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Zero-crossing rate for the sum of two sinusoids or a signal plus noise (Corresp.)

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For the sum of two sinusoids of incommensurable frequencies, the number of zero-crossings per second Z is calculated. By averaging this result over a Rayleigh distribution for the amplitude of one of the sinusoids, Rice's formula is obtained for the number z of zero-crossings per second of a sinusoid plus Ganssian noise of any spectrum. Simple approximations are obtained for z in the high-signal-to-noise-ratio and narrow-band cases. In addition, alternative derivations of Z and z are presented that further illuminate the significance of the foregoing results.

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IEEE Transactions on Information Theory  (Volume:21 ,  Issue: 6 )