Design of Analog Filters with Single Transmission Zeros, Dedicated for HFB Systems

Abstract

This paper deals with the design of analog filter bank that possesses the properties suitable for applications in Hybrid Filter Bank (HFB) systems. The certain expected features of analog filters have been distinguished that are necessary to obtain good approximation of their frequency characteristics using the discrete equivalent filters. At the both ends of HFB’s desired passband, the complex frequency characteristics of analog filters has to be real (under assumption that the amplitudes are non-zero). In case of odd order transmission zeros appearing at any end of HFB passband, the phase characteristics has to equal ±π/2. If any of the above constraints is violated the good approximation of the complex characteristics via discrete equivalence is impossible. To ensure the desired analog-to-discrete equivalence, special kind of analog filters of the 4th order are introduced. The appropriate phase equalization of analog filters is performed using the second order allpass functions. Finally the analog filters of the 6th order and their discrete equivalent FIR filters are obtained. The illustrative example has been given to the readers, where numerical values, approximation errors and detailed frequency characteristics are presented.