Question

a) Construct a flow graph for a 16-point radix-2 decimation-in-frequency FFT algorithm. (8 points) \\ \\ Label all multipliers in terms of powers of $W_{16}$, and also label any branch transmittances that are equal to -1. \\ Label the input and output nodes with the appropriate values of the input and DFT sequences, respectively. b) Determine the number of real multiplications and the number of real additions required to implement the flow graph. (4 points) c) Let input sequence $x[n]$ be given by $x[n] = \begin{cases} 1 & 0 \le n \le 7 \\ 0 & 8 \le n \le 15 \end{cases}$ Use the flow graph of a) to calculate frequency coefficient $X[1]$. (3 points)

          a) Construct a flow graph for a 16-point radix-2 decimation-in-frequency FFT algorithm. (8
points)
\\
\\	Label all multipliers in terms of powers of $W_{16}$, and also label any branch
transmittances that are equal to -1.
\\	Label the input and output nodes with the appropriate values of the input and DFT
sequences, respectively.
b) Determine the number of real multiplications and the number of real additions required to
implement the flow graph. (4 points)
c) Let input sequence $x[n]$ be given by
$x[n] = \begin{cases} 1 & 0 \le n \le 7 \\ 0 & 8 \le n \le 15 \end{cases}$
Use the flow graph of a) to calculate frequency coefficient $X[1]$. (3 points)

a) Construct a flow graph for a 16-point radix-2 decimation-in-frequency FFT algorithm. (8
points)

Label all multipliers in terms of powers of W16, and also label any branch
transmittances that are equal to -1.

Label the input and output nodes with the appropriate values of the input and DFT
sequences, respectively.
b) Determine the number of real multiplications and the number of real additions required to
implement the flow graph. (4 points)
c) Let input sequence x[n] be given by
x[n] = 1 0 ≤ n ≤ 7
0 8 ≤ n ≤ 15
Use the flow graph of a) to calculate frequency coefficient X[1]. (3 points)

Added by Catherine L.

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