AR spectrum estimation based on wavelet representation

A new adaptive AR spectrum estimation method is proposed. The cost function is defined by using the discrete-time wavelet transform coefficients of the linear prediction error. Instead of a single window throughout the whole frequency spectrum, a wavelet-like windowing method is used to increase the frequency resolution of the low-frequency components and to improve the time resolution of the high-frequency components. Special properties of the covariance matrix are used to derive an RLS algorithm which requires O(M²) operations. Simulation results show that the wavelet based spectrum estimation method gives fine frequency resolution at low frequencies and good time resolution at high frequencies, while with conventional methods it is possible to have only one of these characteristics