MATLAB CODE TO VERIFY LINEARTY PROPERTY OF DFT

CODE:

x1=input('Enter the first sequence');

x2=input('enter the second sequence');

alpha=input('Enter a constant');

beta=input('Enter a constant');

z=alpha*x1+beta*x2;

Z=fft(z);

X1=fft(x1);

X2=fft(x2);

sum=alpha*X1+beta*X2;

subplot(2,2,2);

stem(abs(Z));

title('DFT of(alpha*x1+beta*x2)');

xlabel('time index');

ylabel('amplitude');

subplot(2,1,2);

stem(abs(sum));

title('alpha*X1+beta*X2');

xlabel('time index');

ylabel('amplitude');

OUTPUT :

Enter the first sequence[9 8 7 6 5 4 3 2 1]

enter the second sequence[9 8 3 7 1 7 9 4 5]

Enter a constant2

Enter a constant3