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

Article type: Research Article

Authors: Smallwood, David O.^; | Paez, Thomas L.

Affiliations: Sandia National Laboratories, Albuquerque New Mexico 87185

Note: [] This article is a US Government work and, as such, is in the public domain in the United States of America. This work was supported by the United States Department of Energy under Contract DE-AC04-76DP00789. Requests for reprints should be sent to David O. Smallwood.

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.

DOI: 10.3233/SAV-1993-1106

Journal: Shock and Vibration, vol. 1, no. 1, pp. 45-53, 1993