linguistic:voice_change, information:filtering, quality:correction
Auto-correlation of continuous-time signal

Given a signal f (t) {\displaystyle f(t)}, the continuous autocorrelation R f f (τ) {\displaystyle R_{ff}(\tau)} is most often defined as the continuous cross-correlation integral of f (t) {\displaystyle f(t)} with itself, at lag τ {\displaystyle \tau }.

R f f (τ) = ∫ − ∞ ∞ f (t + τ) f (t) ¯ d t = ∫ − ∞ ∞ f (t) f (t − τ) ¯ d t {\displaystyle R_{ff}(\tau)=\int _{-\infty }^{\infty }f(t+\tau){\overline {f(t)}}\,{\rm {d}}t=\int _{-\infty }^{\infty }f(t){\overline {f(t-\tau)}}\,{\rm {d}}t}

where f (t) ¯ {\displaystyle {\overline {f(t)}}} represents the complex conjugate of f (t) {\displaystyle f(t)}. Note that the parameter t {\displaystyle t} in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.