Software implementation of the Recursive Discrete Fourier Transform

Abstract

The Discrete Fourier Transform (DFT) is one of the fundamental operations in digital signal processing. This paper presents a software based implementation of a less known observer based Recursive DFT on a PC ×86 architecture and on a Microchip PIC30 microcontroller. The results are compared with an efficient/optimized Fast Fourier Transform (FFT) implementation. Both algorithms require complex operations with real valued adders and multipliers, thus a complex result has to be calculated separately for the real and imaginary parts. During the implementation floating-point and fixed-point number representation is applied. The comparison is performed based on the required resources and the computational time.