The use of energy comparison to detect cross-talk can detect both the presence of a near-end speaker and a non-convergent echo. Energy detection schemes however,cannot discriminate between the two. Under the assumption that the the desired near end speech is uncorrelated with the far-end speech, the inner product of the error signal and the near end signal can be used to detect double talk.
Consider the systems depicted in Figure 1 below:
Figure 1: Single line AEC architecture
is the far end speech whilst is the near-end speech. Denote a frame of far-end speech with accompanying echo path filter as:
Then the received near-end microphone signal is:
where is zero mean i.i.d. ambient noise. The error signal is given as:
where denotes the estimated variable. We are interested in the expectation of the cross product between the error signal and the microphone signal, thus:
It can be seen that with a convergent filter, is orthogonal to the error signal. Under the assumption that he near end and far end speeches are orthogonal, The the time-frequency domain representation becomes when there is near end speech, hence . The orthogonality based detection scheme is then given as:
where is a threshold parameter. A window is most times applied to remove spurious noise in the detection scheme.
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