Architecture

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates to processing signals. More particularly, the present invention relates to a system and method for processing signals pertaining to a filtering system or digital microphone decimation filter.

2. Description of the Related Art

Digital microphones accept a square wave clock at 64 times the ultimate sample rate of their audio signal, and return a stereo bitstream at that clock rate. The bitstream is the output of a 4 ^th order sigma-delta modulator. The task of a digital microphone interface is to filter the out-of-band noise from this bitstream and decimate it to the audio rate.

In other words, a digital microphone interface accepts a bitstream at 64 times the output sample rate, and decimates it with filtering to the output sample rate to provide the output digital audio stream as a series of samples. As shown by Dattorro et al. (U.S. Patent No. 5,027,306, filed May 12, 1989, entitled "Decimation Filter As For A Sigma-Delta Analog-to-Digital Converter"), which contents are incorporated by reference in their entirety herein, this can be done by brute force using a single FIR filter. For 16 bit quality, they show this filter to be of approx order 2048 (symmetric: 4096).

What is desired is a more efficient and improved digital microphone decimation filter architecture system and method for processing signals thereof.

SUMMARY OF THE INVENTION

In accordance with the invention, there is provided a more efficient and improved digital microphone decimation filter architecture.

In one aspect, the invention provides a filtering system for processing an input signal that includes an input interface, a filtering module, and an output interface. The input interface is operable to receive the input signal in a bitstream. The filtering module is operable to process the input signal through a parallel circuit of filters, wherein the processing is performed using a single/common sample rate (e.g., 48kHz, 32kHz, etc.). The output interface is operable to generate an output signal based on the processed input signal.

In another aspect, the invention provides a method for processing an input signal with a filtering system. The method includes (a) receiving the input signal in a bitstream; (b) processing the input signal through a parallel circuit of filters, wherein the processing is performed using a single sample rate; and (c) generating from the filtering system an output signal based on the processed input signal.

The invention extends to a machine-readable medium embodying a sequence of instructions that, when executed by a machine (e.g., computer, processor, etc.), cause the machine to carry out any of the methods described herein.

These and other features and advantages of the present invention are described below with reference to the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a diagrammatic representation of a filtering system (e.g., digital microphone decimation filter architecture system) according to various embodiments of the present invention.

Figure 2 is a diagrammatic representation of a filtering system (e.g., digital microphone decimation filter architecture system) according to various embodiments of the present invention.

Figure 3a is a diagrammatic representation of a component (e.g., an IIR allpass filter implemented in "one-multiply" form) of the filtering system according to various embodiments of the present invention.

Figure 3b is a diagrammatic representation of a component (e.g., an IIR allpass filter implemented in "two-multiply" form) of the filtering system according to various embodiments of the present invention.

Figure 4 is a diagrammatic representation of a component (e.g., FIR) of the filtering system (e.g., digital microphone decimation filter architecture) according to various embodiments of the present invention. DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Reference will now be made in detail to preferred embodiments of the invention. Examples of the preferred embodiments are illustrated in the

accompanying drawings. While the invention will be described in conjunction with these preferred embodiments, it will be understood that it is not intended to limit the invention to such preferred embodiments. On the contrary, it is intended to cover alternatives, modifications, and equivalents as may be included within the spirit and scope of the invention as defined by the appended claims. In the following

description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. The present invention may be practiced without some or all of these specific details. In other instances, well known mechanisms have not been described in detail in order not to unnecessarily obscure the present invention.

The invention can be implemented in numerous ways, including as a process, an apparatus, a system, a composition of matter, a computer readable medium such as a computer readable storage medium. In this specification, theses implementations, or any other form that the invention may take, may be referred to as techniques. In general, the order of the steps of disclosed processed may be altered within the scope of the invention. It should be noted herein that throughout the various drawings like numerals refer to like parts. The various drawings illustrated and described herein are used to illustrate various features of the invention. To the extent that a particular feature is illustrated in one drawing and not another, except where otherwise indicated or where the structure inherently prohibits incorporation of the feature, it is to be understood that those features may be adapted to be included in the embodiments represented in the other figures, as if they were fully illustrated in those figures. Unless otherwise indicated, the drawings are not necessarily to scale. Any dimensions provided on the drawings are not intended to be limiting as to the scope of the invention but merely illustrative.

