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Develop composite radix DIT-FFT flow graph for N=6=2*3
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We have generated equation for composite radix.

$X(k)=∑_{n=0}^{N_1-1}x(nm_1)W_N^{m_1 nk}+∑_{n=0}^{N_1-1}x(nm_1+1)W_N^{(nm_1+1)k}+∑_{n=0}^{N_1-1}x(nm_1+m_1-1)W_N^{(nm_1+m_1-1)k}$

For N=6=2×3

=$m_1×N_1$

i.e $N_1=3 ,m_1=2$

$X(k)=∑_{n=0}^2x(2n)W_6^{2nk}+∑_{n=0}^2x(2n+1)W_6^{(2n+1)k}$

$=∑_{n=0}^2x(2n)W_6^{2nk}+∑_{n=0}^2x(2n+1)W_6^{(2nk)} W_6^k$

Let, $X(k)=X_1 (k)+W_6^k X_2 (k)$……………………………….(1)

$X_1 (k)=∑_{n=0}^2x(2n) W_6^{2nk}$

$X_1 (k)=x(0)+x(2) W_6^{2k}+x(4)W_6^{4k}$

$X_1 (0)=x(0)+x(2)+x(4)$

$X_1 (1)=x(0)+x(2) W_6^2+x(4)W_6^4$

$X_1 (2)=x(0)+x(2) W_6^4+x(4)W_6^8$

Similarly,

$X_2 (k)=∑_{n=0}^2x(2n+1) W_6^{2nk}$

$X_2 (k)=x(1)+x(3) W_6^{2k}+x(5)W_6^{4k}$

$X_2 (0)=x(1)+x(3)+x(5)$

$X_2 (1)=x(1)+x(3) W_6^2+x(5)W_6^4$

$X_2 (2)=x(1)+x(3) W_6^4+x(5)W_6^8$

Substitute all values in equation 1

$X(0)=X_1 (0)+W_6^0 X_2 (0)$……………………….(i)

$X(1)=X_1 (1)+W_6^1 X_2 (1)$…………………….(ii)

$X(2)=X_1 (2)+W_6^2 X_2 (2)$…………………….(iii)

$X(3)=X_1 (3)+W_6^3 X_2 (3)$

$=X_1 (0)+W_6^3 X_2 (0)$…………………..(iv)

$X(4)=X_1 (4)+W_6^4 X_2 (4)$

$=X_1 (1)+W_6^3 X_2 (1)$………………….(v)

$X(5)=X_1 (5)+W_6^5 X_2 (5)$

$=X_1 (2)+W_6^5 X_2 (2)$………………..(vi)

Now, develop the algorithm flow diagram as per equations (i) to (vi)

enter image description here

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