Non-Uniform Filter Design in the Log-Scale

Abstract

We propose a filtering technique which takes advantage of the possibility of using a very low number of samples for both the signal and the filter transfer function thanks to non-uniform sampling. Following some previous work where we sampled non-uniformly already existing filter transfer functions, we propose now to design directly new filters in the frequency domain. They will be linear with respect to the log-scale. This approach also leads to a summation formula which plays the role of the discrete convolution for classical FIR filters, but with a very reduced number of samples which yields a good efficiency.