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Added weights to KDE and BKDE

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MBulli
2018-02-18 21:11:42 +01:00
parent 62fceaa815
commit a46fe242e8
2 changed files with 18 additions and 18 deletions
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tex/chapters/mvg.tex
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@@ -14,8 +14,8 @@ y[n] = \frac{1}{\sigma\sqrt{2\pi}} \sum_{k=0}^{M-1} x[k]\expp{-\frac{(n-k)^2}{2\
where $\sigma$ is a smoothing parameter called standard deviation.
Note that \eqref{eq:bkdeGaus} has the same structure as \eqref{eq:gausFilt}, except the varying notational symbol of the smoothing parameter and the different factor in front of the sum.
While in both equations the constant factor of the Gaussian is removed of the inner sum, \eqref{eq:bkdeGaus} has an additional normalization factor $N^{-1}$.
This factor is necessary to in order to ensure that the estimate is a valid density function, i.e. that it integrates to one.
While in both equations the constant factor of the Gaussian is removed of the inner sum, \eqref{eq:bkdeGaus} has an additional normalization factor $W^{-1}$.
This factor is necessary to ensure that the estimate is a valid density function, i.e. that it integrates to one.
Such a restriction is superfluous in the context of digital filters, so the normalization factor is omitted.
Computation of a digital filter using the a naive implementation of the discrete convolution algorithm yields $\landau{NM}$, where $N$ is the length of the input signal and $M$ is the size of the filter kernel.