A Subspace Based Analysis of the Modified Forward-Backward Linear Prediction Method

Abstract

In recent years, there has been much activity in the application of forward-backward linear prediction (FBLP) method to estimation of frequencies of sinusoids corrupted by white noise. More recently, Tufts and Kumaresan [1] suggested key modifications to the conventional FBLP method. For the modified FBLP method, they have experimentally shown that the prediction order M=3N/4, where N denotes the number of data samples, yields best frequency estimation performance.

In this paper, we attempt to develop a subspace-based analysis to explain why the performance of the modified FBLP method is superior for the above value of the predictor order. In this analysis, we use the quality of the signal subspace of the estimated autocorrelation matrix as the performance measure and relate this to the predictor order M. The value of M for which the quality is the highest is referred to as the optimal predictor order, and for N= 25 and 48, the near-optimal predictor order matches with the value 3N/4. Computer simultaions are used to support our assertions.

Indexing terms:

• Forward-backward linear prediction
• Subspace-based analysis