ON THE COMPARATIVE ANALYSIS OF THE COOLEY-TUKEY AND BLUESTEIN NUMERICAL FAST FOURIER TRANSFORMS ALGORITHMS FOR DIGITAL SIGNAL PROCESSING

Abstract

ABSTRACT This study was designed to compare the computing efficiency of C-TNADSP and the BNADSP to ascertain a more efficient numerical algorithm necessary for the processing of digital signals. The faster numerical algorithm established in this study is abbreviated with RCC-TNADSP (Resultant Compared C-TBNADSP). The methodology adopted in this work was comparative analysis development design. The major technologies used in this work are the C-TNADSP and BNADSP, and the c++. The c++ served as a signal processing language simulator (SPLS). The execution times of the Cooley-Tukey and the Bluestein algorithms were 3.44 seconds and 3.50 seconds respectively. On comparing the speeds of the fast Cooley–Tukey and the fast Bluestein algorithms we observed that the Cooley-Tukey algorithm has 0.06 seconds speed improvement over the Bluestein algorithm. In line with this outcome, we concluded that the Cooley-Tukey algorithm (C-TNADSP) is faster than the Bluestein algorithm (BNADSP). In the same vein the Cooley-Tukey algorithm (C-TNADSP) is therefore the fastest DSP algorithm. This is however faster than the spectrum of FFT algorithms of O(nlogn) computing speed. The algorithms were tested on input block width 1000 units, and above, and can be implemented on input size of 100 000, and 1000 000 000 without the challenge of storage overflow. The input samples tested in this work was the discretized pulse wave form with undulating shape out of which the binary equivalents were extracted. Other forms of signals may also be tested in this fast algorithm provided they are interpreted in the digital wave type. KEYWORDS: Algorithm, FFT, Cooley-Tukey, Bluestein, Comparison, Analysis, FFT