ON THE ENVELOPE OF A NARROW-BAND SIGNAL IN RANDOM NOISE
Abstract
Under consideration is a random process z(t) = s(t) + n(t), where s(t) AND N(t) are narrow-band, stationary (wide sense) random processes. The amplitude A sub z(t), phase phi sub z(t) and the quadrature components x sub z(t) and y sub z(t) are defined as random processes in terms of the spectral representation of z(t). On the basis of these definitions formulas are derived for theAUTOCORRELATION AND CROSS-CORRELATION FUNCTIONS OF THE PROCESSES A sub z(t) and phi sub z(t). The extent to which z(t) is a good estimate of s(t) 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 x(t) based on the observations z (t sub 1), ... , z(t sub n) is derived for a Guassian (t) and it is shown that this estimate reduces to z(t) for n = 1, t sub 1 = t. The same thing is done for the two-dimensional processes (x sub s(t), y sub s(t)) and A sub s(t), phi sub s(t)). 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 z(t),phi sub z(t)+ lambda sub ot) is strictly stationary and ergodic when x(t) is. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1961
- Accession Number
- AD0259866
Entities
People
- J.r. Brown