  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.
