# Fourier transformation: Determining the axis

I need some help with the Fourier transformation of my data.

My original data is a Distance VS Time:

upon doing a Fourier Transform, I get the following:

I understand that normally after a Fourier transform the data is translated to amplitude/power VS frequency

But I am failing to understand what it is showing on the two axis? .

Also why some of the values are negative when my original data has all positive values?

Any suggestions?

UPDATE 1

After plotting the absolute values I get the following:

So now I can recognize that the x- axis is time, but I still cannot make out the y - axis, is it frequency?

UPDATE 2

Performed a FFTSHIFT so it looks more like this:

which i think is a proper representation except it is still maintaining the same x -axis.

I would look for an error in how you used the plot command. The second plot looks more like a programming error than anything else.

The output of a Fourier transform is usually a set of complex numbers. It looks like in the second plot the numbers are being plotted on an Argand diagram.

Try plotting the real parts, the imaginary parts, or the absolute values of the outputs of the Fourier transform.

• Montgomery-Sm Thanks for the tip, see above (update) I have plotted the absolute values. I can now recognize the x - axis as time but still can't make out the y - axis but it seems like it is frequency. Also the pattern or relation of the third plot seems to be the inverse of 3rd or 4th order line fitting curve on the first plot. – mrdigital Nov 28 '13 at 4:50
• Yes, it is frequency. I should also point out that because you are sampling 7000 pieces of data, and presuming you are using the fast Fourier transform, that you should probably regard the frequencies between 3500 and 7000 as more being -3500 to 0. (Kind of like 11 o'clock is -1 hour before noon.) – Stephen Montgomery-Smith Nov 28 '13 at 4:54
• Montgomery-Sm Yes that is correct, I am using FFT Sorry did not realise I had not mentioned earlier. I have not normalized this data pre-FFT, is that the reason why the frequency peaks are on opposite sides and is it normally a norm to represent them at the center by normalizing the data? Also I failed to understand what you meant by 3500-7500 being more -3500-0? But is it similar to the point I was making with the normalization? – mrdigital Nov 28 '13 at 5:03
• The reason why peaks are on opposite sides is because most of the signal consists of relatively low frequencies (the picture of the data looks like that). The reason they are on opposite sides is because you should really cut the graph in half vertically, and then move the right hand side to the left hand side. Then you would see that most of the signal occurs when the frequency is low. – Stephen Montgomery-Smith Dec 1 '13 at 4:57
• The fast Fourier transform assumes that both the data and result are periodic, in your case with period $N = 7000$. This means that in both the frequency domain and the time domain, that $6999$ is identified with $-1$. And so $3500$ could equally mean $-3500$. (By the way, I assume you have 7000 data points by eye-balling your picture.) – Stephen Montgomery-Smith Dec 1 '13 at 4:59