Design of FIR Nyquist filters with low group delay

Abstract

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.Index Terms-FIR Nyquist filter, low group delay, Remez exchange algorithm.

Closed-Form Design of Generalized Maxflat$R$-Regular FIR$M$th-Band Filters Using Waveform Moments

“…From (6), we get (7) It is clear that the frequency response at is dependent on the frequency responses at ( ). If its stopband response is zero, then the frequency response of will be one in the passband, i.e., the magnitude response of is one, and the group delay is in the passband [16]. Therefore, the design problem of FIR th-band filters with an arbitrarily specified integer group delay can be reduced to the minimization of the error of in the stopband.…”

“…For this reason, the design problem of FIR th-band filters with an arbitrarily specified group delay needs to be considered. A few design methods of FIR th-band filters with an arbitrarily specified group delay have been proposed in [16] by using the Remez exchange algorithm to obtain the equiripple response in the stopband and in [18] by using the eigenfilter to obtain the least squares solution. On the other hand, the design of generalized maxflat FIR half-band filters, a special case of the maxflat -regular FIR th-band filters with an arbitrarily specified group delay ( ), has been studied also, and the closed-form solution has been given in [17], [19], [21], and [22].…”

WLS design of FIR Nyquist filter based on neural networks

“…However, when the sharp magnitude specifications are required, higher order FIR filters are generally needed, and a larger delay results. On the other hand, IIR Nyquist filters have two disadvantages [8]: one is the stability that must be considered, and another is that the existing design methods are generally time consuming.…”

“…The design of Nyquist filters [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] has received a number of applications in data transmission systems, perfect reconstruction filter banks, nonuniform sampling, interpolation filters over the past two decades. Nyquist filters possess the property that their impulse response has uniformly spaced zero-crossings which results in a zero intersymbol interference constraint.…”

“…Nyquist filters possess the property that their impulse response has uniformly spaced zero-crossings which results in a zero intersymbol interference constraint. There are two conventional methods, which are FIR [1][2][3][4][5][6][7][8][9][10] and IIR filter forms [11][12][13][14][15], to design Nyquist filters. FIR Nyquist filters can be designed with an exact linear phase.…”