Investigation of the FFT and its applications in FPGA environment

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Supervisor:
Dr. Kollár Zsolt
Department of Broadband Infocommunications and Electromagnetic Theory

The foundation of the modern digital signal processing is the Discrete Fourier Transform (DFT) and it’s related topics. The Fourier transform and it’s time and frequency domain discretized form, the DFT, means a fundamental change of representation by transforming the signals from time to frequency domain.

Although the significance of the mathematical advantages and possibilities offered by the transformation are undeniable, the direct usage of the DFT formulas in the engineering practice is highly limited, since the complexity is growing exponentially with the number of samples.

In the end the extensive usage of the DFT was made possible by an efficient algorithm, more precisely an algorithm family, at least considering the signal processing aspects. The name of this algorithm family is the Fast Fourier Transform (FFT). Since then, it is virtually unavoidable in the engineering practice, therefore the understanding and learning the practical usage of it is an essential engineering task.

The thesis focuses mainly on the major algorithms of the FFT and realization of those on Field Programmable Gate Arrays (FPGA), then using these results to solve a specific measurement task.

The first part of the thesis deals with the theory of the DFT and its usage in practice, as well as the detailed presentation of the FFT algorithm, which makes possible the efficient calculations. Connected to the first part of the thesis, engineering use-cases of the DFT are shown, furthermore an introduction and a method of usage of and FFT Intellectual property (IP) core within Xilinx FPGA environment is presented.

The results of the first part are utilized in an FFT algorithm based frequency measurement system, implemented on an FPGA, therefore the second part of the thesis opens with the detailed description, design and implementation of this task, which is then concluded by the measurement results and the associated analysis and evaluation.

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