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The reciprocal relations between autocorrelation functions and power spectra, known as Wiener's Theorem, axe extended in a modified form to the case of experimental results obtained by means of filters with finite time constants. If the short-time autocorrelation function φt(τ) and power spectrum Gt(ω) are properly defined, it is found that φt(τ)=eα|τ|2π ∫ −∞∞Gt(ω)cosωτ dωGt(ω)= ∫ −∞∞e−α|τ|φt(τ)cosωτ dτ where 1/α is a time constant. These equations may be used to relate the autocorrelation-function representation of a speech wave to the corresponding spectrographic representation.
Robert M. Fano (Fri,) studied this question.