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This 0 page Class Notes was uploaded by Cassidy Effertz on Monday November 2, 2015. The Class Notes belongs to ECE 4270 at Georgia Institute of Technology - Main Campus taught by Faramarz Fekri in Fall. Since its upload, it has received 22 views. For similar materials see /class/233853/ece-4270-georgia-institute-of-technology-main-campus in ELECTRICAL AND COMPUTER ENGINEERING at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
Isms NMquot 1 I Review ofDTFT Fundamentals ofDSP DTFT ofa real exponential signal Symmetry properties ofthe DTFT ascrefte39lntgg Fourier Importance oftheorems rans orm eorems School of Electrical and Computer Center for Signal and Image Processing Georgia Institute of Technology Definition Consider the real exponential signal D IeC T mm m Its DTFT is obta ed as follows M 7 M 7 1 X m M 1m NJ e Eu 2 Eu 0 n 1702 m Inverse Transform J 3 1702 W Existence ofthe DTFI 1702 1507021 1 M lt m l 61 lt w l liacosm j iasin l lXe l nmeMk nEmXM ltw 1a272acosm 112 72acosm X lt21 lt21 liacosm yem2 JZ 1a 72acosm 1a 72acosm W W 2 1 WW WMWW 1 112 7 2acosm Add mafia 1 7 11 cos lelnn mqncm m s m m X2m Z 1 12 Consider a signal XVI A7 COSWUVL NPWM 1 H 7 in ms m 0 5mm To nd its DTFT break it up into complex AXQ Emma 70905 exponenlia s xn gemrne Uo mrq e Thereforelhe DTFT is A 39 527M mrne fwonm X m Ez e lire Mei lireifwneijw Amvluud u WWW w Mm mum on MW minim m v tum m l WW mmmpmMynu n w l mum mmwm m w it My mm 1 l x mm WNW mm Amt nmtm Wm in tinquot my u l y x mnmivlul w r l umwtnmvm wuilimk mam M le my W Winuww u Animilllvll W l w M limit Mummy m minim w l 7 wt m ll m n M w l l 4 1 ll t WNW ll 7 1mm mmuumlu l39mim39r nmm mama mumsamusmmmms u at ml 7 m l x I exquotmy W in u this one out a n M4 m n n in mm H 7 my 7 mgmr 4 quot n munNM 7mm 5 The DTFT provides a frequency domainquot representation that is invaluable for thinking about and solving DSP problems To use it effectively you must important slg know its properties and certain key theorems be able to combine know the Fourier transforms ofcertain nals timedomain and frequency domain methods appropriately If The continuousvariable impulse is de ned by the following properties 5a 0 for a i 0 highly concentmted 2 I 5ada 1 for g gt 0 area concentrated is Xem 5a Xe05a sampling propeny 5a Xem Xem replicating propeny