Generalized Short-Time Power Spectra and Autocorrelation Functions
Manfred R. Schroeder, Bishnu Saroop Atal · The Journal of the Acoustical Society of America · 1962
“Wiener's theorem” relating the autocorrelation function to the power spectrum of a time function has been modified and extended to the cases in which measurements are made with realizable filters having finite integration times. Similar relationships derived earlier by Fa no are valid only for the case when the power spectrum is measured by means of a bandpass filter with all impulse response e−αt cosωt or the auto-correlation function is measured by averaging through a simple R-C integrator. The generalized relationships derived in this paper are valid for integrators with arbitrary impulse responses. Several different forms of short time representations and their experimental realizations are also discussed. The emphasis in this paper is on physical realizability—not mathematical existence.