A frequency-domain least-squares approach to sinusoidal signal analysis.

摘要

A frequency-domain least-squares sinusoidal signal analysis technique for determining magnitude and phase at a finite collection of frequencies is proposed. Unlike previously reported maximum-likelihood techniques, it is exact, closed-form, applicable to any finite collection of frequencies, and can be applied independent of window choice. It is extended to frequency determination through iteration. The resultant algorithm improves upon previously reported maximum-likelihood methods for subinterval frequency determination by reducing computational order per iteration from N to 1, where N is the number of data points. Subject to a noise floor, there is no limit to achievable accuracy or discrimination. The proposed extension accommodates any window whose continuous-time Fourier transform is known. It is illustrated here with the Kaiser-Bessel window, a near-optimum window with full design parameterization. To achieve reduced computational order, an approach is proposed for the fast computation of discrete-time Fourier transforms when corresponding continuous-time Fourier transforms are known. Its computational order is generally superior to that of a fast Fourier transform. Furthermore, it enables a closed form solution to the discrete-time Fourier transform of a Kaiser-Bessel window in computational order 1. The exceptional performance is demonstrated through analog-to-digital converter performance analysis.