High-resolution frequency analysis by the use of derivatives of the Fourier transform: Application to fluorescence quantum beats

The nu th frequency derivative of the Fourier spectrum obtained by the use of t(nu)-windows is proposed with some applications to practical examples. Derivative power spectra have higher resolution and lower base lines than c onventional spectra (e.g., nu = 0), and are insensitive to the choice of th e beginning of the acquisition duration. For extremely large nu, the spectr um is not resolved well. The optimal value of nu is determined so that the main body of the product of the window t(nu) and the signal is accommodated in the range where the SIN ratio is relatively high. This criterion is suc cessfully applied to a signal generated from a known spectrum and to fluore scence quantum beats in pyrimidine at zero and nonzero magnetic fields.