Comments on and extensions to "Evaluation of Fourier integrals using a FFT with improved accuracy and its applications"

The evaluation of Fourier integrals using fast Fourier transform (FFT) employing the Narasimhan scheme is examined. It is observed to be a special case of spline interpolation. His method is effective when the sampling rate is sufficiently high and piecewise linear approximation between sampling points is adequate. If knowledge about the signal smoothness is available, further improvement in accuracy can be achieved by judicious choice of high degree spine interpolant.