Pre-envelopes of nonstationary bandpass processes

✍ Scribed by Harry Urkowitz

• Book ID: 103084067
• Publisher: Elsevier Science
• Year: 1964
• Tongue: English
• Weight: 375 KB
• Volume: 277
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(64)90036-5

✦ Synopsis

Many of the useful properties of pre-envelopes of real waveforms are shown to hold when the notion of pre-envelope is applied to random processes which are not wide-sense stationary. In particular, if x(t) represents a real random process which is not wide-sense and d?(t) is its Hilbert transform, then x(t) and 3(t) have the same autocovariance functio% and have zero crosscovariance at the same instant. The autocovariance function of the pre-envelope z(t), given by z(t) = x(t) +$(t), is twice the pre-envelope of the autocovariance function of x(t).

The notion of a timedependent power density spectrum allows a simple interpretation of a bandpass random process which is not wide-sense stationary. The well-known form of the autocovariance function of a wide-sense stationary bandpass process carries over with simple changes to processes which are not wide sense stationary.