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 a1, a2, a3 in terms of W6 so that X[1] is obtained correctly?

\({a_1} = - 1,{a_2}\; = W_6^2\;,{a_3}\; = {W_6}\)

\({a_1} = \; - 1,{a_2}\; = \;{a_6},{a_3}\; = \;W_6^2\)

\({a_1} = \;1,{a_2}\; = W_6^2\;,{a_3}\; = {W_6}\;\)

\({a_1} = \;1,{a_2}\; = \;{W_6^1},{a_3}\; = W_6^2\)

Consider a six-point decimation-in-time Fast Fourier Transform (FFT) a

1.	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 a1, a2, a3 in terms of W6 so that X[1] is obtained correctly?
A.	\({a_1} = \; - 1,{a_2}\; = \;{a_6},{a_3}\; = \;W_6^2\)
B.	\({a_1} = \;1,{a_2}\; = W_6^2\;,{a_3}\; = {W_6}\;\)
C.	\({a_1} = \;1,{a_2}\; = \;{W_6^1},{a_3}\; = W_6^2\)
D.	\({a_1} = - 1,{a_2}\; = W_6^2\;,{a_3}\; = {W_6}\)
Answer» D. \({a_1} = - 1,{a_2}\; = W_6^2\;,{a_3}\; = {W_6}\)

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