Fundamental relations between LMS spectrum analyzer and recursive least squares estimation

Author

McGee, W.F.

Author_Institution

Ottawa-Carleton Inst. for Electr. Eng., Ottawa Univ., Ont., Canada

Volume

36

Issue

1

fYear

1989

fDate

1/1/1989 12:00:00 AM

Firstpage

151

Lastpage

153

Abstract

The least-mean-square (LMS) spectrum analyzer of B. Widrow et al. has been shown to be a means for the calculation of the discrete Fourier transform (DFT) (ibid., vol.CAS-34, no.7, p.814-19, 1987). It uses N periodic complex phasors whose frequencies are equally spaced between DC and the sampling frequency. The phasors are weighted and summed to generate a reconstructed signal, the weights are adapted to provide a least-squares fit between the reconstructed signal and and the input signal whose spectrum is desired. Here, the LMS spectrum analyzer is shown to solve the problem of minimizing the exponentially weighted sum of errors, and results in a recursive estimator. A filter bank model is also deduced

Keywords

errors; estimation theory; filtering and prediction theory; least squares approximations; poles and zeros; signal processing; spectral analysis; transfer functions; DFT; LMS spectrum analyzer; complex phasors; discrete Fourier transform; errors; exponentially weighted sum; filter bank model; least-mean-square; poles and zeros; recursive least squares estimation; signal processing; transfer function; Digital filters; Digital signal processing; Equations; Frequency; Image reconstruction; Least squares approximation; Nonlinear filters; Recursive estimation; Spectral analysis; Speech processing;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/31.16585

Filename

16585