1. Computation of Z-transform---MATLAB
Consider a discrete-time pulse x[n]=u[n]-u[n-10].
a. Plot x[n] as a function of n and use the definition of the Z-transform to find X(z).
b. 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.
c. Find the poles and the zeros of X(z) and plot them in the z-plan. Use MATLAB to plot the poles and zeros.
2. 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]
a. Find an expression for Y(z)
b. Do a partial expansion of Y(z)
c. Find the inverse Z-transform y[n] and verify your results using MATLAB.