Gabor expansion for adaptive echo cancellation

A good echo cancellation algorithm should have a fast convergence rate, small steady-state residual echo, and less implementation cost. The normalized least mean square (NLMS) adaptive filtering algorithm may not achieve this goal. We show that using the Gabor expansion is a way to achieve this goal. For direct digital signal processing compatibility the Gabor expansion introduced in this paper is for discrete-time signals, although the Gabor expansion also can be used for continuous-time signals. The Gabor expansion can be defined as a discrete-time signal representation in the joint time-frequency domain of a weighted sum of the collection of functions (known as the synthesis functions). There are several design issues in the echo canceller based on the Gabor expansion: the design of the analysis functions for the far-end speech, the design of the analysis functions for the near-end signal containing the echo plus the near-end speech, the design of the adaptive filters in the subsignal path, and the design of the synthesis functions. All the adaptive filters are designed using identical NLMS adaptive filtering algorithms.