A sinusoidal signal analysis technique for fast, accurate, and discriminating frequency determination

A sinusoidal signal analysis technique is extended to frequency determination. It improves upon previously reported maximum-likelihood methods 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 an FFT. 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 A/D converter performance analysis