Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to X[I] is shown in the figure. Let W_6 = ( - j2 6 ). In the figure, what should be the values of the coefficients a1, a2, a3 in terms of W6 so that X[I] is obtained correctly?

Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to X[I] 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 a₁, a₂, a₃ in terms of W₆ so that X[I] is obtained correctly?

Answer: Option D