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Ryan Boyden added subsection_Fourier_Statistics_VCA_VCS__.tex
over 8 years ago
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\subsection{Fourier Statistics} VCA/VCS, delta variance, MVC, SPS/Bicoherence, wavelet %Just use the +Text to create a new separated text box for each category (here \subsubsection{}) into it.
\subsubsection{Velocity Channel Analysis and Velocity Coordinate Spectrum}
Velocity Channel Analysis (VCA) and Velocity Coordinate Spectrum (VCS) are techniques that isolate how fluctuations in velocity contribute to differences between spectral cubes (cite Authorea text?) by fitting a one-dimensional Power Spectrum to power laws. For runs W1T2t0.2 and W2T2t0, we compute the three-dimensional Power Spectrum of their the Fourier transforms. To obtain the VCA, we calculate a one-dimensional Power spectrum by integrating the 3D Power Spectrum over the velocity channels, and then radially averaging the obtained 2D Power Spectrum over the two-dimensional spatial frequencies. A portion (trying to emphasize how only a portion is fit to the power law) of the now 1-D Power Spectrum is then fit to a single-power law. We derive the VCS from different integration techniques. Here, we reduce the 3D Power Spectrum to one dimension by averaging over the spatial frequencies. Since the VCS yields two distinct power law relations, we fit the 1D power spectrum to a segmented linear model similar to Koch et al. (2015), (using the method established by ???). Thus, VCA yields a 1D Power Spectrum as a function of spatial frequency, while VCS yields a 1D Power Spectrum as a function of velocity-channel frequency (frequency equivalent of velocity). ...Figures
