Discrete Hilbert transform filtering

Abstract

A discrete filtering technique based on the discrete Hilbert Transform (DHT) is presented. The filtering method and its implementation are shown to compare favorably with DFT and FFT filtering. The comparison is presented in terms of complexity of hardware implementation and error accumulation. The DHT itself and derived discrete filter transforms are each presented in matrix form and may be implemented with the same hardware in either series or parallel form. In this manner a large variety of filtering characteristics may be implemented by changes of the stored coefficients only. While the filtering process is a circular convolution, direct convolution filters are obtainable also, by using one row of the matrix only, and are realizable in the form of an FIR (non-recursive) digital filter.