Perturbation analysis of a SVD based method for the harmonic retrieval problem

Abstract

Model based spectral estimation techniques consist of essentially two steps. The first step is the estimation of a parameter set from the data and the second step consists of extracting the relevant information from the parameter set. A numerical evaluation of the overall procedure can be performed by conducting a perturbation analysis of the two steps separately. We demonstrate this by studying the linear prediction approach for estimating the frequencies of sinusoids in white noise. It is shown that in the first step the continuity of the generalized inverse and the concept of angle between subspaces play an important role. The continuity concept helps explain the need for a low rank approximation and the quality of the approximant is appraised by using the notion of angle between subspaces. For the second step the sensitivity of the zeros of the predictor polynomial becomes an important consideration and is examined.