Decimated signal diagonalization for fourier transform spectroscopy

A nonlinear parameter estimator with frequency-windowing for signal process ing, called Decimated Signal Diagonalization (DSD), is presented. This meth od is used to analyze exponentially damped time signals of arbitrary length corresponding to spectra that are sums of pure Lorentzians: Such time sign als typically arise in many experimental measurements, e.g., ion cyclotron resonance (ICR), nuclear magnetic resonance or Fourier transform infrared s pectroscopy, etc. The results are compared with the standard spectral estim ator, the Fast Fourier Transform (FFT). It is shown that the needed absorpt ion spectra can be constructed simply, without any supplementary experiment al work or concern about the phase problems that are known to plague FFT. U sing a synthesized signal with known parameters, as well as experimentally measured ICR time signals, excellent results are obtained by DSD with signi ficantly shorter acquisition time than that which is needed with FFT. Moreo ver, for the same signal length, DSD is demonstrated to exhibit a better re solving power than FFT.