A Family of Nyquist Filters Based on Generalized Raised-Cosine Spectra

Data transmission over bandlimited channels requires pulse shaping to eliminate or control Inter-Symbol Interference (ISI). A widely used filter for this purpose is the raised cosine filter which satisfies Nyquist’s first criterion. We design a phase compensator so that the square-root raised-cosine filter also satisfies Nyquist’s first criterion. Such a technique is particularly useful to accommodate two different structures for the receiver, one with a filter matched to the transmitting filter and one without any matched filter. In the case of a raised cosine spectrum with full excess bandwidth, we show that the phase compensator corresponds to a pure time delay. We also extend the raised-cosine spectra to a more general family of Nyquist filters which their compensated square-root spectra satisfy Nyquist’s criterion. In practice, it is important that the transmitting and receiving filters be well approximated with short impulse responses. From this point of view, the raised cosine spectrum is not necessarily the best choice for Nyquist filter design. A new family of Nyquist pulses are designed such that they have faster asymptotic decay compared to the raised-cosine filter impulse response.