The decimation$-$in$-$frequency FFT algorithm was developed in Section $3$ for radix $2,$ i$.$e$.,N=2^{?}$

$u.$ A similar approach leads to a radix$-3$ algorithm when $N=3^{?}$

$u.$

$($a$)$ Draw a flow graph for a $9-$point decimation$-$in$-$frequency algorithm using a $33$ decomposition of the DFT$.$

$($b$)$ For $N=3^{?}$

$u,$ how many complex multiplications by powers of $W_N$ are needed to compute the DFT of an $N-$point complex sequence using a radix$-3$ decimation$-$in$-$frequency FFT algorithm?

$($c$)$ For $N=3^{?}$

$u,$ is it possible to use in$-$place computation for the radix$-3$ decimation$-$infrequency algorithm?