Increasing accuracy of frequency estimation by decimation

The problem of estimation of a frequency of a complex sinusoidal signal buried in white measurement noise is considered. It is shown that, for a fixed model order, the variance of the autoregressive frequency estimates can be significantly reduced if the signal is decimated prior to modeling. To obtain comparable results by means of processing the signal in the original time scale, one may be forced to use autoregressive models of very high orders. Therefore the major advantage of decimation is dramatic reduction in computation.

1 Introduction

Consider the problem of estimation of a frequency of a complex sinusoidal signal buried in white measurement noise. The problem of frequency estimation is archetypical. There is a large body of statistical literature devoted to comparison of various spectrum estimation techniques in terms of their accuracy and/or resolution - see e.g. [1], [3], [4], [6]–. The aim of this paper is different. We focus on a particular parametric frequency estimation technique and investigate how its accuracy is affected by the time scale adopted for the underlying signal model.