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Signals and Systems (Lab) Resource Person : Hafiz Muhammad Ijaz

Signals and Systems (Lab) Resource Person : Hafiz Muhammad Ijaz

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Signals and Systems (Lab) Resource Person : Hafiz Muhammad Ijaz

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  1. Signals and Systems (Lab) Resource Person : Hafiz Muhammad Ijaz COMSATS Institute of Information Technology Lahore Campus www.powerpointpresentationon.com

  2. EXPERIMENT # 11 Z-Transform and its MATLAB implementation .

  3. In This Lab… • Introduction to Z-Transform • How to implement Z-transform and Inverse Z-transform in MATLAB? • What is meant by Region of Convergence (ROC) • Pole Zero Plot • Stable and Unstable Systems • Impulse Response and Step Response • MATLAB Implementation of inverse Z-transform using Partial Fraction Expansion • How to use Z-Transform to solve Difference Equations using MATLAB?

  4. Introduction to Z-Transform Bilateral Z-Transform Unilateral Z-Transform Inverse Z-Transform

  5. MATLAB Implementation of Z-Transform

  6. Solution of Example 1 syms z x0=3; x1=5; x2=4; x3=3; Xz=x0*(z^0)+x1*(z^-1)+x2*(z^-2)+x3*(z^-3); pretty(Xz)

  7. Solution of Example 1 Cont… syms z x=[3 5 4 3]; n=[0 1 2 3]; X=sum(x.*(z.^-n)); pretty(X)

  8. The command ztrans and iztrans

  9. Solution of Example 2 syms n z f = 2^n ; Z = ztrans(f) Zt = simplify(Z) iz=iztrans(Z)

  10. Discrete Time System Properties

  11. Pole-Zero Plot and Stability num=[.1 .1]; den=[1 -1.5 0.7]; zplane(num,den) Is this system is STABLE??

  12. Pole-Zero Plot Cont… figure(2) H=tf(num,den,1); pzmap(H)

  13. Step Response figure(3) subplot(2,1,1) num=[.1 .1]; den=[1 -1.5 0.7]; dstep(num,den) subplot(2,1,2) Stepz(num,den)

  14. Impulse Response figure(4) subplot(2,1,1) dimpulse(num,den) subplot(2,1,2) impz(num,den)

  15. Partial Fraction Expansion of a Rational Function

  16. The Command residue

  17. Solution of Example 4 num=[ 1 3 1]; den=[ 1 0 -3 2] [R,P,K]=residue(num,den)

  18. Solution of Difference Equation using Z-Transform Thus

  19. Solution of Example 5 syms n z Y X=ztrans(0.9^n,z) Y1=z^(-1)*Y; Y2=z^(-2)*Y; G=Y+0.5*Y1+2*Y2-X; SOL=solve(G,Y); pretty(SOL); y=iztrans(SOL,n);

  20. Tutorial Questions

  21. Summary • Introduction to Z-Transform • implement Z-transform and Inverse Z-transform using MATLAB. • Region of Convergence (ROC) • Pole Zero Plot • Stable and Unstable Systems • Impulse Response and Step Response • MATLAB Implementation of inverse Z-transform using Partial Fraction Expansion • Solution of Difference Equations using MATLAB.

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