A new synthesis approach for non-uniform filters in the log-scale: proof of concept

Abstract

We theoretically describe and give the proof of a new way to synthesize filters that are affine in the log–log scale in the frequency domain and are especially appropriate to filter non-uniformly sampled data, and take advantage of a very low number of signal samples and filter coefficients. This approach leads to a summation formula which plays the same role as the discrete convolution for the usual finite impulse response filters.