Please help me with this DFT system problem Consider the 6po

Please help me with this DFT system problem

Consider the 6-point sequence: x[n] = {2,1, 0,1, 2,1}. Suppose a radix-2 decimation- in-time (DIT) FFT algorithm is used to compute the DFT. Can x[n] be directly used as input to the DIT flowgraph? If yes, why? If no, modify the signal in a manner suitable for the application of the radix-2 algorithm. How many stages of the DIT flowgraph are required? Compute the DFT of the (possibly modified) signal using the radix-2 DIT FFT algorithm. Show the intermediate values at the output of every butterfly configuration in each stage of the DIT algorithm. Compute the reduction in complexity achieved by using the FFT algorithm compared to direct computation of the DFT of the original length 6 signal. Use the number of complex multipliers for comparison.

Solution

clear all;

close all;

%x=[1 2 3 4]

x=input(\'enter the input sequence\');

n=input(\'enter the lenth of DFT\');

subplot(4,1,1);

stem(x);

xlabel(\'time\');

ylabel(\'amplitude\');

title(\'input signal\');

y=fft(x,n);

subplot(4,1,2);

stem(y);

xlabel(\'frequency\');

ylabel(\'amplitude\');

title(\'discrete fourier transform\');

z=abs(y);

subplot(4,1,3);

stem(z);

xlabel(\'frequency\');

ylabel(\'magnitude\');

u=angle(y);

subplot(4,1,4);

stem(u);

xlabel(\'frequency\');

ylabel(\'phase plot\');

gtext(\'kl university\')

output :

enter the input sequence[1 2 3 4]

enter the lenth of DFT16

%implimentation of DFT using DIT-FFT.

clear all;

close all;

x=input(\'enter the sequence\');

subplot(3,1,1);

stem(x);

xlabel(\'time\');

ylabel(\'magnitude\');

title(\'input sequence\');

N=length(x);

y=(zeros(1,N));

x=bitrevorder(x);

g=1;

for m=1:1:(log(N)/log(2))

for n=1:1:N/2^m

for p=1:1:2^(m-1)

            a=x(g);

            b=x(g+2^(m-1));

            y(g)=a+b+exp(-i*2*pi*(p-1)/2^m);

            y(g+2^(m-1))=a-b*exp(-i*pi*(p-1)/2^m);

            g=g+1;

end

        g=2*m*n+1;

end

    g=1;

for t=1:1:N

        x(t)=y(t);

end

end

subplot(3,1,2);

stem(abs(x));

xlabel(\'time\');

ylabel(\'magnitude\');

title(\'magnitude of DIT-FFT sequence\');

subplot(3,1,3);

stem(angle(x));

xlabel(\'angle\');

ylabel(\'amplitude\');

title(\'angle of DIT-FFT\');

gtext(\'kluniversity\');

disp(abs(x))