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## Linear System Analysis II

by: Sarina Wintheiser

123

0

4

# Linear System Analysis II ECE 312

Sarina Wintheiser
CSU
GPA 3.8

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
4
WORDS
KARMA
25 ?

## Popular in ELECTRICAL AND COMPUTER ENGINEERING

This 4 page Class Notes was uploaded by Sarina Wintheiser on Tuesday September 22, 2015. The Class Notes belongs to ECE 312 at Colorado State University taught by Staff in Fall. Since its upload, it has received 123 views. For similar materials see /class/210297/ece-312-colorado-state-university in ELECTRICAL AND COMPUTER ENGINEERING at Colorado State University.

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Date Created: 09/22/15
EE 312 Linear Systems ll Final Exam Review Test is 2 hr open book open notes Calculator no computer Allowed Exam is Comprehensive material from entire semester NOTE SHOW YOUR WORK BOX ALL ANSWERS EXPRESS ALL LAPLACE Z AND FOURIER TRANSFORMS AND TRANSFER FUNCTIONS AS RATIONAL POLYNOMIALS REVIEW Post Midterm We will fill out missing info in class Z Transform One sided fnl m Zfnlifnlz Directly from definition sum geometric series n n1 S1aa2aquot Z ak1a k0 1 a 2 m k 1 IFIaIlt1S1aa Z a 7 k0 1 3 Thus a L Z Pole Locations 1 a Use Tables Use Properties Linearity Time shift z 1 2 unit delay Convolution Xnyn H XZYz ixkyn k km IVT lirEFz FVT lirr11zi1 Fz IF z 1Fz has NO poles in Izl 2 1 Z Z Inverse Z Transform PFE of Use tables E z Easy if Fz is power series or polynomial in z 1 Symbolic long division to get a few terms Integral definitions don t use LTI System Representation ODE Solve for yn yn 7 09yn 1 01Xn Implicit Time Domain Non zero ICs 01 01z TF2 Yz HZXz Hz m Z 0 9 Explicit Time Domain Zero ICs IR yn hnxn hn 0109quot n 2 0 Explicit Time Domain 0 n lt 0 Zero ICs System Properties Memory HRFIR Causality Proper Stability no poles in Izl 2 1 Invertibility bi proper Bilateral Z Transform Fm zbfngt i nw fn a Fbz amp ROC left sided right sided two sided inverse formula Use tables both LS and RS and split signal into LS and RS pieces Sampling Process X0 Xln X130 X0 Xst Xpt Impulse Modulator Ideal sampler Zero Order Hold X0J Xs0 Xp0 1 D 27139 X500 ZXwnws a 7 aliasing us gt 2mm Shannon and Xs0 ixnTe j T n DiscreteTime Fourier Transform Xo aaXN ixmwm 2 or Xn ltigtXQ Xn XttnT X 2 Xz for z 61 Z domain plot Directly from Definition Tables Use Properties Linearity Time shift z 1 2 unit delay Convolution in time xn nkLX QYQ Multiplication in time xnynlt gt2iX Q YQ 7r Periodicity XQ XQ 21c Parseval i xn 2 XQl2d 2 F Dquot er

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