A Frequency Domain Method for the Generation of Partially Coherent Normal Stationary Time Domain Signals - David O. Smallwood; Thomas L. Paez (Shock and Vibration)
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.