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# Is it possible to obtain the imaginary parts along with real part in the evaluation of fast fourier transform?

Asked by rizwana junaid on 13 Oct 2012

I have a program , a part of which is shown below:

X=x(:,1); %assigning X, all the values of x of length n.

Y = fft(X,n); % calculating the fast fourier transform of X.

T=fft(t,n); %calculating the fast fourier transform of time.

plot(log10(T),log10(Y.^2),'R')

After the execution of the program, I get the spectral plot, but a warning too: Warning: Imaginary parts of complex X and/or Y arguments ignored.

This means imaginary parts has been excluded. I am keen interested in, if I am be able to get the plot which will involve both real and imaginary parts. I will be much thankful, if anyone take interst to clear my problem.

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Answer by Wayne King on 13 Oct 2012
Edited by Wayne King on 13 Oct 2012

That is because you want to plot only the magnitude of the DFT coefficients, or the magnitudes squared

` plot(log10(abs(T)),log10(abs(Y).^2),'r')`

I have no idea why you are taking the Fourier transform of your time vector, that is not the frequency vector.

You need to create a meaningful frequency vector by knowing the number of points and the sampling frequency (interval)

```   t = 0:0.001:1-0.001; %sampling interval is 0.001
Fs = 1000;
x = cos(2*pi*100*t)+randn(size(t));
xdft = fft(x);
freq = 0:Fs/length(x):Fs/2;
xdft = xdft(1:length(x)/2+1);
plot(freq,20*log10(abs(xdft)))```

Of course in the DFT coefficients, you certainly have the imaginary parts.

Wayne King on 13 Oct 2012

You're squaring the original data, but then you're taking the Fourier transform, the Fourier transform is in general complex-valued. It does not matter whether you square the time data first.

rizwana junaid on 13 Oct 2012

Thank you so much for your responsive act.

I still dont understand. suppose If the original data is squared first X=x^2,

then fft of X is performed which have all the imaginary and real parts. then why does it not give the imaginary parts? and gives the warning.

Wayne King on 13 Oct 2012

The warning is because you are trying to use plot(), which is for 1-D data with a complex-valued function. You can plot the real and imaginary parts separately:

```   t = 0:0.001:1-0.001; %sampling interval is 0.001
Fs = 1000;
x = cos(2*pi*100*t)+randn(size(t));
xdft = fft(x);
freq = 0:Fs/length(x):Fs/2;
xdft = xdft(1:length(x)/2+1);
plot(freq,real(xdft),'b');
hold on;
plot(freq,imag(xdft),'r'); legend('Real','Imaginary')```