Simplified Cooley-Tukey numerical fast fourier transforms algorithm for digital signal processing

Abstract

Our contemporary global society is driving towards making all actions and activities digitalized. In Nigeria for instance the Broadcasting Institution is determine to go all digitalized in the year 2018. The speed and scope of transmitting from analog to digital remain issues that need scientific resolution. In view of the foregoing an efficient computing algorithmic platform is a requirement for effective transition from analog to digital transmission. This research was therefore designed to develop a simplified Cooley-Tukey numerical FFT algorithm (SC-TNADSP) necessary for processing digital signals in digital computers. In order to attain this aim, the following objectives were considered; investigation of the Cooley-Tukey FFT numerical algorithm for digital signal processing, re-indexing of the Cooley-Tukey FFT numerical algorithm, decomposition of the re-indexed Cooley-Tukey FFT numerical algorithm, and simplification of the decomposed Cooley-Tukey FFT numerical algorithm. The methodology adopted in this work was iterative and incremental development design. The major technologies used in this work were the Cooley-Tukey numerical algorithm, the wave form analog signal representation, and the C++ programming language. The study set the pace for its goal by re-indexing, decomposing, and simplifying the default Cooley-Tukey FFT numerical algorithm. The simplified algorithm resulted from the re-indexing and modification of the Cooley-Tukey FFT algorithm. The authors by this result therefore succeeded in developing an algorithm that is faster than the Cooley-Tukey FFT numerical algorithm. The improved efficiency of the Cooley-Tukey FFT algorithm is accounted for by the obvious reduction in the number of operations and operators in the SC-TNADSP. When implemented, the SC-TNADSP yielded four products, one addition, and one exponentiation as against the default Cooley-Tukey FFT algorithm which has eleven products, one addition and two divisions. Since the increase in the number of operators increases the length of operation, it is therefore reasonable to infer that the algorithm with fewer numbers of operators will run shorter execution time than the one with greater operators. Consequently, the average execution time of the SC-TNADSP is 1.70ms against 3.44ms of the Cooley-Tukey FFT numerical algorithm In line with the above outcomes; we conclude that the SC-TNADSP is of greater efficiency than the Cooley-Tukey FFT numerical algorithm.

Keywords: Cooley-Tukey, Algorithm, Simplified, Fast, FFT, Efficiency, Signal, Numerical