I am working with Outgoing longwave Radiation dataset and am basically trying to perform the below mentioned procedure. But I do not know what removing three harmonics of the seasonal cycle means. Also It would be convenient if you could let me know how its done in MATLAB or NCL NCAR Command Language).
" Since we are interested in synoptic to intraseasonal timescales, our main results (those of the OLR power) are based on spectral quantities that have been calculated for many successive overlapping (by 2 months) 96-day segments of the multiyear OLR dataset. The results are not sensitive to this overlap. To help prevent aliasing, the first three harmonics of the seasonal cycle are removed. Then for each segment the mean and linear trend are removed in time by a least squares fit, and the ends of the series are tapered to zero. The data windowing provided by the tapering helps to minimize the effects of spectral leakage, and the overlapping of segments minimizes the loss of data by the tapering. After tapering, complex FFTs are performed in longitude to obtain Fourier coefficients (in zonal planetary wavenumber space) for each time and for each latitude. Further complex FFTs are applied in time to these coefficients to obtain the wavenumber-frequency spectrum for each latitude. Finally, the OLR power is averaged over all available segments of the 18-yr record, and is further summed for the latitudes between 15S and 15N. "
Low pass or high pass filter, depending on which harmonics. Typically LPF at the threshold you are interested in. MATLAB will have a built-in function for this - https://www.mathworks.com/help/signal/ref/lowpass.html
In this instance, you will need to set your wpass to be slightly above your anticipated base frequency so it gets inside the pass-band, and your higher harmonics will be attenuated.
In the frequency domain this is even easier, just set anything above/below +-wpass to 0 so you get a square filter of magnitude 1 about the origin with positive and negative ends at wpass, and the rest is 0 - shown here in fig a:
https://flylib.com/books/2/729/1/html/2/images/0131089897/graphics/05fig13.gif
Then you inverse-fft and this is your LPF'd time-domain signal.
You can try using EMD (Empirical Mode Decomposition) method in Matlab, which decompose the signal into different bands, then you just sum the decompositions that do not have the harmonics
You will find your answer in this link:
https://www.mathworks.com/matlabcentral/answers/407416-how-to-remove-particular-harmonic-in-the-time-series
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