About modification of one-dimensional fast Fourier transform on algorithm of Cooley-Tukey

In the present paper we give the description a method of finding the discrete Fourier Transform, which allows to reduce the cost of computer time to calculate compared to the classical algorithm. Fast algorithms for calculating the Fourier transform are very relevant and actual, they have many applications in problems of digital processing of one-dimensional and multi-dimensional signal and processing of different images, for example, satellite images. A common algorithm is a sequential calculation of the one-dimensional Discrete Fourier Transform by rows and columns. There are various methods of acceleration of the algorithm, one of which is implemented in this article. It is presented the software implementation of the modified algorithm of Cooley-Tukey analog for the Discrete Fourier Transform for the one-dimensional signal with the number of counts p · 2 s, p, s N. For this algorithm, we developed a program in the computer algebra system MATLAB. It has been tested on a set consisting of a 16384 counts of one-dimensional signal. The time of calculations for the classical algorithm and for modified algorithm of Fast Fourier Transform is carried out. As a result, the average computer time for the modified algorithm gives about 20 % time reduction. In addition, in the article it is provided a general description of the Discrete Fourier Transform algorithm and indicated opportunities for increasing of the speed of computing. Also, it is considered a modified algorithm of Cooley-Tukey analog for the Fast Fourier Transform of one-dimensional and multidimensional signals.