FFT pruning applied to time domain interpolation and peak localization

The efficiency of the fast Fourier transform may be increased by removing operations on input values which are zero, and on output values which are not required. This is applied to interpolation of complex and real valued time domain functions. For real functions, analytic signal concepts may be used to get the Hilbert transform as a byproduct, and applied to the cross correlation function this gives an efficient and accurate method for peak localization.