3
$\begingroup$

My apology if following question is too simplistic to be asked but I have the following code which generates a nice sine wave for me:

N=64;
X=zeros(N,1);
X(2)=-32j;
X(N)=32j;
x=ifft(X);
stem(real(x));

enter image description here

Now I was thinking I should be able to construct a cosine wave in the similar way by changing the X(2) and X(N) values into some real mirrored values say X(2)=-32 and X(N)=32. However, the output is not what I want i.e. a cosine wave

enter image description here

Improve this question
$\endgroup$

1 Answer 1

Reset to default
4
$\begingroup$

You must keep in mind that for a real-valued signal, second half of your spectrum is a complex conjugate of all values below the Nyquist frequency. In your case:

X(2) = -32
X(N) = 32

as you can see the coefficients are not the complex conjugate of each other. Because of that you are ending up with round-off errors, since two frequency components are cancelling each other out.

Here is some modification to your code:

clc, clear all, close all
fs = 32;
dt = 1/fs;

N=64;
X=zeros(N,1);
X(2)=32;
X(N)=conj(X(2));
s=ifft(X)';

td = linspace(0, (length(s)-1)*dt,     length(s));

stem(td, s, 'b', 'linewidth', 2)
grid on
legend({'reconstructed signal'})

Which gives:

enter image description here

Improve this answer
$\endgroup$
4
  • $\begingroup$ Thanks for the answer. So what you changed in my code was basically changing X(N)=32 into X(N)=conj(32) . What's the mathematical interpretation of this? i.e. conjugate of a real value. $\endgroup$
    – Bababarghi
    Commented Oct 23, 2015 at 12:28
  • $\begingroup$ Complex conjugate $\endgroup$
    – jojeck ♦
    Commented Oct 23, 2015 at 12:34
  • $\begingroup$ conj(32) is 32, so X(N)=conj(32) is the same of X(N) = 32, or did I miss something ? The error of OP was just he did X(2) = -32 instead of X(2) = 32. But I like your way to do it, it prevents errors. $\endgroup$
    – MaximGi
    Commented Feb 26, 2016 at 9:11
  • 1
    $\begingroup$ If you are asking about the line X(N)=conj(X(2)); then it is there to automatically calculate the coefficient when OP wants to play with the code. Indeed X(N) will be 32 in the example above. $\endgroup$
    – jojeck ♦
    Commented Feb 26, 2016 at 9:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.