An Algorithm for Efficient Computation of the Fast Fourier Transform Over Arbitrary Frequency Intervals

Abstract

In many signal processing and telemetry applications only a portion of the Discrete Fourier Transform (DFT) of a data sequence is of interest. This paper develops an algorithm which enables computation of the FFT only over the frequency values of interest, reducing the computational complexity. As will be shown, the algorithm is also very modular which lends to efficient parallel processing implementation. This paper will begin by developing the frequency selective FFT algorithm, and conclude with a comparative analysis of the computational complexity of the algorithm with respect to the traditional FFT.