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small lit fix

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toni
2018-02-24 13:58:41 +01:00
parent 1b6445fa65
commit 8523e7040d
2 changed files with 2 additions and 2 deletions
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tex/chapters/mvg.tex
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@@ -5,7 +5,7 @@
% Repetitive Box filter to approx Gauss % Repetitive Box filter to approx Gauss
% Simple multipass, n/m approach, extended box filter % Simple multipass, n/m approach, extended box filter
Digital filters are implemented by convolving the input signal with a filter kernel, i.e. the digital filter's impulse response. Digital filters are implemented by convolving the input signal with a filter kernel, i.e. the digital filter's impulse response.
Consequently, the filter kernel of a Gaussian filter is a Gaussian with finite support \cite[120]{dspGuide1997}. Consequently, the filter kernel of a Gaussian filter is a Gaussian with finite support \cite{dspGuide1997}.
Assuming a finite-support Gaussian filter kernel of size $M$ and a input signal $x$, discrete convolution produces the smoothed output signal Assuming a finite-support Gaussian filter kernel of size $M$ and a input signal $x$, discrete convolution produces the smoothed output signal
\begin{equation} \begin{equation}
\label{eq:gausFilt} \label{eq:gausFilt}

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tex/chapters/relatedwork.tex
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@@ -42,7 +42,7 @@ In general, it is desirable to omit a grid, as the data points do not necessary
However, reducing the sample size by distributing the data on a equidistant grid can significantly reduce the computation time, if an approximative KDE is acceptable. However, reducing the sample size by distributing the data on a equidistant grid can significantly reduce the computation time, if an approximative KDE is acceptable.
Silverman \cite{silverman1982algorithm} originally suggested to combine adjacent data points into data bins, which results in a discrete convolution structure of the KDE. Silverman \cite{silverman1982algorithm} originally suggested to combine adjacent data points into data bins, which results in a discrete convolution structure of the KDE.
Allowing to efficiently compute the estimate using a FFT algorithm. Allowing to efficiently compute the estimate using a FFT algorithm.
This approximation scheme was later called binned KDE (BKDE) and was extensively studied \cite{fan1994fast} \cite{wand1994fast} \cite{hall1996accuracy} \cite{holmstrom2000accuracy}. This approximation scheme was later called binned KDE (BKDE) and was extensively studied \cite{fan1994fast} \cite{wand1994fast} \cite{hall1996accuracy}.
While the FFT algorithm poses an efficient algorithm for large sample sets, it adds an noticeable overhead for smaller ones. While the FFT algorithm poses an efficient algorithm for large sample sets, it adds an noticeable overhead for smaller ones.
The idea to approximate a Gaussian filter using several box filters was first formulated by Wells \cite{wells1986efficient}. The idea to approximate a Gaussian filter using several box filters was first formulated by Wells \cite{wells1986efficient}.