Suppose x[n] is the eight-point complex-valued sequence with real part xr[n] and imagina...

Suppose x[n] is the eight-point complex-valued sequence with real part x_r[n] and imaginary part x_i[n] shown in Figure P8.41 (i.e., x[n] = x_r [n]+jx_i[n]). Let y[n] be the four-point complex-valued sequence such that Y [k], the four-point DFT of y[n], is equal to the odd indexed values of X[k], the eight-point DFT of x[n] (the odd-indexed values of X[k] are those for which k = 1, 3, 5, 7).

Determine the numerical values of y_r[n] and y_i[n], and the real and imaginary parts of y[n].