Computing convolution of multifrequency signal employing truncated fast Fourier transform algorithms

The use of fast Fourier transform (FFT) alsorithms to compute the discrete Fourier transform and its inverse for multifrequency signals was analyzed. The use of truncated FFT algorithms to eliminate redundant computations associated with finding unneeded spectral samples is explained. The number of multiplications is found as a function of the number of non zero samples of the discrete spectrum of a signal for N = 256 and N = 300 assuming that non zero samples follow one another in the spectrum. It is found that there is a significant range of numbers of non zero samples for the truncated version for which truncated algorithms provide a significant reduction in the number of operations. It is noted that for certain relative positioning of non zero samples in the spectrum the benefit is increased significantly.