Digital microphones are often used in professional audio applications. Some of the advantages and shortcomings of working with digital microphones are described in a White Paper: "Digital Microphones and AES42" v2.1, May 11, 2010, which contents are incorporated by reference in their entirety herein. According to various embodiments of the present invention, a new and more efficient digital microphone decimation filter architecture is presented. A key to this architecture is the use of two parallel filter paths. Each path operates at the output sample rate, and comprises a shorter FIR filter followed by a series of allpass stages. The FIR filter is designed to remove all but the last octave of out-of-band noise. The allpass stages (e.g., implemented with IIR filters such as power symmetric elliptic filters) are designed such that when the two paths are summed together, the out-of- band noise for the final octave cancels out, leaving only the desired signal. This architecture has several advantages over previous approaches. Like the approach of Dattorro et al., U.S. Patent No. 5,027,306, which is incorporated by reference herein, the FIR input is a bitstream; thus, the FIR step comprises only addition operations, and no multiplier is required. In contrast to Dattorro et al., the FIR filter in this architecture is considerably shorter (e.g., order 256), thus the shift register for storing the incoming bitstream is reduced by a factor of at least 8. Unlike the traditional Cascaded Integrator Comb (CIC) approach, this architecture does not use an intermediate sample rate. The allpass filters each operate at the output sample rate, and accept data from the FIR at the output sample rate. Thus the math can be done using a single accumulator. Finally, the allpass filters are of low complexity, requiring only a few multiplies per output sample. This means that an actual parallel multiplier is not required.

Figure 1 is a diagrammatic representation of a filtering system 100 (e.g., digital microphone decimation filter architecture system) according to various embodiments of the present invention. Filtering system 100 includes an input interface 101, a filtering module 102, and an output interface 103. From the digital microphone (DMIC), a bitstream at 64x sample rate (e.g., 64x48kHz = 3.072 MHz) at 1 bit wide is received at input interface 101, which is then processed by two parallel FIR filters. Each FIR filter operate at the sample rate. Each FIR filter generates an output word (e.g., 22 bit at 48kHz). The bitstream is then processed by two IIR Allpass filters. Each IIR Allpass filter operate at the sample rate and can change the phase but not the amplitude of the received signal. Each IIR Allpass filter generates an output word (e.g., 24 bit at 48kHz), which are sum together to generate a digital audio output at the sample rate. It is appreciated that according to various

embodiments, filtering module 102 does not implement a multi-sample rate design, but rather a single rate design. The design criteria can be based on 16 bit quality - noise below -96db or -lOOdb. A delay module is presented so that one of the FIR filter is operating at half the 64x sample rate (therefore, 32 sample @ 48kHz) out of step from the other FIR filter. Since IIR Allpass filters can change the phases, the output of the Allpass filters can be in phase for summation resulting in reinforcement of the sample point and cancellation of half the sample point away. Therefore, a more efficient filtering system can be realized.

Detailed Mathematical Basis

Figure 2 is a diagrammatic representation of a filtering system 200 (e.g., digital microphone decimation filter architecture system) according to various embodiments of the present invention. Filtering system 200, which is similar to filtering system 100, includes an input interface 201, a filtering module 202, and an output interface 203. The input bitstream, represented as X;, is a series of single bit values representing either a +1 or -1 signal, having a sample rate 64 times the output sample rate. The output signal is represented as Y _n , a stream of 24 bit words in 1.23 two's complement format at output sample rate. The time relation between n and i is that i runs at a rate 64 times that of n, and that a minimum of 288 values of X; must be received for the calculation of Y _n . It is convenient to define Xo as the input sample received just prior to begin to compute Yo. Note that the actual delay between receipt of X; and the output of Y _n is arbitrary. However, the delay should be consistent among all channels, and as small as practical.

The output sample Y _n is the sum of two substreams, Y0 _n and Yl _n , also operating at the output sample rate. In other words:

Y _n = Y0 _n + Yl _n

Each of these substreams is the output of a series of three allpass filters operating at the output sample rate. Each of the six allpass filters has its own filter coefficient k, which is a positive number less than one. Allpass filters can be implemented in a number of ways. For example, Figure 3a is a diagrammatic representation of a component 300 (e.g., an IIR allpass filter implemented in "one- multiply" form) of the filtering system according to various embodiments of the present invention. The "one-multiply" form requires a single multiplication and three addition operations. For another example, Figure 3b is a diagrammatic representation of a component 320 (e.g., an IIR allpass filter implemented in "two-multiply" form) of the filtering system according to various embodiments of the present invention. The "two-multiply" form requires two multiplications and two addition operations. For exemplary purposes, both Figures 3a and 3b are based on the 0c IIR Allpass filter in Figure 2, which can be adapted for any of the other IIR Allpass filters (e.g., 0a, Ob, la, lb, lc) in Figure 2 as well. The results are mathematically equivalent. Both will be described here; the "two-multiply" form seems more appropriate for an optimal implementation.

