Synthesises of a Frequency-Time Filter Bank Based on Weyl-Heisenberg Complex Bases

Abstract

This work is dedicated to the synthesis of a bank of digital filters for frequency-time analysis of complex discrete signals defined on a finite interval. For this purpose, it is proposed to use a special toolkit - a complex signal bases of Weyl-Heisenberg. It is shown that this approach allows to flexibly adjust the time-frequency characteristics of digital filters in accordance with the desired pattern and leads to a multi-speed multi-channel filter procedure, allowing for a fast computational implementation. The final formulas describing the filter bank are obtained, and an analysis of its computational efficiency is given.