On Two-Stage Nyquist Pulse Shaping Filters

This correspondence outlines a method for designing two-stage Nyquist filters. The Nyquist filter is split into two equal and linear-phase finite-length impulse response spectral factors. The per-time-unit multiplicative complexity, of the overall structure, is included as the objective function. Examples are then provided where Nyquist filters are designed so as to minimize the multiplicative complexity subject to the constraints on the overall Nyquist filter. In comparison to the single-stage case, the two-stage realization reduces the multiplicative complexity by an average of 48%. For two-stage sampling rate conversion (SRC), the correspondence shows that it is better to have a larger SRC ratio in the first stage.