Each of the filter sections will be denoted by its substream number (0 or 1) and its section letter (a, b or c). Each filter has a coefficient k, and a delay memory Z _n . In the one multiply form, substream 0 can be described:

YO _n = Z0c _n _i + koc(Y0b _n - Z0c _n _i)

Z0c _n = Y0b _n + k _Oc (Y0b _n - Z0c _n _i)

Y0b _n = Z0b _n-1 + k _ob (Y0a _n - Z0b _n _i)

Z0b _n = Y0a _n + k _ob (Y0a _n - Z0b _n -i)

Y0a _n = Z0a _n _i + k _Oa (W0 _n - Z0a _n _

Z0a _n = W0 _n + k _Oa (W0„ - Z0a _n _i)

Or in the two multiply form:

YO _n = Z0c _n _i + ko _c Z0c _n

Z0c _n = Y0b _n - ko _c ZOC _n -i

Y0b _n = Z0b _n _i + k _ob Z0b _n

Z0b _n = Y0a _n - k _ob Z0b _n _i

Y0a _n = Z0a _n _i + k _Oa Z0a _n

Z0a _n = W0 _n - k _Oa Z0a _n _i

In both cases W0 _n is the output of the FIR filter for substream 0. Substream 1 is similar:

Yl _n = ZlCn-l + k _lc (Y0b _n - Zlc _n -l)

ZlCn = Ylbn + k _lc (Y0b _n - Zlc _n-1 )

Ylbn = Zlbn-i + k _lb (Y0a _n - Zlb _n _i)

Zlbn = Yla _n + k _lb (Y0a _n - Zlb _n _i)

Yla _n = Zla _n -i + k _la (W0 _n - Zla _n _i)

Zla _n = Wl _n + k _la (W0 _n - Zla _n _i) Or in the two multiply form:

YI„ = = Zlc _n _i + k _lc Zlc _n

Zlc _n = Ylb„ - k _lc Zlc _n _i

Ylb„ = Zlb _n . A + k _lb Zlb _n

Zlb _n = Yla„ - k _lb Zlb _n-1

Yla„ = Zla _n _ i + k _la Zla _n

Zla _n = W1„- - k _la Zla _n _i

The FIR filter outputs are the sums of products of the FIR filter coefficients times the corresponding input values X;. The 256 coefficients are even (symmetric with or without a central value), so that Co = C255, Ci=C254, etc. The two substreams use the same coefficients, but operate on data spaced one half output sample (or 32 input samples) apart. Thus:

W0 _n = CoX(64n-255) + C ₁ X(64n-254) · · · + C ₂ 55X(64n)

Wl _n = CoX(64n-287) + C ₁ X(64n-286) · · · + C ₂ 55X(64n+32)

Implementation

A digital microphone decimation filter module/system implementing a preferred embodiment of the present invention processes N stereo streams of digital microphone data, at a clock rate R which can be either 3.072MHz or 2.048MHz. The module/system produces 2*N audio output streams, at a sample rate of 48 or 32 kHz respectively, compatible with the audio router.

The digital microphone interface comprises a single clock output pin

DMIC_MCLK producing a square wave at the selected clock rate R, and N input pins DMIC_SDIn accepting a bit stream from a stereo pair of digital microphones. The format of this data is described in Appendix 1 below.

The control interface for the module/system comprises a rate select input DMIC_RATE which selects the value of R, and an enable bit for each of the N streams. When the enable bit is negated, the associated DMIC_SDI input is ignored, the audio data output is not computed, and the associated delay registers are cleared to zero. When all enable bits are negated, the DMIC_MCLK becomes quiescent at a zero value.

The module/system contains a single coefficient ROM (presumably a synthesized logic ROM) containing the coefficients. The coefficients are 18 bits, and because they are symmetric, only 128 coefficients are stored. The coefficients have maximum decimal significance of around 0.025. They are stored at 32 times their actual value, that is with a value slightly less than 1 for the largest coefficient (Cm), in 1.17 format. The factor of 32 comprises a factor of 2 because of the pairing of operations (see below), and a scale factor of 16.

