This question is related to the Fast Fourier Transform (FFT) algorithm. (a) Consider the sequence x[n] = {1, 1, −1, −1, −1, 1, 1, −1}. (1) Determine the DFT X[k] of x[n] using the decimation-in-time FFT algorithm. (b) Now, compute the DFT Y [k] of the following sequence y[n] using the decimation-in-time FFT algorithm: y[n] = {1, −2, 1, −1, 1, −1, 2, −1}. (2) (c) Compare the efficiencies of computing the 8-point FFT of x[n] and y[n]. Is it possible to compute one of them more efficiently? (d) Apart from computing the FFT using the decimation-in-time algorithm, you have also been introduced to the computation of FFT using decimation-in-frequency. Plot the flow graph for an 8-point decimation-in-frequency FFT algorithm