Lecture 9

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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 08/17/2011 for the course ECSE 304 taught by Professor Chenandbacsy during the Spring '11 term at McGill.

### Page1 / 8

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online