Because the input data stream X; is a stream of single bits, no multiplication is required in the computation of W _n ; the sums can be produced by conditional additions or subtractions. Because the coefficients are symmetric, only 128 conditional add/subtracts are required per sum. If the two input samples associated with a given coefficient are different, the accumulator remains unchanged; if both are 1, two times the coefficient is added, and if both are 0, two times the coefficient is subtracted. Because of this pairing, the ROM value represents twice the value of the coefficient.

The resulting Wi signal is guaranteed to have a value within [-1,1] when the coefficients have their proper value; with scaling the value is now [-16,16], implying that there are 4 bits of word growth in the sum of products operation.

Were the accumulator to merely accommodate the FIR operation, it must have 22 bits, in 5.17 format with scaling, or equivalently 1.21 format when the result is scaled back to unity gain.

Based on the above, each of the two substreams will have its own

accumulator. At the beginning of each 48 kHz sample period, both accumulators for each channel are cleared. Then the 128 values of the coefficient ROM are

sequentially accessed. For each substream for each channel, the two shift register bits associated with that ROM are examined. For example, for substream 1 and C _1; X(64n- 254) and X(64n-i) are examined. If they are of different values, nothing is added into the accumulator. If they are both 1, then the coefficient is added to the accumulator; if they are both zero, the coefficient is subtracted from the accumulator. After all 128 coefficients are processed, the accumulators contain the W0 _n and Wl _n values. Next the allpass filters can be implemented.

Figure 4 is a diagrammatic representation of a component 400 (e.g., FIR) of the filtering system (e.g., digital microphone decimation filter architecture) according to various embodiments of the present invention. A simple architecture of component 400 to implement the shift registers uses a 64 long, 1 bit wide input shift register to acquire 64 single bit values for each channel during each 48 kHz sample period. At the end of sample period prior to when Y _n is being computed, this will contain values X(64n-63) through X(64 _n These 64 bits are then shifted as a 64 bit word into a 64 bit wide x 5 word long compute shift register. During the sample period when Y _n is being computed, this contains X(64 _n -3i9) through X( _64n ). Note that 32 bits of the final word of this shift register (containing X(6 _4n -3 i9) through X(6 _4n -288)) are never used and need not exist.

The allpass filter nodes can have word growth, so that even though the W0 _n and Wl _n values are limited to [-1,1], the accumulator should have some headroom.

Furthermore, since the multiplications in the allpass filters can produce fractional bits, some footroom is also beneficial. Two bits of footroom are sufficient. The two multiply allpass internal node is a highpass pole, so its gain is l/(l-k). Since the largest k we have is about 0.9, the gain is about 10, so 4 bits of headroom are necessary. The actual format of the accumulators is thus 5.23. The delay memories

Zij _n are in the same format.

The 6 Kjj coefficients are positive numbers, 16 bits in 0.16 format (see

Appendix 2). The multiplications can be implemented as hard-coded shift and add operations, thus these coefficients are not stored in any ROM.

Use of the two multiply form of the allpass allows storage to be minimized.

The multiplications are implemented as adds and subtracts of the shifted multiplicand to the accumulator. The sequence of operations is as follows (the example is for substream 0):

Begin with W0 _n in the accumulator, and Za0 _n-1 in the 'a' delay memory, Zb0 _n _ i in the 'b' delay memory, and Zc0 _n -i in the 'c' delay memory.

Multiply the contents of the 'a' delay memory by -ko _a and accumulate the result. The accumulator now contains W0 _n - koaZOan.i . = Z0a _n .

Swap the accumulator and the 'a' delay memory. The accumulator now contains Za0 _n-1 and the delay memory contains Z0a _n .

Multiply the contents of the 'a' delay memory by ko _a and accumulate the result. The accumulator now contains Za0 _n-1 + k _Oa Z0a _n . = Y0a _n .

Multiply the contents of the 'b' delay memory by -k _0b and accumulate the result. The accumulator now contains Y0a _n - ko _b Z0b _n-1 . = Z0b _n .

Swap the accumulator and the 'b' delay memory. The accumulator now contains Zb0 _n-1 and the delay memory contains Z0b _n . Multiply the contents of the 'b' delay memory by k _0b and accumulate the result. The accumulator now contains ZbO _n-1 + k _Ob Z0b _n . = Y0b _n .

Multiply the contents of the 'c' delay memory by -ko _c and accumulate the result. The accumulator now contains Y0b _n - ko _c Z0c _n-1 . = Z0c _n .

Swap the accumulator and the 'c' delay memory. The accumulator now contains ZcO _n-1 and the delay memory contains Z0c _n .

Multiply the contents of the 'c' delay memory by ko _c and accumulate the result. The accumulator now contains ΖΰΟ _η-1 + ko _c Z0c _n . = Y0 _n .

