A new relation between "twiddle factors" in the fast Fourier transformation

Abstract

The fast Fourier transformation algorithm (FFT) probably is the most important algorithm in the digital signal processing. It is an efficient algorithm to the discrete Fourier transformation which determines the frequency components of a discrete time-varying signal. Nowadays, it has a huge impact on the modern society because the FFT is running on more billion devices (e.g. smartphones) on the planet all the time and this tendency is continuously increasing. Moreover, this algorithm plays a key role in the computer science and engineering. Consequently, a well optimized algorithm can save tremendous resources (calculation capacity and memory). This paper presents a new relation between "twiddle factors" and gives an optimised form to the existing relations. In the paper the experimental results prove the efficiency of the proposed relations. By the new relations every radix-r and split-radix FFT will be more efficient because it accelerates the algorithm and/or saves memory.