Under the Hood¶
We strongly recommend everyone to follow the procedure as instructed here when using WaLSAtools — a user-friendly tool — which gives you all information you need to do your analysis. However, for experts who want to make themselves familiar with the techniques and codes under the hood, inspect them and modify/develop/improve them, some of the main codes are also provided below. Please note that all codes and their dependencies are available in the GitHub repository.
Spectral Analyzer¶
WaLSA_speclizer
This code computes power spectrum and its statistical significance level for a 1D signal (or all pixels of an image sequence, i.e., a 3D cube) using FFT (Fast Fourier Transform), Lomb-Scargle, Wavelet, and HHT (Hilbert-Huang Transform) analysis techniques. In addition, the code can output mean power spectrum (averaged over power spectra of several pixels) as well as dominant frequency and power using the above-mentioned analysis methods.
WaLSA_speclizer.pro
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k-ω Analysis and Fourier Filtering¶
WaLSA_QUB_QUEEFF
A variant of the QUEEns Fourier Filtering (QUEEFF) code, to compute k-ω diagram and perform Fourier filtering in the k-ω space.
WaLSA_qub_queeff.pro
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This code uses the following routine (originanly from Rob Rutten) to compute the k-ω power.
WaLSA_plotkopower_funct.pro
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B-ω Analysis¶
WaLSA_bomega
This routine computes and plots B-ω diagram, based on the approach introduced in this scientific article.
WaLSA_bomega.pro
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Detrending and Apodisation¶
WaLSA_detrend_apod
All signals are detrended (linearly, or using higher-order polynomial fits if desired) and apodised (using a Tukey window, i.e., tapered cosine) prior to all spectral analyses (unless otherwise it is omitted).
Here is the code used for detrending and apodising the signals. The spatial apodisation for the k-ω diagram, are performed inside the WaLSA_plotkopower_funct.pro.
WaLSA_detrend_apod.pro
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Wavelet Analysis¶
WaLSA_wavelet
A modified/extended variant of wavelet.pro (of Torrence & Compo) to compute wavelet power spectrum and its related parameters.
WaLSA_wavelet.pro
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This code also uses the following routine to plot the wavelet power spectrum (along with confidence levels and cone-of-influence regions).
WaLSA_plot_wavelet_spectrum.pro
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Cross Correlations: 1D power spectra¶
WaLSA_cross_spectrum
Calculating cross-spectrum (also known as co-spectrum or cross-power), coherence, and phase relationships between two time series, where the 1D power spectra are obtained with FFT (Fast Fourier Transform),
Lomb-Scargle, Wavelet (global, oglobal, and sensible), and HHT (Hilbert-Huang Transform), using the WaLSA_speclizer.pro.
WaLSA_cross_spectrum.pro
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Cross Correlations: Wavelet power spectra¶
WaLSA_wavelet_cross_spectrum
As a largely modified/extended variant of the wave_coherency.pro (of Torrence), this code calculates co-spectrum, coherence, and phase relationships between two time series, where the wavelet power spectra are obtained, thus cross-correlation parameters also have two dimensions.
WaLSA_wavelet_cross_spectrum.pro
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This code also uses the following routine to plot the wavelet co-spectrum and coherence spectrum (along with confidence levels, cone-of-influence regions, and phase lags).
WaLSA_plot_wavelet_cross_spectrum.pro
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