Lecture 9

Lecture 9 - Lecture 9 Time and Freq. Analysis of D-T LTI...

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1 Lecture 9 – Time and Freq. Analysis of D-T LTI Systems ECSE304 Signals and Systems II ECSE 304 Signals and Systems II Lecture 9: Frequency Analysis of System Approximations to Ideal Filters Reading: O and W - Sections 6.6 and 6.7 Boulet - Chapter 14 Richard Rose McGill University Dept. of Electrical and Computer Engineering 2 Lecture 9 – Time and Freq. Analysis of D-T LTI Systems ECSE304 Signals and Systems II • Ideal Filters – Low-Pass, High-Pass, Band-Pass • Look at Approximations of Ideal Filters using First and Second Order Systems Outline
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3 Lecture 9 – Time and Freq. Analysis of D-T LTI Systems ECSE304 Signals and Systems II Outline [Lathi, page 547] • Pole inside the unit circle near z=1 • Zero at origin • Low pass characteristic • Modifies phase response only • Zero at z=-1 • Modifies amp- litude and phase • More poles near z=1 • Closer to ideal low pass characteristic • Poles inside the unit circle near z=-1 • High pass characteristic 4 Lecture 9 – Time and Freq. Analysis of D-T LTI Systems ECSE304 Signals and Systems II • The frequency response of an ideal low pass filter with cut-off frequency is given by: • The impulse response is non-causal (From O and W Ex. 5.12): • … real-time implementation of the filter is not possible Ideal Low-Pass Filter ω 1 W −2π He lp j () kk otherwise lp j c ,, , , , , , ωπ = −≤ = R S T 12 1 0 1 0 …… hn n n n lp cc c [] sin == F H G I K J π sinc c c c
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5 Lecture 9 – Time and Freq. Analysis of D-T LTI Systems ECSE304 Signals and Systems II • Magnitude and phase of for Review: DFDT of () j Xe ω 0 a > j X e j ) 1 (1 ) a 1 ) a + ( ) 12 tan 1 aa ( ) tan 1 −− [] , , 1 n xn aun a R a =∈ < 0 1 1 jn j n j n ae ae ωω +∞ = == n aun 222 1 / ( 1 c o s ) s i n j a a =− + 1 sin t a n 1c o s j a a ⎛⎞ ⎜⎟ ⎝⎠ ) Note Low Pass Characteristic 6 Lecture 9 – Time and Freq. Analysis of D-T LTI Systems
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This note was uploaded on 08/17/2011 for the course ECSE 304 taught by Professor Chenandbacsy during the Spring '11 term at McGill.

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Lecture 9 - Lecture 9 Time and Freq. Analysis of D-T LTI...

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