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Detection of the peak of an arbitrary spectrum

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1 Author(s)

A new procedure is described for determining that frequency at which the spectrum of a signal has its absolute peak. The salient feature of the procedure is that it does not explicitly involve the estimation of the spectrum of the signal itself. Specifically, it is shown that the limit of the iterated normalized auto-correlation [see (8) and (9)] of a function, f(t) , is a pure cosine wave whose frequency corresponds to the location of the peak of the spectrum of f(t) . Furthermore, if one is willing to accept an estimated peak frequency of maximum energy to within a given finite spectral resolution, then the procedure terminates after a specified finite number of iterations. Results from a computer simulation of the procedure are described. The areas of application of this procedure are discussed, and the results indicate that this method of detecting a signal (i.e., by the peak of its spectrum) merits further consideration. It is important to note that the consideration of random processes has not been undertaken in this initial study; the results apply to the spectral peak of a deterministic signal only.

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Information Theory, IEEE Transactions on  (Volume:10 ,  Issue: 3 )