Block diagram of a subband echo canceler in .NET

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Example of lterbank with 16 complex subbands
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+1 +1 and sin m 1/2 n N 2 to modulate the prototype lter to 2. Applying cos m 1/2 n N 2 M M produce the complex-coef cient bandpass lters, Am (z), m = 0, 1, . . . , M 1, as shown in Figure 10.18. The overall lter s magnitude response is shown in Figure 10.19(c). In this example, the synthesis lterbank is identical to the analysis lterbank; i.e., Sm (z) = Am (z) for m = 0, 1, . . . , M 1.
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3. Decimating lterbank outputs by M to produce the low-rate signals sm (n), m = 0, 1, . . . , M 1, for the far-end and dm (n) for the near-end. 4. Performing the adaptation and echo cancelation for each individual subband with 1/M sampling rate. This produces error signals em (n), m = 0, 1, . . . , M 1. 5. The error signals at these M bands are synthesized back to the full-band signal using the bandpass lters Sm (z). Figure 10.19(d) shows the lterbank performance.
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Example 10.4: For the same tail length, compare the computational load between the adaptive echo cancelers of two subbands (assume real coef cients) and full band. More speci cally, given that the tail length is 32 ms (256 samples at 8 kHz sampling rate), estimate the required number of multiply add operations.
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Subband implementation requires 2 128 multiplications and additions for updating coef cients at half of the sampling rate. In comparison, the full-band adaptive lter needs 256 multiplications and additions at sampling rate. This means subband implementation needs only half of the computations required for a full-band implementation. In this comparison, the computation load of splitting lter is not counted since this computation load is very small as compared to the coef cients update using the adaptive algorithm.
10.6.4 Delay-Free Structures
The inherent disadvantage of subband implementations is the extra delay introduced by the lterbank, which splits the full-band signal into multiple subbands and also synthesizes the processed subband signals into a full-band signal. Figure 10.20 shows the algorithm delay of subband adaptive echo canceler. A delay-free subband acoustic echo canceler can be implemented by adding an additional short fullband adaptive FIR lters W0 (z), which covers the rst part of the echo path and its length is equal to the total delay introduced by the analysis/synthesis lters plus the block-processing size. The subband adaptive lters model the rest of the echo path. Figure 10.21 illustrates the structure of delay-free subband acoustic echo cancelation.
Example 10.5: For a 16-band subband acoustic echo canceler with delay-free structure, calculate the minimum lter length of the rst FIR lter. Given that the lterbank is a linear phase FIR lter with 128 taps. The lterbank (analysis and synthesis) delay is 128 samples and the processing block delay is 16 samples. Therefore, the total delay due to lterbank is 128 + 16 = 144 samples. In this case, the length of the rst FIR lter W0 (z) is at least 144.
10.6.5 Implementation Considerations
As shown in Figure 10.8, an effective technique to reduce lter length is to introduce a delay buffer of samples at the input of adaptive lter. This buffer compensates for delay in the echo path caused by the propagation delay from the loudspeaker to the microphone. This technique saves computation since it effectively covers impulse response samples without using adaptive lter coef cients. For example,
Algorithm delay Near-end + P(z) d(n) Analysis filterbank Echo cancelation in subbands Synthesis filterbank Full-band signal