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

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