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Optimum digital pulse shaping filters

We study the design of moderate-length discrete-time pulse-shaping filters used in data communications, focusing on the tradeoff between ISI, out-of-band power, and filter length. Oversampling ratio M=2 and 4 is studied for both symmetric and asymmetric impulse responses. Numerical minimization of out-of-band power, subject to constraints on ISI, is our primary tool.