Fast RLS Fourier analyzers in the presence of frequency mismatch

TitleFast RLS Fourier analyzers in the presence of frequency mismatch
Publication TypeConference Paper
Year of Publication2004
AuthorsXiao, Y., L. Ma, R. K. Ward, and L. Xu
Conference NameCircuits and Systems, 2004. ISCAS '04. Proceedings of the 2004 International Symposium on
PaginationIII - 497-500 Vol.3
Date Publishedmay.
Keywordsadaptive Fourier analyzer, cosine term coefficient estimation, fast RLS Fourier analyzer, Fourier analysis, frequency mismatch, FRLS algorithm, least squares approximations, noisy sinusoidal signal, recursive estimation, recursive least square, signal processing, sine term coefficient estimation, spectral analysis

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.


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