A design method for cascade form digital nyquist filters with zero intersymbol interference

Abstract

In data communication systems, a Nyquist waveform shaping filter is an important element. The Nyquist filter not only restricts the bandwidth of the data signal, but also realizes zero intersymbol interference where the time response intersects zero at equal intervals except at one point. This paper discusses a design method of a digital Nyquist waveform shaping filter for sampled signals. In particular, the method proposes realization of overall zero intersymbol interference when an identical transfer function is used for both the transmitter and receiver filters. In this method, the transfer function coefficients are used as approximate variables. They are divided into coefficient xf for time response approximation and xf that approximates the frequency response. The condition for zero intersymbol interference is given as the linear equation for xt. Therefore, the approximation variable xt for realization of zero intersymbol interference is obtained from solution of the linear equation. On the other hand, the frequency response is optimized with the iterative approximation due to the observation that the relation between xf and the approximation function is nonlinear. The proposed method is applicable to both the FIR filter and the IIR filter for which the conventional method is not applicable. Further, the effect of the quantization errors in the multiplier coefficients and in the internal signal on the intersymbol interference is analyzed, and an estimation formula is obtained.

Derivative-controlled design of linear-phase FIR filters via waveform moments

“…The blockwise waveform moments around the center can also be defined in the same manner (12) where is the center of the impulse response defined by (3). Similarly, the following decomposition holds: (13) In the following section, we will examine the relationship between and the magnitude response of linear-phase FIR filters.…”