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)}, -00 < t < oo}. The spectral density matrix is decomposed into the form [GxAf)] = [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. © 1993 John Wiley & Sons, Inc. *