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.
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© 1950 Acoustical Society of America.
1950
Acoustical Society of America
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