c 1 –c 4  are selected to provide the required filter NTF and signal transfer function (STF). The loop-filter equations and corresponding NTFs and STFs for distributed feedback loop filters, as well as for alternate filter topologies suitable for practicing the inventive principles, can be derived from the discussions of Norsworthy et al.,  Delta - Sigma Converters, Theory, Design and Simulation,  IEEE Press (1997). 
   The principles of the present invention are equally applicable to cascaded delta-sigma modulators topologies, such as delta-sigma modulator topology  700  shown in  FIG. 7 . Delta-sigma modulator topology  700  is based on two cascaded delta-sigma modulator stages  701   a  and  701   b . Each modulator stage  701   a – 701   b  includes a corresponding loop second (2 nd ) order loop filter  702   a / 702   b , a noise shaping quantizer  703   a / 703   b , and a feedback loop  704   a / 704   b . Noise shaping quantizers  703   a – 703   b , in the illustrated embodiment, utilize topology  206  discussed above in conjunction with  FIG. 2 . In alternate embodiments, the number of cascaded delta-sigma modulator stages  701   a – 701   b , and/or the order of loop filters  702   a – 702   b  will vary, depending on the desired noise and signal transfer functions. 
   In sum, the present principles provide for the implementation of efficient filters, such as IIR filters, and noise shapers (delta-sigma modulators). Generally, an outer noise shaping loop operates as a filter having a given filter response. An inner noise shaping loop performs noise shaping in the feedback path of the outer noise shaping loop. By using a high oversampling rate, the inner noise shaping loop translates noise in the outer loop output signal to much higher frequencies, such that fewer feedback bits are required in the outer loop feedback path to achieve full feedback accuracy. Fewer feedback bits result in a feedback system, in either hardware or software, with multipliers and adders of fewer numbers of bits. 
   Filters according to the principles of the present invention have a number of advantageous applications. For example, digital lowpass and highpass audio filters are realistically implemented with a minimum of hardware and/or software. Audio filtering normally performed in the analog domain is now performed in the digital domain. In turn, audio formats, such as the SACD format, can be extended to multiple-speaker audio systems, including audio systems utilizing main and subwoofer speakers. 
   While a particular embodiment of the invention has been shown and described, changes and modifications may be made therein without departing from the invention in its broader aspects, and, therefore, the aim in the appended claims is to cover all such changes and modifications as fall within the true spirit and scope of the invention.