dlti systems and z transform
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DLTI Systems and Z TransformTRANSCRIPT
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Discrete Time Systems and Z Transform 1
Electrical Engineering Program RIT Dubai
EEEE 789 SP: Digital Control
Practice Session onDiscrete Time Systems and Z Transform
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Discrete Time Systems and Z Transform 2
Problem 1a. Solve the following difference equations b. Using MATLAB compute the output and plot them.
Solution
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Discrete Time Systems and Z Transform 3
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% a)a=.5; b=[0 2];n = 0:30;y0 = 0;x0 = 0;x = zeros(size(n));x(1) = 1;y=recur(a,b,n,x,x0,y0);subplot(221),stem(n,y)title(’1a)’)xlabel(’n’)ylabel(’y[n]’)y(1:5) % displays y for n=0 to 5, used to double-check hand answers% b)a=2; b=[0 2];n = 0:30;y0 = 0;x0 = 0;x = zeros(size(n));x(1) = 1;y=recur(a,b,n,x,x0,y0);subplot(222),stem(n,y)title(’1b)’)xlabel(’n’)ylabel(’y[n]’)y(1:5)% c)a=[1.2 .32]; b = [1 -1];y0 = [1 2];x0 = 0;x = ones(size(n));y=recur(a,b,n,x,x0,y0);subplot(223),stem(n,y)title(’1c)’)xlabel(’n’)ylabel(’y[n]’)y(1:5)
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Discrete Time Systems and Z Transform 5
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6Discrete Time Systems and Z Transform
Problem 2A discrete-time signal x[n] has z-transform
Determine the z-transform V(z) of the following signals:
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Problem 2 Solution
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Problem 2 Solution
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9Discrete Time Systems and Z Transform
Problem 3Compute the z-transform of the discrete-time signals (a)-(j). Express your answer as a ratio of polynomials in z whenever possible.
(h) x[n] = n for n=0,1,2 and x[n] = -n for all n≥3(i) x[n]= (n -1)u[n] – nu[n-3](j) x[n] = (0.25)-n u[n-2]
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Problem 3 Solution
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Problem 3 Solution
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Problem 3 Solution
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Problem 3 Solution
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Problem 3 Solution using MATLAB
syms x n zx=heaviside(n)-heaviside(n-1)+2*(heavisi de(n-l)-heaviside(n-2))X=simplify(ztrans(x))
syms x n zx=heaviside(n)-heaviside(n-2)+2*heaviside(n-2)X=simplify(ztrans(x))
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syms x n zx=exp(O.S*n)*heaviside(n)+heaviside(n-2);X=simplify(ztrans(x)J
syms x n zx=exp(0.5*n)* (heaviside(n)-heaviside(n-2))+heaviside(n-2);X- simplify(ztrans(x))
Problem 3 Solution using MATLAB
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syms x n z pix=sin (pi*n/2) *heaviside(n-2);X=simplify(ztrans(x))
syms x n zx=((O.SJ"nJ*n*heavi side(n);X=simplify(ztrans(x))
syms x n zx=heaviside(n)-n*heaviside{n-l)+((l/3)"n)*heaviside(n-2);X=simplify(ztrans(x))
Problem 3 Solution using MATLAB
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syms x n zx=n*(heaviside(n)-heaviside(n-3))-n*heaviside(n-3);X=zsimplify(ztrans (x))
syms x n zx=(n-l)*heaviside(n)-n*heaviside(n-3);X=simplify(ztrans(x))
syms x n zx=(0.25"{-n))*heaviside{n-2);x-=simplify(ztrans(x))
Problem 3 Solution using MATLAB
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Problem 4Compute the inverse z-transform x[n] of the transforms (a)-(h).
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Problem 4 Solution
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Problem 4 Solution
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Problem 4 Solution
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Discrete Time Systems and Z Transform 22
Problem 5 Find the inverse z-transform x[n] of the transforms that follow. Determine x[n] for all n.
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Problem 5 Solution
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Problem 5 Solution
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Problem 5 Solution