BOUNDS ON LEAST-SQUARES 4-PARAMETER SINE-FIT ERRORS DUE TO HARMONIC DISTORTION AND NOISE

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.