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# Exam2Review - Exam 2 Review EE 341 Discrete Time Linear...

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Exam 2 Review EE 341 Discrete Time Linear Systems Fall 2007 Howard Jay Chizeck University of Washington Seattle, Washington

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2 X(T) X(2T) X(3T) X(0) 0T2 T Signal x s (t) consists of a train of continuous time impulses—take off the arrow heads to get x[n], a discrete time signal
3 Consider this in the frequency domain—take Fourier Transform of x(t) Not actual shape—drawn this way for pedagogical convenience ω X( ω ) x(t) ω b "bandwidth"

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4 • A impulse train (in continuous time ) has a Fourier transform that is an impulse train in frequency Spacing between pulses in time is T Spacing between pulses in frequency is 2 π /T Increasing period in time domain decreases it in frequency domain (and vice versa )
5 aliasing ω copies due to sampling. ω copies overlap = aliasing undersampled (aliased) Aliasing happens when is too small; that is, the spaces between samples T are too big.

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6 Continuous time signal, x(t) Fourier Transform, X( ω ) i f x ( t ) a p e r o d c = ωω π d e X t x t j ) ( 2 1 ) ( Continuous and aperiodic = dt e t x X t j ) ( ) ( Continuous and aperiodic
7 Continuous time signal, x(t) Fourier Series Coefficients if x ( t ) p e r io d ic t jk k k o e a t x ω −∞ = = ) ( P o T / 2 π ω= T P is period of x(t) Continuous and periodic = 2 / 2 / ) ( 2 P P o T T kt j o k dt e t x a Discrete and aperiodic

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8 Fourier Transforms of Periodic Sequences For continuous time periodic signals, we can find the
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## This note was uploaded on 04/07/2008 for the course EE EE 341 taught by Professor Chezick during the Spring '08 term at University of Washington.

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Exam2Review - Exam 2 Review EE 341 Discrete Time Linear...

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