New Interpolation Formulas for Apodized, Magnitude-Mode Fourier Transformed Spectra

Abstract

Interpolation techniques for the magnitude-mode discrete Fourier transformed (DFT) spectra of exponentially damped sinusoids have been developed. However, simple formulas to interpolate the apodized DFT spectra have not been given, except those used to interpolate the Hanning-apodized spectra. In this paper, we derive simple interpolation formulas using the sine-bell and rectangle windows. It is found that the formulas for the rectangle window are essentially identical to Lorentzian interpolation. Furthermore, we derive generalized formulas to interpolate DFT spectra apodized by a family of sin α( X) windows, which includes the rectangle, sine-bell, and Hanning windows. We call the proposed interpolation “generalized” because any integer value of α can be used. Simulation results show that the accuracy of interpolation is improved remarkably with increases in the value of the parameter α.