Accession Number:

AD0259866

Title:

ON THE ENVELOPE OF A NARROW-BAND SIGNAL IN RANDOM NOISE

Descriptive Note:

Corporate Author:

BELL TELEPHONE LABS INC WHIPPANY N J

Personal Author(s):

Report Date:

1961-06-01

Pagination or Media Count:

1.0

Abstract:

Under consideration is a random process zt st nt, where st AND Nt are narrow-band, stationary wide sense random processes. The amplitude A sub zt, phase phi sub zt and the quadrature components x sub zt and y sub zt are defined as random processes in terms of the spectral representation of zt. On the basis of these definitions formulas are derived for theAUTOCORRELATION AND CROSS-CORRELATION FUNCTIONS OF THE PROCESSES A sub zt and phi sub zt. The extent to which zt is a good estimate of st is considered. In particular, it is shown that this estimate continues to become better as the signal-to-noise power ratio increases. A maximum-likelihood estimate of xt based on the observations z t sub 1, ... , zt sub n is derived for a Guassian t and it is shown that this estimate reduces to zt for n 1, t sub 1 t. The same thing is done for the two-dimensional processes x sub st, y sub st and A sub st, phi sub st. A theorem is stated which enables one to estimate directly the autocorrelation and cross-correlation functions of the amplitude and phase of a strictly stationary, ergodic process. In particular, it is shown that the two-dimensional process A sub zt,phi sub zt lambda sub ot is strictly stationary and ergodic when xt is. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE