Typical algorithms for acoustic echo cancellation (AEC) are time domain based using a convolutive mixture with a runtime on orders of , where is the length of the echo tails and is the length of the time window used. Computing the optimal filter in time-frequency domain has the advantage of reducing the computational burden by replacing the convolution with multiplication. Consider the systems depicted in Figure 1 below:
Figure 1: Single line AEC architecture
The problem at hand is to correctly estimate the filter taps such that to minimize the error. The presence of the signal may cause the adaptive system to cancel out the speech signal, thus leading most AECs updating the filter coefficients only when there is no speech detected. Now consider a received signal
where is additive noise. Also consider that is known. We want to estimate such that is minimized, where
A sample result for this estimating the filter weights in the frequency domain is shown in Figure 2.
Figure 2: Performance of frequency domain AEC
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