Spectral estimation based on singular value decomposition techniques

Abstract

In many practical situations such as in radar, sonar, speech processing, biomedical and geophysics, samples of noisy signals are available and it is required to develop a suitable model or estimate its spectral contents. Tradionally, modelling is done in the context of linear prediction while spectrum estimation is determined via fast calculations on the periodogram. A multitude of modern modelling and spectrum estimation techniques have emerged the last decade to improve the performance of the classical methods. A net success has been registered with these new methods, specially in the often realistic situation of short data length, a case where, generally, classical methods perform poorly. A new optimal approach developed in the context of model reduction will be applied for the problem of modelling and spectrum estimation of signals. A parametric ARMA model is explicitly derived to fit a finite set of samples from a noisy signal. Singular value decomposition of a Hankel data matrix is performed and a natural order of the model is suggested from the relative magnitude of the determined singular values. Unnecessary high order noise modelling is therefore eliminated and noise frequencies are suppressed to produce the desired deterministic frequencies of the signal. The new algorithm for optimal signal modelling and spectrum estimation is tested for various practical situations of short data length, different signal to noise ratios and in the presence of close deterministic frequencies in the signal. The performance of the new technique is compared, in all these cases, with the classical Periodogram and Blackman-Tukey methods and most of the popular modern techniques of Yule-Walker, Burg, Cadzow, Beex, Kung, MUSIC, Prony, Pisarenko and Tufts.