Like Laplace transform, the Symbolic Toolbox in MATLAB supports symbolic

computation of Z-transform (ztrans) and inverse Z-transform (iztrans):

There are many ways to represent a discrete-time system. For a FIR system, the

most straightforward way is to specify its impulse response.

To get our previous example on the FIR system, we can use the following command:

we can implement a IIR filter such as

[tex] H(z) = \frac{1}{1+0.5Z^{-1}} [/tex]

To obtain the pole locations, we can use the residuez command:

Pictorially, we can also derive the pole and zero plot using zplane:

computation of Z-transform (ztrans) and inverse Z-transform (iztrans):

syms n

x = (0.5)^n;

X = ztrans(x)

X =

2*z/(2*z-1)

iztrans(X)

ans =

(1/2)^n

There are many ways to represent a discrete-time system. For a FIR system, the

most straightforward way is to specify its impulse response.

x = [1 2 3 0 1 -3 4 1]; % input

im = [0.25 0.25 0.25 0.25]; % impulse response

y = conv(x,im);

subplot(2,1,1);

stem(x);

subplot(2,1,2);

stem(y);

To get our previous example on the FIR system, we can use the following command:

y = filter(im,1,x)

y =

0.2500 0.7500 1.5000 1.5000 1.5000 0.2500 0.5000 0.7500

we can implement a IIR filter such as

[tex] H(z) = \frac{1}{1+0.5Z^{-1}} [/tex]

b = 1;

a = [1 0.5];

y = filter(b,a,x);

subplot(2,1,1);

stem(y)

subplot(2,1,2);

impz(b,a)

To obtain the pole locations, we can use the residuez command:

[r,p,k] = residuez(b,a)

r =

1

p =

-0.5000

k =

[ ]

Pictorially, we can also derive the pole and zero plot using zplane:

zplane(b,a)

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