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In order to optimize the design of a coherent phase-shift-keyed (CPSK) system, it is necessary to estimate the amount of degradation produced by intersymbol interference. In this paper, an upper bound to the probability of error of -ary CPSK systems is given when an ideal CPSK signal is passed through a linear time-invariant noisy filter. This bound can be used to estimate the maximum amount of deterioration produced by intersymbol interference, and hence to choose the filter and channel parameters appropriately. It is assumed that all symbols have equal a priori probabilities and that the noise is Gaussian.