Generalized raised-cosine filters

Data transmission over bandlimited channels requires pulse shaping to eliminate or control intersymbol interference (ISI). Nyquist filters provide ISI-free transmission. Here we introduce a phase compensation technique to design Nyquist filters. Phase compensation can be applied to the square-root of any zero-phase bandlimited Nyquist filter with normalized excess bandwidth less than or equal to one. The resulting phase compensated square-root filter is also a Nyquist filter. In the case of a raised-cosine spectrum, the phase compensator has a simple piecewise-linear form. 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 a matched filter. We also use the phase compensation technique to characterize a more general family of Nyquist filters which subsumes raised-cosine spectra. These generalized raised-cosine filters offer more flexibility in filter design. For instance, the rate of asymptotic decay of the filter impulse response may be increased, or the residual ISI, introduced by truncation of the impulse response, may be minimized. Design examples are provided to illustrate these choices.