Greetings!I have problems with interpreting Fourier analysis results. What I was trying to do is - determine the phase of business cycles, by analysing GDP dynamics (time series).I have two calculating programmes:1st programme (Fourier transform) resulting data set:see 1st attachment2nd programme (Discrete Fourier transform) resulting data set:see 2nd attachmentBy using this tutorial: http://support.numxl.com/entries/26876407-Discrete-Fourier-Transform-Using-NumXL-WizardBut what should I do with this data - how to perform analysis and interpret it?Thanks!
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Fourier transform for GDP data series
- Thread starter Kida
- Start date
Greetings!I have problems with interpreting Fourier analysis results. What I was trying to do is - determine the phase of business cycles, by analysing GDP dynamics (time series).I have two calculating programmes:1st programme (Fourier transform) resulting data set:see 1st attachment2nd programme (Discrete Fourier transform) resulting data set:see 2nd attachmentBy using this tutorial: http://support.numxl.com/entries/26876407-Discrete-Fourier-Transform-Using-NumXL-WizardBut what should I do with this data - how to perform analysis and interpret it?Thanks!
Suppose you have a simple harmonic motion, say a pendulum whose position is given by
p(x) = 5 cos (\(\displaystyle \frac{\pi}{4}\, t\))
That is every eight seconds, it repeats itself [a frequency of 8 Hz]. Suppose you did a Fourier Transform on the data from such a function [sampled the function 128 times over 8 seconds and did an FT on the results], and plotted the FT. You would get a spike at an f (frequency value) of \(\displaystyle \frac{\pi}{4}\) with an amplitude of 5 [depending on just how you scaled you FT]. [Note: you would also get a spike at the negative frequency value but that is an artifact of the FT in this case.]
If you added another cosine term you would get another spike and so forth. The same applies for any function. The frequency component represent a repeat factor of a certain amount and the amplitude of the frequency component represents how strong that component is.