Title :
Generalization of the Wiener-Khinchin theorem
Author_Institution :
Hunter Coll., City Univ. of New York, NY, USA
Abstract :
We generalize the concept of the autocorrelation function and give the generalization of the Wiener-Khinchin theorem. A full generalization is presented where both the autocorrelation function and power spectral density are defined in terms of a general basis set. In addition, we present a partial generalization where the density is the Fourier transform of the characteristic function but the characteristic function is defined in terms of an arbitrary basis set. Both the deterministic and random cases are considered.
Keywords :
Fourier transforms; correlation methods; random processes; signal processing; spectral analysis; Fourier transform; Wiener-Khinchin theorem; autocorrelation function; characteristic function; deterministic signals; general basis set; partial generalization; power spectral density; random signals; signal analysis; Autocorrelation; Differential equations; Eigenvalues and eigenfunctions; Fourier transforms; Frequency; NASA; Signal analysis; Stochastic processes;
Journal_Title :
Signal Processing Letters, IEEE
