I have seven years geo-chemical helium radon concentration time series data. In mentioned FFT technique so many peaks are found. I want to find proper periodicity of my data by both FFT and ACF method.
1.Checkout some nice explanations given at
https://www.dataq.com/data-acquisition/general-education-tutorials/fft-fast-fourier-transform-waveform-analysis.html
2. It may be worthwhile to obtain and examine FFt plot by dropping one by one signal samples from the beginning .
3. If you have an initial estimate of frequency then a suitable filter could be tried.
4. For ACF try to filter out the mean in case this has not been done. (detrend).
5. If the signal contains some random process you may like to explore power spectral density / innovative process. assuming ergodicity.
Good Luck
Cheers
The spectrum of a signal x(t) is the Fourier transform of the autocorrelation function of x(t). This is the Wiener-Khinchin theorem, The problems with that are:
- the autocorrelation function is not known, and
- there is only a limited (finite) amount of data available
First the autocorrelation function must be estimated from x(t). Both for the estimation and for obtaining the FT there is the problem of the data being finite in practice.
Blackman and Tukey spectral estimation uses the biased estimate of the autocorrelation function and then a finite limit 'M' for the truncation of the estimation of the FT summation.
Do visit your library and read about spectral estimation. Or read the excellent paper "Spectrum analysis - a modern perspective" by Kay and Marple (attached).
Kankana Seal have you found any suitable method to find periodicity of a time series data.
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