linear convolution y(n) = x(n)*h(n)
1. The following sequences x(n) and h(n) are given:
x(n) = 3δ(n) + 7δ(n+2) - 10δ(n-1) + 5δ(n-2)
h(n) = 6δ(n) + 4δ(n-1) + 2δ(n-3)
(a) Using the appropriate property of z-transform to find the linear convolution y(n) = x(n)*h(n)
(b) Find also the linear convolution using table method, and then compare the results.
2. Find the z-transform and ROC of the sequence
x(n) = 3(-?/?)^n u(n) – 2(3)^n u(-n-1)
Also, find the poles and zeros of the above z-transform
3. Find the inverse z-transform of X(z) using partial fraction method. NOTE: assume x(n) is
right sided.
Also, find the poles and zeros of X(z)
4. Can you obtain the z-transform of u[n] at z = 0? If you can, what is its value? If you cannot,
why not?
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