Implementation of Recursive Discrete Fourier Transform

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Dr. Kollár Zsolt
Department of Broadband Infocommunications and Electromagnetic Theory

Discrete Fourier Transform (DFT) is one of the fundamental operations in digital signal processing. This thesis presents a possible implementation of the Recursive Discrete Fourier Transform (R-DFT) on x86 architecture PC, PIC30 architecture microcontroller system and reconfigurable hardware (FPGA), and compares its property with the well-known Fast Fourier Transform (FFT). R-DFT applies the observer-based structure which calculates the DFT of signal sequence and results new spectral values for every single new input.

This thesis on the one hand focuses on the implementations of R-DFT, which was simulated in Matlab, on the other hand compares the results of the simulation and the implemented PC, microcontroller and FPGA solutions. The algorithm needs complex adders and multipliers for the calculations, which are implemented as real-valued fixed-point number representation, thus a complex result is calculated separately for the real and imaginary part. Comparison covers the differences between R-DFT and already various implemented FFT solutions (e. g. resources, latency, sensitivity to quantization error, etc.).


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