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The generation of impulse-equivalent pulse trains

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1 Author(s)

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.

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Information Theory, IRE Transactions on  (Volume:8 ,  Issue: 5 )