Stochastic filtering

Abstract

Digital filters convolve a signal with an impulse response. This is equivalent to computing a weighted sum of delayed versions of the signal, with the signal versions indexed by their sample-delay and the weights given by the filter impulse response. This talk explores a different approach to filtering. Rather than computing a weighted sum of data values, the stochastic filter uses a sequence of random indices to select output data values from delayed versions of the signal. No summation is done. The probability distribution of the random indices is made identical to the normalized modulus of the impulse response of the corresponding conventional filter. For indices with negative weights, data values are negated. For a random index sequence s(n) the stochastic filter output is simply y(n)=±x(n−s(n)). The output of such a stochastic filter is noisy but it is equal in the mean to the output of the corresponding conventional filter. If the sequence of random indices is identically and independently distributed then the noise is spectrally white. Such a filter can be useful for estimating spectral parameters with minimal computation. The principle is illustrated by an application to double-talk detection for telephones.