Interpolation of Spectral Data Using the Shift Theorem of the Discrete Fourier Transform

Abstract

We present a method for interpolating discrete spectral data using the shift theorem of the discrete Fourier transform. The advantages of the method as compared to ordinary curve fitting and similar direct interpolation methods are that, being based on the discrete Fourier transform, our method is also very fast for large sample volumes if used with the fast Fourier transform (FFT) algorithm. In contrast to direct interpolation methods in spectral space, our method does not modify the modulus of the inverse Fourier transform of the shifted profile, so that the spectral content of the signal is preserved. The basis of the method also makes it suitable for analyzing hot-band structures in vibrational spectra. The method is illustrated with two examples.