diff --git a/tex/chapters/mvg.tex b/tex/chapters/mvg.tex index bf55196..3bddaca 100644 --- a/tex/chapters/mvg.tex +++ b/tex/chapters/mvg.tex @@ -5,7 +5,7 @@ % Repetitive Box filter to approx Gauss % 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. -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 \begin{equation} \label{eq:gausFilt} diff --git a/tex/chapters/relatedwork.tex b/tex/chapters/relatedwork.tex index 80d0c1c..ac93b28 100644 --- a/tex/chapters/relatedwork.tex +++ b/tex/chapters/relatedwork.tex @@ -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. 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. -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. The idea to approximate a Gaussian filter using several box filters was first formulated by Wells \cite{wells1986efficient}.