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The generation of impulse-equivalent pulse trains. (English) Zbl 0137.13702
Author’s summary: “The necessary and sufficient conditions for a function to be the autocorrelation function of a waveform consisting of a finite length train of pulses of various amplitudes is derived. The number of pulse trains having a given realizable autocorrelation function is determined. An “impulse-equivalent” pulse train is defined as one that yields, as closely as is theoretically possible, the same autocorrelation function that a single pulse gives. It is shown that impulse-equivalent pulse sequences exist for all lengths; the number of classes of these sequences is exponentially related to their length. It is demonstrated that all impulse-equivalent pulse trains can be generated by exciting a linear digital filter with two input pulses that correspond in time to the initiation and to the termination of the desired output sequence.”

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
93E10 Estimation and detection in stochastic control theory
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