Exact Interpolation of Apodized, Magnitude-Mode Fourier Transform Spectra

Abstract

A procedure is developed for the exact interpolation of apodized, magnitude-mode Fourier transform (FT) spectra. The procedure gives the true center frequency, i.e., the location of the continuous peak, from just the largest three discrete intensities in the discrete magnitude spectrum. The procedure is applicable for the peaks in the apodized magnitude spectrum of a time signal of the form f( t) = cos( ωt) exp(– t/τ). There are no restrictions on the value of the damping ratio T/τ. The procedure is demonstrated for the sine-bell and Hanning windows and is generalizable to other windows which consist of a sum of constants and sine/cosine terms. This includes the majority of commonly used windows.