Adaptive AR spectral estimation based on wavelet decomposition of the linear prediction error

A new adaptive AR spectral estimation method is proposed. While conventional least-squares methods use a single windowing function to analyze the linear prediction error, the proposed method uses a different window for each frequency band of the linear prediction error to define a cost function to be minimized. With this approach, since time and frequency resolutions can be traded off throughout the frequency spectrum, an improvement on the precision of the estimates is achieved. In this paper, a wavelet-like time-frequency resolution grid is used so that low-frequency components of the linear prediction error are analyzed through long windows and high-frequency components are analyzed through short ones. To solve the optimization problem for the new cost function, special properties of the correlation matrix are used to derive an RLS algorithm on the order of M(2), where M is the number of parameters of the AR model. Computer simulations comparing the performance of conventional RLS and the proposed methods are shown. In particular, it can be observed that the wavelet-based spectral estimation method gives fine frequency resolution at low frequencies and sharp time resolution at high frequencies, while with conventional methods it is possible to obtain only one of these characteristics.