A fast sinusoidal signal analysis technique for the determination of complex frequencies

A fast sinusoidal signal analysis technique is generalized to the complex domain of frequencies, where the imaginary component of frequency denotes an exponential envelope. The generalized method improves upon previously reported maximum-likelihood methods for exponentially-enveloped sinusoids by reducing the per iteration computational order from N to 1, where N is the number of data points. The generalized method is based upon the Laplace transform rather than the Fourier transform. And since the generalized method accommodates any window whose continuous-time Fourier or Laplace transform is known, it enables existing frequency-domain interpolative techniques for sinusoids to be applied to the analysis of exponentially-enveloped sinusoids. The proposed technique is used to develop an efficient algorithm for the study of spectroscopic signals.