Graphically determine the convolution of the xn and the

Question

1) Graphically determine the convolution of the x[n] and the unit step sequence u[n]. Include a sketch of your answer.

2) For a causal, continuous time LTI system, determine the impulse response given the transfer function H(s):

H[s] = (5 + 2s)/(s² - s -6)

3) Using time domain techniques, determine the impulse response of the following discrete time LTIC system (subject to zero initial state):

y[n+2] +0.5y[n+1] - 0.14y[n]=2x[n+2]+x[n+1]

4) Determine the inverse z-transform given:

X[z] = (1 - 1/2.z^-1)/(1+ 3/4.z^-1 +1/8.z^-2)    |z| > 1/2

5) Starting with the definition of the z-transform, show that the discrete time Fourier transform is equivalent to the unit circle in the z-plane.