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In linear transversal filters for signal processing, the impulse response of the filter is syntheszed in a sampled form by means of a tapped delay line with weighted and summed taps. The synthesis procedure consists of sampling the specified impulse response at appropriate intervals and using the sample values as the tap weights. A nonuniform sampling procedure for the synthesis of the impulse response is introduced, which can produce results more conveniently than the classical Shannon sampling procedure because of the simplicity of the transversal filter implementation. According to the new procedure, in the time domain the samples are taken at points where the instantaneous phase of the impulse response is a multiple of ir radians. The spectral distribution which ensues in the frequency domain consists of a series of spectra all having the same fractional bandwidth. The transversal filters synthesized by this sampling criterion are referred to as phase-sampled impulse response (PSIR) filters. An important application of PSI R filters is to the generation and matched filtering of a large class of AM and FM waveforms.