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# fft - University of Rhode Island Department of Electrical...

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University of Rhode Island Department of Electrical and Computer 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 to compute 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 - st dt Continuous-Time Fourier Transform: x ( t ) X ( ) where X ( ) = R -∞ x ( t ) e - jωt dt z Transform: x [ n ] X ( z ) where X ( z ) = n = -∞ x [ n ] z - n Discrete-Time Fourier Transform: x [ n ] X ( e j Ω ) where X ( e j Ω ) = n = -∞ x [ n ] e - j Ω n The Laplace transform is used to to find a pole/zero representation of a continuous-time signal or system, x ( t ), in the s-plane. Similarly, The z transform is used to find a pole/zero representation of a discrete-time signal or system, x [ n ], in the z-plane. The continuous-time Fourier transform (CTFT) can be found by evaluating the Laplace trans- form at s = . The discrete-time Fourier transform (DTFT) can be found by evaluating the z transform at z = e j Ω .

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fft - University of Rhode Island Department of Electrical...

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