written 6.5 years ago by |
We have generated equation for composite radix.
X(k)=∑N1−1n=0x(nm1)Wm1nkN+∑N1−1n=0x(nm1+1)W(nm1+1)kN+∑N1−1n=0x(nm1+m1−1)W(nm1+m1−1)kN
For N=6=2×3
=m1×N1
i.e N1=3,m1=2
X(k)=∑2n=0x(2n)W2nk6+∑2n=0x(2n+1)W(2n+1)k6
=∑2n=0x(2n)W2nk6+∑2n=0x(2n+1)W(2nk)6Wk6
Let, X(k)=X1(k)+Wk6X2(k)……………………………….(1)
X1(k)=∑2n=0x(2n)W2nk6
X1(k)=x(0)+x(2)W2k6+x(4)W4k6
X1(0)=x(0)+x(2)+x(4)
X1(1)=x(0)+x(2)W26+x(4)W46
X1(2)=x(0)+x(2)W46+x(4)W86
Similarly,
X2(k)=∑2n=0x(2n+1)W2nk6
X2(k)=x(1)+x(3)W2k6+x(5)W4k6
X2(0)=x(1)+x(3)+x(5)
X2(1)=x(1)+x(3)W26+x(5)W46
X2(2)=x(1)+x(3)W46+x(5)W86
Substitute all values in equation 1
X(0)=X1(0)+W06X2(0)……………………….(i)
X(1)=X1(1)+W16X2(1)…………………….(ii)
X(2)=X1(2)+W26X2(2)…………………….(iii)
X(3)=X1(3)+W36X2(3)
=X1(0)+W36X2(0)…………………..(iv)
X(4)=X1(4)+W46X2(4)
=X1(1)+W36X2(1)………………….(v)
X(5)=X1(5)+W56X2(5)
=X1(2)+W56X2(2)………………..(vi)
Now, develop the algorithm flow diagram as per equations (i) to (vi)