A Matrix-Valued Wavelet KL-Like Expansion for Wide-Sense Stationary Random Processes

Matrix-valued wavelet series expansions for widesense stationary processes are studied in this paper. The expansion coefficients a are uncorrelated matrix random process, which is a property similar to that of a matrix Karhunen-Loève (MKL) expansion. Unlike the MKL expansion, however, the matrix wavelet expansion does not require the solution of the eigen equation. This expansion also has advantages over the Fourier series, which is often used as an approximation to the MKL expansion in that it completely eliminates correlation. The basis functions of this expansion can be obtained easily from wavelets of the Matrix-valued Lemarié–Meyer type and the power-spectral density of the process.