Jp. Deyst et al., BOUNDS ON LEAST-SQUARES 4-PARAMETER SINE-FIT ERRORS DUE TO HARMONIC DISTORTION AND NOISE, IEEE transactions on instrumentation and measurement, 44(3), 1995, pp. 637-642
Least-squares sine-fit algorithms are used extensively in signal-proce
ssing applications, The parameter estimates produced by such algorithm
s are subject to both random and systematic errors when the record of
input samples consists of a fundamental sine wave corrupted by harmoni
c distortion or noise, The errors occur because, in general,such sine-
fits will incorporate a portion of the harmonic distortion or noise in
to their estimate of the fundamental, Bounds are developed for these e
rrors for least-squares four-parameter (amplitude, frequency, phase, a
nd offset) sine-fit algorithms, The errors are functions of the number
of periods in the record, the number of samples in the record, the ha
rmonic order, and fundamental and harmonic amplitudes and phases, The
bounds do not apply to cases in which harmonic components become alias
ed.