Time-varying spectral estimation using symmetric smoothing

The purpose of this paper is to discuss the use of linear phase adaptive filters in the tracking of time-varying sinusoids. Efficient algorithms for filters of this type have recently been proposed [1,2]. The filter of interest is an FIR operator consisting of 2M+1 coefficients. The center coefficient is constrained to be unity and the remaining coefficients have even symmetry about this point. Because of these constraints the filtering process may be viewed as one of symmetrically smoothing the input signal-hence the filter is termed the symmetric smoother. The filter coefficients are adapted so as to minimize a time weighted average of the square of the filter output. In this paper, two such algorithms considered: the exact least squares technique [2] and the LMS gradient algorithm [3]. Results illustrating the properties of the symmetric smoother in both a stationary and time-varying environment are presented. On the basis of these results, it is concluded that care must be exercised when interpreting the spectral estimates obtained from a linear phase filter.