TRACKING CAPABILITY AND FLOATING-POINT ERROR ANALYSIS IN MULTIRATE COMPLEX RECURSIVE WEIGHTED LEAST-SQUARES ALGORITHM

This paper presents an analysis of a multirate complex recursive weigh ted least squares (MC-RLS) algorithm based on an analytic signal. Conv entional adaptive filters for multiple sinusoid extraction have been b ased on lattice filter structures or gradient methods because of their low computational cost and/or low sensitivity to quantization errors. On the other hand, the RLS algorithm is easy to introduce assuming ti me-variant quantities in the algorithm when sinusoid frequencies have the time-varying property. However, the relationship between the track ing capability and the quantization error of the least-squares (LS) al gorithm in the transversal structure has not been reported. In additio n, an improvement algorithm for these errors have not been reported. I n this paper, we shall describe a new RLS algorithm in a transversal f ilter structure with a superior transient property, reduced sensitivit y to quantization errors, and low computational cost. First, an analyt ic signal-based autoregressive model is introduced and the MC-RLS algo rithm is shown. Then, using an excess mean-square error of the MC-RLS algorithm, the tracking capability shown to be unaffected by the analy tic transform and the decimation. In addition, the floating-point erro r and the computational cost of the MC-RLS algorithm are analyzed. It is shown that both floating-point error and computational cost are sma ller than those of conventional RLS algorithms that use real signals.