# Signal processing using MATLAB

Computation of Z-transform---MATLAB

Consider a discrete-time pulse x[n]=u[n]-u[n-10].

Plot x[n] as a function of n and use the definition of the Z-transform to find X(z).

Use the Z-transform of u[n] and properties of the Z-transform to find X(z). Verify that the expressions obtained above for X(z) are identical.

Find the poles and the zeros of X(z) and plot them in the z-plan. Use MATLAB to plot the poles and zeros.

Inverse Z-transform -MATLAB

We are interested in the unit-step solution of a system represented by the difference equation

y[n]=y[n-1]-0.5y[n-2]+x[n]+x[n-1]

Find an expression for Y(z)

Do a partial expansion of Y(z)

Find the inverse Z-transform y[n] and verify your results using MATLAB.

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#### Solution Preview

Computation of Z-transform---MATLAB

Consider a discrete-time pulse x[n]=u[n]-u[n-10].

Plot x[n] as a function of n and use the definition of the Z-transform to find X(z).

Matlab code:

U=[1 1 1 1 1 1 1 1 1 1];

n=0:9;

figure;stem(n,U);

title('x(n)=u(n)-u(n-10)');

Z transform of this signal is: X(z)=1+z-1+z-2+z-3+z-4+z-5+z-6+z-7+z-8+z-9

Use the Z-transform of u[n] and properties of the Z-transform to find X(z). Verify that the expressions obtained above for X(z) ...

#### Solution Summary

The expert examines signal processing using MATLAB. The Z-transforms for discrete time signals in MATLAB are examined.