Modified Forward-Backward Linear Prediction: Improvements and Criterion for Detection of the Number of Sinusoids

Abstract

The modified forward-backward linear prediction (MFBLP) method of estimating the frequencies of sinusoids corrupted by white noise, proposed recently by Tufts and Kumaresan [1], has been receiving much attention. In the MFBLP method, there is an implicit assumption that the number of sinusoids is either known or it can be estimated using some criteria.

In this paper, we first suggest sonic improvements to the MFBLP method and then propose a novel method for detection of the number of sinusoids. The improvements are obtained by using a cleaned desired response vector and a better lower rank approximate of the data matrix in the solution for the predictor coefficients. The detection criterion is based on the application of the information theoretic criteria for model selection, introduced by Akaike (AIC) and by Schwartz and Rissanen (MDL). The method is novel in that the computations involved over and above those needed for singular value decomposition (which is an essential step in the MFBLP method) are marginal. Computer simulations are used to demonstrate the usefulness of our methods.

Indexing terms:

• Spectral estimation
• Forward-backward linear prediction
• Detection of the number of sinusoids