Properties of real-zero signals
(1970) Proceedings of the 1970 international symposium on information theory — Location: Noordwijk, Netherlands (15.June.1970)
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- Abstract
- Abstract only given, substantially as follows. The properties derived by G. Polya and E.C. Titchmarsh for band-limited deterministic signals are extended to bandlimited processes. It is shown that the number of zeros /b n/(/b T/) (complex and real) of the process with a magnitude <or=T is such that the limit /b n/(/b T/)/2/b T / for /b T/ rarr infinity equals 2/b W/, where /b W/ is the signal bandwidth. It is also shown that these zeros determine the process in the mean-square-sense. Real zero signals (e.g. with no complex zeros) have a zero-crossing rate equal to 2/b W/ and are defined in the mean-square-sense (except for a scale factor) by their zero-crossings. Special attention is given to the class of real-zero signals whose successive samples alternate in sign. This class of signals has one zero-crossing in each Nyquist interval with probability one; it is the basis for a communication system described in another paper. The characteristic function and correlation function of this type of signal are derived.
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Fawe, A. L., & Boorstyn, R. R. (1970). Properties of real-zero signals. Proceedings of the 1970 international symposium on information theory, 1 pp. https://hdl.handle.net/2078.5/230742