Nyquist Filter Design using POCS Methods: Including Constraints in Design

TL;DR

This paper reviews the use of POCS methods for designing constrained FIR filters, focusing on Nyquist filters, and introduces an extension to existing techniques to improve flexibility in constraint handling.

Contribution

It proposes a simple extension to existing POCS-based Nyquist filter design methods, enhancing flexibility and ease of incorporating various constraints.

Findings

Demonstrates the effectiveness of the extended POCS method

Highlights the flexibility in accommodating multiple constraints

Provides a comparative analysis with existing methods

Abstract

The problem of constrained finite impulse response (FIR) filter design is central to signal processing and arises in a variety of disciplines. This paper surveys the design of such filters using Projection onto convex sets (POCS) and discusses certain commonly encountered time and frequency domain constraints. We study in particular the design of Nyquist filters and propose a simple extension to the work carried out by Haddad, Stark, and Galatsanos in [1]. The flexibility and the ease that this design method provides in terms of accommodating constraints is one of its outstanding features.