1.- Let r = (ro, X1,..., IN-1) € CN. Compute the discrete Fourier transforms of the following vectors with components given by: a) rk = a*, a> 0. N – 1 (":"). b) Ik k c) *k = cos (2TWOK:/N), wo ¢ Z. ( 1, if k = 0, 1, . , m, if k = m + 1,..., N – m – 1, k = N – m, ..., N – 1, or d) *k тEN, 2m +1 < N. 0,

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1.- Let r = (xo, T1,. .. , IN-1) € CN. Compute the discrete Fourier transforms of the following vectors with
components given by:
a) rk = a*,
a > 0.
N – 1
b) xk =
k
c) Tk = cos (2nwok/N), wo £ Z.
{
1,
if k = 0, 1, ... , m,
k = N – m, ..., N – 1,
or
d) rk =
m e N,
2m +1< N.
0,
if k = m +1, ..., N – m – 1,
Transcribed Image Text:1.- Let r = (xo, T1,. .. , IN-1) € CN. Compute the discrete Fourier transforms of the following vectors with components given by: a) rk = a*, a > 0. N – 1 b) xk = k c) Tk = cos (2nwok/N), wo £ Z. { 1, if k = 0, 1, ... , m, k = N – m, ..., N – 1, or d) rk = m e N, 2m +1< N. 0, if k = m +1, ..., N – m – 1,
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