Practical method for nullifying ripple effect from FIR-Hilbert transformer

Abstract

ABSTRACT When an FIR-Hilbert transformer with an even-numbered filter order of N is used in real-time signal processing, a delay line should be placed in parallel to compensate for the delay time of N/2 arising from the FIR-Hilbert transformer. In general, the FIR-Hilbert transformer possesses a ripple governed by a filter order, a transition bandwidth, among others. In contrast, the delay line does not possess any ripple. Then, an issue regarding the ripple is encountered during signal processing. In this letter, a practical method is proposed to nullify the ripple effect in signal processing. A simple solution is that the same ripple exists on the Hilbert transformer and delay line. Subsequently, two Weaver’s modulators for generating the USB signal are placed in parallel, and the real part of one of the two is used for a delay line and the imaginary part of the other of the two is used for a Hilbert transformer. When the same FIR-LPF is introduced into each of the two, the ripple effect can be nullified.