Fast Fourier Transformation (FFT) on low sampling rate data

I am studying 1 year geomagnetic data that has sampling rate of 1 minute. I need to perform Fast Fourier Transformation to distinguish different frequencies in my data but my main interest is to focus on the frequency between 0.01 to 0.1 Hz. My question is, is it even possible since according to my readings, I need higher resolution data, e.g: 1 sec. If it's im/possible, why? Thanks.

Answer 1

[David Goodmanson]

Hi Muhammed,

The highest frequency that you can get to with the fft is the Nyquist frequency, which is half the sampling rate. This is (1/2)*(1/60) which is .0083 Hz, approximately .01 Hz. Even that is pushing it quite a bit in terms of data quality.

As you suspected, you are at least a factor of 10 short in the data rate.

(To represent an oscillation you need to see the signal go up and then down, so you need at least two time samples per cycle, or no more than 1/2 cycle per time sample. Working back from that gives the expression above).

At .1 Hz and 60 sec sampling time you would have 6 cycles per sample.

[Adib Yusof]

Thank you for your answer. I have one more question. Say I acquire the 1 sec data later and I perform FFT on it. Can I do it for one whole year in one run, or do I have to perform FFT to a defined and small time window, say 30 mins and repeat the process (using for loops) for how many it is needed?

[David Goodmanson]

There are about 3.2e7 seconds in a year, and Matlab can easily do an fft of that size. If you split the data into, say, one-week pieces then none of those ffts can have anything to say about oscillations that take more than about a week, so you lose low frequency data.

You might want to look into some alternatives to the straight fft such as the periodogram and Welch's method.

[Adib Yusof]

Thank you very much David you have been such a great help! Wishing you a good day! :)