Let xk 5 3 9 1 2 7 3 2 8 6 4 hk 2 5 2 7 9 6 a Find the 10

Let x(k) = [5 3 9 1 2 7 3 2 8 6 4], h(k) = [2 5 2 7 9 6]

a.) Find the 10 point circular convolution of x(k) and h(k).

b.) Find the 11 point circular convolution of x(k) and h(k).

c.) Find the 12 point circular convolution of x(k) and h(k)

d.) Find the 13 point circular convolution of x(k) and h(k).

e.) Find the 14 point circular convolution of x(k) and h(k).

f.) Find the 15 point circular convolution of x(k) and h(k)

Solution

h(n) = 6(n) - .6(n - no This system is an idealized example of a system that would introduce reverberation. Assume that N = 4 n0 \' (a) Determine the N-point DFT H(k) of h(n). (b) Now consider the N-point DFT H1 (k) of a sequence h1 (n) specified by H (k) = 1 k = 0,1,..., N - 1 H(k) Determine h (n). Hint: If you have trouble evaluating t e IDFT summation directly, express H1 (k) as a polynomial in WN 0 and observe that the h1 (n) are coefficients of WNnk*