In parallel, the analogous process is done to substream 1.

Finally, the two substreams are added together, the result is saturated from its 5.23 format to [-1,1] as 1.23 format, and then output to the audio router.

The above process can be repeated for additional channels using the same accumulators but different delay memories. 256 clocks should be allocated for each channel.

The total facilities required:

Shared resources for all channels:

18 bit by 128 word ROM

Control logic including coding of the 'k' coefficients

Per Channel resources:

352 bits of shift register and associated muxes

24 bits of output register

168 bits of delay memory and associated muxes

Time shared among channels for each accumulator pair: 56 bits of accumulator

2 28 bit adder/subtractors

Quality

This implementation has been designed to meet "16 bit" quality standards. It is possible to use a shorter FIR and shorter coefficient words to decrease the resources further at the cost of audio quality. Such tradeoffs could be more thoroughly investigated in MATLAB. Appendix 1: Digital Microphone Interface Format

The digital microphones all operate using an interface comprising a

DMIC_MCLK signal, which is a square wave clock input into one or two digital microphone circuits, and a DMIC_SDI signal, which is the data output from the digital microphone circuits. When two mics are used, they are configured so that the DMIC_SDI from both mics is multiplexed into one signal line for the stereo configuration.

a. Signal Voltages and Levels

Digital Microphone pads must be designed to accommodate the particular digital microphones used.

b. Signal Timing

The DMIC_MCLK signal is a 50% duty cycle square wave at 64 times the sample frequency. At 48kHz sample rate, this means a clock of 3.072MHz. Some microphones (e.g., a National product) have a maximum clock frequency of 2.4MHz; this does not allow for full audio bandwidth operation. Some microphones also operate at a clock frequency of 2.048MHz, and thus a sample rate of 32kHz.

The DMIC_SDI data input signal provides Pulse Density Modulation (PDM) information as "left" data in response to the falling edge of DMIC_MCLK, and "right" data in response to the rising edge. The data delay time from the active edge of DMIC_MCLK to valid data on DMIC_SDI varies among the manufacturers, as does the hold time of valid data on DMIC_SDI following the subsequent

DMICJV1CLK transition. An optimum interface should latch the DMIC_SDI data on the MCLK falling edge immediately prior to the next DMIC_MCLK transition. This will allow the maximum timing margin on the DMIC_SDI data delay, without placing any restriction on a positive value for its hold time. Assuming no signal skew, this design allows for data delay timing margins of 89 nsec and 113.25 nsec, and data hold margins of 48 nsec and 106 nsec respectively for Akustica and National parts. See the timing diagrams below for details.

Note that while some microphones specify that there is a finite (typically 200msec) "data invalid" time during power-up, there is no need to deal with this in the hardware.

48 kHz Sample Rate, 3.072 MHz DMIC_MCLK

MCLK xssazzxssazzxssazzxssazzxssazzxssazzxs DMIC_MCLK azzzzzzzzzzzxs s sssssssss azzzzzzzzzzzxs

DataStrobe zzzzzzzzzxssazzzzzzzzxssazzzzzzzzxssaz

DMIC_SDI r43 leff ^{^} r43 righ r43 lef ^{^} r

33 nsec 0 = 0= 7 nsec

Data delay of 33 nsec, data hold of 7 nsec typical of Akustica parts.

DMIC_SDI is sampled on the rising edge of DataStrobe.

32 kHz Sample Rate, 2.048 MHz DMIC_MCLK

MCLK xsazxsazxsazxsazxsazxsazxsazxsazxsazxs

DMIC_MCLK azzzzzzzzzzzxs s sssssssss azzzzzzzzzzzxs

DataStrobe zzzzzzzzzzxsazzzzzzzzzxsazzzzzzzzzxsaz

DMIC_SDI ^{^} r443 lefr r443 righrr443 lefr

90 nsec 0 = 0 = 65 nsec

Data delay of 90 nsec, data hold of 65 nsec typical of National parts.

DMIC_SDI is sampled on the rising edge of DataStrobe.

