A Frequency Domain Method for the Generation of Partially Coherent Normal Stationary Time Domain Signals

Abstract

A procedure for generating vectors of time domain signals that are partially coherent in a prescribed manner is described. The procedure starts with the spectral density matrix,[Gxx(f)], that relates pairs of elements of the vector random process{X(t)},−∞<t<∞. The spectral density matrix is decomposed into the form[Gxx(f)]=[U(f)][S(f)][U(f)]'where[U(f)]is a matrix of complex frequency response functions, and[S(f)]is a diagonal matrix of real functions that can vary with frequency. The factors of the spectral density matrix,[U(f)]and[S(f)], are then used to generate a frame of random data in the frequency domain. The data is transformed into the time domain using an inverse FFT to generate a frame of data in the time domain. Successive frames of data are then windowed, overlapped, and added to form a vector of normal stationary sampled time histories,{X(t)}, of arbitrary length.