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# use FFT in matlab and get phase plot

Asked by Passband Modulation on 14 Aug 2012

i have some polymers characterized by transmission terahertz time domain spectroscopy (THz-TDS).

ive now the time domain data in Excel, with column A being (Delay ps), column B (Reference), column C (Amplitube nA) as follows.

i would like to have "FFT phase of column C" minus "FFT phase of column B", and then plot the phase (after deduction) as a function of frequency.

i am told this could be done by adding

` plot(freq,angle(fft(X(:,3)))-angle(fft(X(:,2))))  `

after

```   [X,TXT,RAW] = xlsread('yourfile.xls');
xdft = fft(X(:,2));   xdft = fft(X(:,2));
% sampling interval -- assuming equal sampling
DT = X(2,1)-X(1,1);
% sampling frequency
Fs = 1/DT;
DF = Fs/size(X,1);
freq = 0:DF:Fs/2;
xdft = xdft(1:length(xdft)/2+1);   phi = angle(xdft);```

anyway it does not work

the command window shows

??? Error using ==> plot Vectors must be the same lengths.

Error in ==> Untitled at 12 plot(freq,angle(fft(X(:,3)))-angle(fft(X(:,2))))

Michael Quinn on 14 Aug 2012

Not knowing your data size/shape, I can only offer some suggestions on what to look at. Instead of your plot() command, make a new variable:

```PhaseDifference = angle(fft(X(:,3)))-angle(fft(X(:,2)));
```

Then look at its size compared to the size of freq:

```size(PhaseDifference)
size(freq)
```

It looks like (from the error) that they are different. You'll need to figure out how to fix this so that you can successfully plot them.

Passband Modulation on 15 Aug 2012

thank you Michael Quinn, but i am not familiar with this. anway thx again.

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Answer by Elige Grant on 14 Aug 2012
Edited by Elige Grant on 14 Aug 2012

Here are the frequencies associated with the output from FFT:

```Nt =              % Number of time samples
Fs =              % sample frequency (= 1/dt)
df = Fs/Nt;       % frequency increment
Nyq = Fs/2;       % Nyquist frequency
```
```if mod(Nt,2) == 0 % Nt is even
freq = ifftshift(-Nyq : df : Nyq-df);
else              % Nt is odd
freq = ifftshift([sort(-1*(df:df:Nyq)) (0:df:Nyq)]);
end
```

Then you can just do a xlim on the plot to zoom in on a specific frequency range.

## 1 Comment

Passband Modulation on 15 Aug 2012

really thx a lot. these are the background info and the related questions on them.