Find hk the 10 point dft of hn and compute the output

Question

An LTI discrete-time system has the unit-impulse response.

h[n]=(-1)ⁿu[n]

Consider the following input to the system.

x[n]=u[n]-u[n-3]

with zero initial conditions.

a) Find X[k], the 10 point DFT of x[n].

b) Find H[k], the 10 point DFT of h[n].

c) Compute the output response of the system y[n], 0 ≤ n ≤ 4, using the convolution sum.

d) Compute the output response of the system y[n], 0 ≤ n ≤ 4, using the DFT and IDFT.