Let

x[n] = 0,  n < 0, n > 7,

 be a real eight-point sequence, and let X[k] be its eight-point DFT.

(a) Evaluate

 in terms of x[n].

(b) Let 

u[n] = 0,  n < 0, n > 7,

be an eight-point sequence, and let V[k] be its eight-point DFT, 

If V[k] = X(z) at z = 2exp(j(2πk + π)/8) for k = 0….. 7, where X(z) is the z-transform of x[n], express v[n] terms of x[n].

(c) Let 

w[n] = 0,  n < 0, n > 3

be a four-point sequence, and let W[k] be its four-point DFT. 

If W[k] = X[k] + X [k + 4], express w[n] in terms of x[n].

(d) Let 

y[n] = 0,  n < 0, n > 7,

be an eight-point sequence, and let Y[k] be its eight-point DFT. If express y[n] in terms of x[n]

Part A X|k]e(2a/8)kn t%39 Part D S 2X(k]. k = 0, 2, 4. 6. k = 1. 3, 5, 7. 0. Y(k]