University of Rhode Island Department of Electrical puter Engineering ELE 436: Communication Systems FFT Tutorial 1 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 pute the Fourier transform with a microprocessor or DSP based system. It is the speed and discrete nature of the FFT that allows us to analyze a signal’s spectrum with Matlab or in real-time on the SR770 2 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: ∞ − Laplace Transform: x(t) ⇔ X(s) where X(s) = R x(t)e stdt −∞ ∞ − Continuous-Time Fourier Transform: x(t) ⇔ X(jω) where X(jω) = R x(t)e jωtdt −∞ ∞ −n z Transform: x[n] ⇔ X(z) where X(z) = P x[n]z n=−∞ ∞ jΩ jΩ−jΩn Discrete-Time Fourier Transform: x[n] ⇔ X(e ) where X(e ) = P x[n]e n=−∞ The Laplace transform is used to
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