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EL 6183 Week 7

# EL 6183 Week 7 - EL 6183 EE 4163 EL Digital Signal...

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Monday 03/23/09 EL 6183 / EE 4163 DIGITAL SIGNAL PROCESSING LAB DTFT DFT FFT and LAB # 7 EL 6183 EE 4163 EL 6183 EE 4163 Digital Signal Processing Lab Digital Signal Processing Lab

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EL 6183 EL 6183 Digital Signal Processing Lab Digital Signal Processing Lab 1. Quiz # 3 today/tomorrow 1. Discrete Time Fourier Transform 1. Discrete Fourier Transform 1. Fast Fourier Transform Tuesday March 23, 2009
EL 6183 EL 6183 Digital Signal Processing Lab Digital Signal Processing Lab Fourier Transform in the Digital Domain x(t) X(F) x s (nT) Xs(F) x s (nT) x(n) X(f) s F F f with =

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EL 6183 EL 6183 Digital Signal Processing Lab Digital Signal Processing Lab Fourier Transform in the Digital Domain X(F) F s Fs/2 Fs/2 - Fs/2 Xs(F) 1 1/2 1/2 - 1/2 1 f: 1 1/2 1/2 - 1/2 X(f) 1
EL 6183 EL 6183 Digital Signal Processing Lab Digital Signal Processing Lab Fourier Transform in the Digital Domain 1/2 - 1/2 X(f) f DTFT of x(n) = +∞ = -∞ = - n n fn j e n x f X π 2 ). ( ) ( f is a continuous variable. It is almost impossible to compute and store X(f) as is.

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EL 6183 EL 6183 Digital Signal Processing Lab Digital Signal Processing Lab Fourier Transform in the Digital Domain We will compute a few points (samples) of X(f). We will choose a certain number of points that are representative of X(f). 1/2 X(f) f 0 1 2 3 N/2 - 1 N/2 k N-point DFT of x(n) N k f = The continuous digital frequency range is divided into N parts
EL 6183 EL 6183 Digital Signal Processing Lab Digital Signal Processing Lab Fourier Transform in the Digital Domain N-point DFT of x(n): = - = = - 1 0 2 ). ( ) ( N

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EL 6183 Week 7 - EL 6183 EE 4163 EL Digital Signal...

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