### replace primed

parent 7aaf38cc
 ... ... @@ -105,7 +105,7 @@ label:WAKE, TYPE=string, NBIN=real, FILTERS=string-array; \begin{center} \caption{Wakefield command summary} \label{tab:wakefieldcmd} \begin{tabular}{|l|p{0.6\textwidth}|l|} \begin{tabular}{|l|l|} \hline \tabhead Command & Purpose \\ \hline ... ... @@ -220,7 +220,7 @@ $$f_i = \frac{7\cdot f_{i-4} + 24\cdot f_{i-2} + 34\cdot f_{i} + 24\cdot f_{i+2} and$$f_i = \frac{7\cdot f_{i-2} + 24\cdot f_{i-1} + 34\cdot f_{i} + 24\cdot f_{i+1} + 7\cdot f_{i+2}}{96}.$$For the derivative a standard second order stencil is used:$$f\primed_i = \frac{f_{i-2} - 8\cdot f_{i-1} + 8\cdot f_{i+1} - f_{i+2}}{h}f'_i = \frac{f_{i-2} - 8\cdot f_{i-1} + 8\cdot f_{i+1} - f_{i+2}}{h} This filter was designed by Ilya Pogorelov for the ImpactT implementation of the CSR 1D model. The FFT based smoothers calculate the Fourier coefficients of the line density. Then they set all coefficients corresponding to frequencies above a certain threshold to zero. Finally the back-transformation is calculate using this coefficients. The two filters differ in the way they identify coefficients which should be set to zero. \texttt{FixedFFTLowPass} uses the n lowest frequencies whereas \texttt{RelativeFFTLowPass} searches for the coefficient which has the biggest absolute value. All coefficients which, compared to this value, are below a threshold (measure in percents) are set to zero. For the derivative the coefficients are multiplied with the following function (this is equivalent to a convolution): ... ...
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