Parameter Estimation of Noise Corrupted Sinusoids

Details Parameter Estimation of Noise Corrupted Sinusoids Parameter Estimation of Noise Corrupted Sinusoids

2011-04-14

arxiv.org/abs/1104.2736v7

Mathematics

General Mathematics

24 pages, 7 figures

Scientific paper

Existing algorithms for fitting the parameters of a sinusoid to noisy discrete time observations are not always successful due to initial value sensitivity and other issues. This paper demonstrates the techniques of FIR filtering, Fast Fourier Transform, circular autocorreltion, and nonlinear least squares minimization as useful in the parameter estimation of amplitude, frequency and phase exemplified for a low-frequency time-delayed sinusoid describing simple harmonic motion. Alternative means are described for estimating frequency and phase angle. An autocorrelation function for harmonic motion is also derived.

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