Department of Mathematics and Statistics
Arizona State University
When the frequencies are known, the method determines magnitude and phase in closed form. Otherwise, it improves upon previously reported maximum-likelihood methods for determining real and complex frequencies by reducing the 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 of frequencies.
When the frequencies lie in the complex domain, the Laplace transform rather than the Fourier transform is used. The method accommodates any window whose continuous-time Fourier or Laplace transform is known.
The method is applied to two examples: the performance analysis of oversampled analog-to-digital converters (used, for example, in digital audio and wireless phones), and the analysis of spectroscopic signals.