Fast RLS Fourier analyzers in the presence of frequency mismatch

Adaptive Fourier analyzers are used to estimate the coefficients of the sine and cosine terms of a noisy sinusoidal signal assuming the frequencies are known. The recursive least square (RLS) Fourier analyzer is a powerful algorithm that provides excellent performance. However, it is computationally very intensive. Furthermore, in real-life applications, the signal frequencies may differ from their assumed or supposed values. This difference, referred to as frequency mismatch (FM), may significantly deteriorate the performance of the RLS. In this paper, we first propose two fast RLS (FRLS) algorithms by utilizing the inherent characteristics of the estimation problem. The new FRLS algorithms perform almost the same as the RLS, while require considerably less computations. Next, the RLS as well as the proposed two FRLS algorithms are modified by incorporating a new adaptive scheme that alleviates the influence of the FM. Extensive simulations are provided to clarify our claims on the proposed FRLS algorithms, and to show that all the modified Fourier analyzers are capable of accommodating the FM very effectively.