FFT Tutorial

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Getting to Know the FFT

What is the FFT? FFT = Fast Fourier Transform. The FFT is a faster version of the Discrete
Fourier Transform (DFT). The FFT utilizes some clever algorithms to do the same thing as the
DTF, but in much less time.
Ok, but what is the DFT? The DFT is extremely important in the area of frequency (spectrum)
analysis because it takes a discrete signal in the time domain and transforms that signal into its
discrete frequency domain representation. Without a discrete-time to discrete-frequency transform
we would not be able to compute the Fourier transform with a microprocessor or DSP based system.


Review of Transforms
Was the DFT or FFT something that was taught in ELE 313 or 314? No. If you took
ELE 313 and 314 you learned about the following transforms:


Understanding the DFT
How does the discrete Fourier transform relate to the other transforms? First of all, the
DFT is NOT the same as the DTFT. Both start with a discrete-time signal, but the DFT produces
a discrete frequency domain representation while the DTFT is continuous in the frequency domain.
These two transforms have much in common, however. It is therefore helpful to have a basic
understanding of the properties of the DTFT.



Matlab and the FFT
Matlab's FFT function is an e®ective tool for computing the discrete Fourier transform of a signal.
The following code examples will help you to understand the details of using the FFT function.