Design of FIR Nyquist filters using the Remez exchange algorithm

Abstract

In this paper, we propose a method of designing FIR Nyquist filters with zero intersymbol interference by using the Remez exchange algorithm directly. First, we present some magnitude properties of FIR Nyquist filters with zero intersymbol interference. It is known from the time-domain condition of zero intersymbol interference that the magnitude response of Nyquist filters in the passband is mainly dependent on the stopband magnitude. Therefore, the design problem of Nyquist filters becomes optimization of the magnitude response in the stopband. By using the Remez exchange algorithm in the stopband directly, we formulate the design problem in the form of a linear problem. The filter coefficients can be computed by simply solving the linear equations, and the optimal coefficients with equiripple stopband response are easily obtained after a few iterations. The proposed procedure is computationally more efficient than the existing procedures. Finally, we extend the proposed procedure to the design of matched Nyquist filter pairs, multistage Nyquist filters, and so on. Some design examples are presented to demonstrate the effectiveness of the proposed procedure. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(6): 22–29, 1997