Adaptive filtering in sub-bands

Abstract

Adaptive filtering in sub-bands, that is adapting several short filters in parallel on sub-sampled frequency subbands, is an attractive alternative to implement a long adaptive FIR filter, this both for computational efficiency and for faster convergence. The sub-sampling process introduces aliased versions of the original signals; it is shown how to annihilate these by adequate adaptive cross-terms. The computational complexity is improved nearly proportionally to the number of sub-bands, and the convergence speed is improved as well, making this scheme attractive for applications like acoustic echo cancellation.

Residual echo signal in critically sampled subband acoustic echo cancellers based on IIR and FIR filter banks

“…We evaluate the feasibility of these positions below. (21). Therefore, the residual echo signal properties remain unchanged, and a tonal component appears around Obviously, the spectrum of the loudspeaker signal is rejected around the notch, and the echo signal around this frequency cannot be predicted and, hence, cancelled.…”

“…For aliasing cancellation in cascaded MRAB and MRSB [22], we use (17) Using (1) and (2) in (8), we have det (18) and, thus, (19), shown at the bottom of the page, where If we ignore the off-diagonal terms in (19) (no CRCI) and use (18), we have (20) In order to gain more insight into (20), we evaluate it on the unit circle and write (21) When is a highly selective lowpass prototype PS-IIR filter such as shown in Fig. 2, is nonzero over a very narrow bandwidth around Furthermore, has a real impulse response:…”

“…First, the subband signals are aliased, which limits the echo cancellation performance [20] and second, the multirate analysis banks (MRAB's) and the multirate synthesis banks (MRSB's) introduce extra delay and computational complexity. Cross-adaptive filtering was proposed by Gilloire and Vetterli [21] in order to solve the interband aliasing problem. They performed a study of the generic critically sampled two-band AEC unit with finite impulse response (FIR) MRAB and MRSB and demonstrated the necessity of performing cross-channel identification (CRCI) [5].…”

Subband adaptive filtering for acoustic echo control using allpass polyphase IIR filterbanks

“…In subband adaptive filtering, adaptive filters are applied in each of frequency subbands [1], [2]. Here we consider adaptive filters based on the least mean squares (LMS) algorithm [3], [4].…”

“…These include 1) noncritical subsampling [9], [10] in which the sample rate is reduced by less than the critical factor; 2) the application of cross-adaptive filters [1] between the subbands to explicitly filter the aliasing components; 3) overbandlimiting the signal in each subband so that energy nulls are created in the spectrum at frequencies where aliasing would otherwise be generated [11]. All three proposed methods of solution carry penalties as reported in [2]; 1) has an increased computational cost, 2) has been found to have problematic convergence speed, and 3) causes spectral distortions.…”