Appendix 2: All pass Filter Coefficients

These coefficients correspond to requirements of 96dB attenuation at 28kHz: k _0a = 2894/65536 = 0.0442

kob = 21667/65536 = 0.3306

k _0c = 46002/65536 = 0.7019

k _la = 10755/65536 = 0.1641

k _lb = 33747/65536 = 0.5149

kic = 58644/65536 = 0.8948

Appendix 3: FIR Filter Coefficients

These coefficients correspond to requirements of +/- O. ldB ripple 0-20kHz, lOOdB attenuation 76kHz to 116kHz, and 130dB above 124kHz. All are expressed as integer values. The actual coefficients are stored effectively as 1.17 format (divided by 131072), and the original FIR values are 1/32 of the these (divided by 4194304): Co = 1; Ci = 2; C ₂ = 3; C ₃ = 4; C ₄ = 6; C ₅ = 8; C ₆ = 11; C ₇ = 15; C ₈ = 20; C ₉ = 26; C ₁₀ = 33; Cii = 41; Ci, = 51; Ci, = 63; C _u = 76; Ci ₅ = 91; Ci ₆ = 109; C _i7 = 128; Ci ₈ = 149; Ci ₉ = 173; C ₂₀ = 198; C ₂ i = 225; C ₂₂ = 254; C ₂₃ = 285; C ₂₄ = 317; C ₂₅ = 350; C ₂₆ = 383; C ₂₇ = 416; C ₂₈ = 448; C ₂₉ = 479; C ₃₀ = 507; C _3i = 533; C ₃₂ = 554; C ₃₃ = 569; C ₃₄ = 578; C ₃₅ = 579; C ₃₆ = 571; C ₃₇ = 553; C ₃₈ = 522; C ₃₉ = 478; C ₄₀ = 418; C ₄₁ = 341; C ₄₂ = 247; C ₄₃ = 132; C^ = -4; C ₄₅ = -163; C ₄₆ = -345; C ₄₇ = -553; C ₄₈ = -787; C ₄₉ = -1048; C ₅₀ = -1336; C51 = -1652; C ₅₂ = -1996; C ₅₃ = -2368; C ₅₄ = -2766; C ₅₅ = - 3190; C ₅₆ = -3638; C ₅₇ = -4109; C ₅₈ = -4601; C ₅₉ = -5109; C ₆₀ = -5632; C ₆ i = -6166; C ₆₂ = -6706; C ₆₃ = -7248; = -7786; C ₆₅ = -8315; C ₆₆ = -8828; C ₆₇ = -9320; C ₆₈ = - 9783; C ₆₉ = -10210; C ₇₀ = -10593; C _7i = -10924; C ₇₂ = -11195; C ₇₃ = -11397; C ₇₄ = - 11522; C ₇₅ = -11562; C ₇₆ = -11507; C ₇₇ = -11349; C ₇₈ = -11080; C ₇₉ = -10692; C ₈₀ = - 10176; C ₈₁ = -9526; C ₈₂ = -8735; C ₈₃ = -7796; C ₈₄ = -6703; C ₈₅ = -5452; C ₈₆ = -4039; C ₈₇ = -2461; C ₈₈ = -714; C ₈₉ = 1201; C ₉₀ = 3286; C91 = 5539; C ₉₂ = 7958; C ₉₃ = 10540; C ₉₄ = 13280; C ₉₅ = 16172; C ₉₆ = 19210; C ₉₇ = 22384; C ₉₈ = 25686; C ₉₉ =

29105; C ₁₀₀ = 32630; C ₁₀ i = 36246; C ₁₀₂ = 39940; C ₁₀ = 43698; C ₁₀ = 47504; C ₁₀₅ = 51340; C ₁₀₆ = 55191; C ₁₀₇ = 59038; C ₁₀₈ = 62862; C ₁₀₉ = 66646; C ₁₁₀ = 70370; Cm = 74016; Cm = 77565; Cm = 80999; C _ll4 = 84299; C = 87447; Cue = 90426; Cm = 93220; C = 95814; C _n9 = 98193; Ci ₂ o = 100343; C _m =102252; C _m = 103909; C ₁₂₃ = 105305; C ₁₂₄ = 106432; C ₁₂₅ = 107283; C ₁₂₆ = 107853; C ₁₂₇ = 108138.

Advantages of the present invention allow for an efficient combination of FIR and IIR filters that take advantage of a single bit input signal. The IIR filters allow the FIR to be more efficient by having lesser coefficients (e.g., order 256 vs order 4096). Further, due to the lesser coefficients, a single accumulator (e.g., register) can be used.

Although the foregoing invention has been described in some detail for purposes of clarity of understanding, it will be apparent that certain changes and modifications may be practiced within the scope of the appended claims.

Accordingly, the present embodiments are to be considered as illustrative and not restrictive, and the invention is not to be limited to the details given herein, but may be modified within the scope and equivalents of the appended claims.