Hi everyone....
I have a data set with 15000 data points. I want to transform the data to frequency domain using FFT. For FFT to be fully fast, it required 2^n data points. This mean that it only can transform 2^13 data points, which is 8192 of 15000. I processed the data using R software and I found that FFT can transform all the data points, i.e. 15000 data points. I wish to know to what are the differences between transforming 8192 data points and 15000 data points? Could someone explain to me?
Thank you.
Hi Ken, you need to Add zero values at the end of the data sets to get data as 2^n for the extended period. While doing FFT the number of points are going to reduce by half comparing with Fourier transforms. Hence adding zero value is the common practice.
The size of your FFT represents the number of points at which you are going to sample the data spectra. This means that your frequency step is defined as Fs/Nfft (where Fs is your sampling rate and Nfft the FFT size). If you crop your data (15000 samples) to 8192 samples, then only the first 8196 data samples are used to calculate the FFT. If you want to use your full data set (15000 samples) you can define your FFT size as 15000 or 2^14=16384. The second option is called zero-padding as mentioned in a previous reply (you are adding zeros at the end of the data set to fulfill the required number of points) . Using a shorter FFT size than your data set is not recommended since it does not use all the data. Therefore, if you want to use a 2^N size, you should use the first power of 2 that contains the amount of samples in your data set. Using zero-padding helps in other matters like Gibbs effects (ripple at the boundaries of the pass band) and increases the resolution of the spectra. As far as your FFT size contains all the data in your data set, there is no difference in the resulting spectra except the resolution. If you use a shorter FFT then part of the data is not accounted for and the spectra can be different than what is expected.
if you use fft function in matlab you will see that it is better to use 2^14 point. matlab will automatically add zero to end of your signal. if you use 2^13 point, you will have slope around your main frequencies.
Hi, yes. you should add zeros to 16384=2^14. it means that your signal length must be 16384.
Thanks. I'm now working on the climatology data. My data sets have 17893, 17996 and 17866 data points. The software was fixed (not adjustable) to power-of-two closest to the available number of data points for FFT. So, it process the data up to 16384 only. Is there any difference between transforming all data points and 16384 data points? Why it is not recommended to abandon the remaining data?
In the MATLAB, if i am doing calculation FFT {1,2,3,4,5,6} . I got results as { 21, -3+5.196i, -3+1.732i, -3, -3-1.732i, -3-5.196i}
Here all the researchers are saying that in MATLAB after the data it adds [0,0,0,....] as per requirement for 2 ^n.
While doing same thing from self written python code i am getting result as {21, -9.65-3j, 3-4j, 1.6568+3, -3, 1.65-3j, 3+4j, -9.65+3j} for data {1,2,3,4,5,6,0,0}
Note: Results for proper 2^N point FFT i.e if I choose {1,2,3,4,5,6,7,8} I am getting correct results, by self written code.
I had the same question My data is 501 long and i and now after i did the zero padding should i take the result of it or ahould i just ignore it and take only the 501 result to do more calculations on it?
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