Design of FIR Nyquist filters with low group delay

• Published in: IEEE transactions on signal processing 1999-05, Vol.47 (5), p.1454-1458
• Main Authors: Zhang, X., Yoshikawa, T.
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Approximation; Computational efficiency; Delay; Design methodology; Detection, estimation, filtering, equalization, prediction; Digital filters; Equations; Exact sciences and technology; Filter bank; Finite impulse response filter; Frequency response; Group delay; IIR filters; Impulse response; Information, signal and communications theory; Linear equations; Mathematical analysis; Nonlinear filters; Optimization; Signal and communications theory; Signal processing algorithms; Signal, noise; Telecommunications and information theory
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.757243

A new method is proposed for designing FIR Nyquist filters with zero-crossing impulse response and low group delay. It is first shown that FIR Nyquist filters that satisfy the zero-crossing time-domain condition have a frequency response property where both the magnitude and phase responses in the passband are dependent on the stopband response. Therefore, the design problem will become a magnitude approximation in the stopband. The proposed procedure is based on the formulation of a linear problem by using the multiple Remez exchange algorithm in the stopband directly. Hence, the filter coefficients can be computed by solving linear equations, and the optimal solution with an equiripple stopband response is easily obtained after applying an iteration procedure. Although the proposed Nyquist filters have an approximate linear phase response, its group delay is lower than the conventional FIR Nyquist filters. The proposed procedure is computationally efficient because it only solves a set of linear equations. Finally, the characteristics of the low-delay FIR Nyquist filters are examined, and the performance is compared with the conventional FIR Nyquist filters.