# Question about Fourier transformation in Matlab

1. Dec 23, 2016

### Frank Einstein

Hello everybody.

I am triying to calculate a band-pass filter using the fourier transform.
I have a vector with 660 compomponents; one for each month. I am looking for a phenomenon which has a periodicity between 3 and 7 years (it's el niño, on the souhtern pacific ocean). I want to make zero all the coefficients of the fourier transform except the ones which are in between 3 and 7 years. I have tried to remove all of the coefficients which are between the 36th (12*3) and 84th (12*7). Then, I proceed to do the same thing in the other half of the series to mantain simmetry.

But once I make the inverse fourier transform and I plot it, the results don't match whith what I want.

Can someone tell me where is my faliure?

Code used:
niniofourier=fft(ninios);

for i=1:35
niniofourierb(i)=0;
end

for i=85:330
niniofourierb(i)=0;
end

for i=36:84
niniofourierb(i)=niniofourier(i);
end

for i=331:576
niniofourierb(i)=0;
end

for i=577:624
niniofourierb(i)=niniofourier(i);
end

for i=625:660
niniofourierb(i)=0;
end

niniosi=ifft(niniofourierb);
figure(4)
plot (niniosi)

2. Dec 23, 2016

### vela

Staff Emeritus
You're selecting the wrong part of the DFT. You don't want coefficients 36 through 84.

You have 660 months worth of samples, so $X_k$ (for $k=0, 1, \dots, 330$) corresponds to a cycle that has an angular frequency of $k\omega_0$ where $\omega_0=2\pi/660\text{ rad/month}$. What you want to do is determine the range of $k$ that corresponds to angular frequencies between $2\pi/36\text{ rad/month}$ and $2\pi/84\text{ rad/month}$.

3. Dec 23, 2016

### Frank Einstein

Thank you very much; I am using now this code:
for i=1:660
if (i-1)/660<pi/18
if (i-1)/660> pi/42
niniofourierb(i)=niniofourier(i);
else
niniofourierb(i)=0;
end
else
niniofourierb(i)=0;
end
end
niniosi=ifft(niniofourierb);
figure(4)
plot (niniosi)

But it seems like I still got it wrong. I am obtaining something which makes no sense

I have done the same filter using a low pass filter and I obtain reasonalbe results.

4. Dec 23, 2016

### vela

Staff Emeritus
I have no idea what that plot is supposed to represent.

Don't forget that like before you also have to take care of the other half of the spectrum.

5. Dec 23, 2016

### Frank Einstein

I have plotted the inverse fourier transform of the series in which all the coefficients except those between 2π/36 and 2π/84 are zero.
In the code that I have posted is figure(4)
EDIT:
auxTWO=fliplr(niniofourier(1:330));
for i=1:330
niniofourierb(i+330)=auxTWO(i);
end
niniosi=ifft(niniofourierb);
niniosib=niniosi(1:330);
If I add this code to make the mirroring of the first half, I still get an awful figure

Last edited: Dec 23, 2016
6. Dec 23, 2016

### FactChecker

It sounds like you are removing the coefficients of the very periodicity that you expect it to have. Shouldn't those be the ones you keep? If you remove the period, you should expect noise. Is that what you expected? Is that what you got?

PS. Before you go too far, I think you should apply some time series analysis like Box-Jenkins and see what autocorrelations are in the data.