An Acoustic echo canceller has problems adaptating under noisy or double-talk conditions. The adaptation process requires a precise identification of the temporarily changed room impulse response. To do this, both minimizing the step size parameter of the Least Mean Square (LMS) method to be as small as possible and giving up on updating the adaptive filter coefficients have been considered. This paper describes an adaptive cross-spectral technique that is robust to adaptive filtering under noisy or double-talk conditions and for colored signals such a speech signal. The cross-spectral technique was originally developed to measure the impulse response in a linear system. Here we apply in the adaptive cross-spectral technique to solve the acoustic echo cancelling problem. This cross-spectral technique takes the ensemble average of the cross spectrum between input and error signals and the averaged cross spectrum is divided by the averaged power spectrum of the input signal to update the filter coefficients. We have confirmed that the echo signal is suppressed by about 15 dB even under double-talk conditions. We also explain that this method has a systematic error due to using a short time block for estimating the room impulse response. Then we investigate overlapping every last half block by the following first half block in order to reduce the effect of the systematic error. Finally, we compare our method with the Frequency-domain Block LMS (FBLMS) method because both methods are implemented in the frequency domain using a short time block.

The Multiple input-output INverse/filtering Theorem (MINT) proves that N + 1 inverse filters are necessary to precisely control sound at N points in a space, and gives the minimum orders of such filters. In this paper, we propose the Indefinite MINT Filters (IMFs) for adding one or more control points to the above framework without increasing the number of inverse filters. Although the controllability of the new point is not sufficient, that of the other points is still maintained high enough by the principle of the MINT. In a two point sound control (using two inverse filters), the IMFs could reduce the squared error to the desired sound up to - 10 dB at the second point which is not controlled by the MINT.