GATE 2019 Electronics & Communication Q28

Question

Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to X[1] is shown in the figure. Let $W_6 = \exp\left(-\frac{j2\pi}{6}\right)$. In the figure, what should be the values of the coefficients $a_1, a_2, a_3$ in terms of $W_6$ so that X[1] is obtained correctly?

Answer

$a_1 = -1, a_2 = W_6^2, a_3 = W_6^2$

Answer

$a_1 = 1, a_2 = W_6^2, a_3 = W_6$

Answer

$a_1 = 1, a_2 = W_6, a_3 = W_6^2$

Answer

$a_1 = -1, a_2 = W_6^2, a_3 = W_6$