Dear LabView Engineers
No action item: this is just a bug report
concerning the poor-quality Gaussian random
variables in LabView. A workaround
is given.
* Trying to accomplish?
Generate Gaussian noise in Labview
* What is the problem?
The built-in vi "Gaussian~White~Noise"
generates poor-quality random numbers.
* What is the origin of the problem?
LabView is using an algorithm
which yields random numbers of poor
statistical quality.
* What is the suggested fix?
In the next release, implement the
Box-Muller method, as described in the
book "Numerical Recipes", Section 7.2.
Thanks! By the way, LabView is a great
product overall. You engineers do a
good job.
********* detailed description follows *****
\footnote{The expressions given for the variance of the skew
(\ref{eq:skewSigmaDont},\ref{eq:skewSigmaDo}) and kurtosis
(\ref{eq:kurtosisSigma}) have been validated against
numerical data generated in LabView (version 5.01fd). These
experiments uncovered serious deficiencies in the LabView vi
\texttt{Gaussian~White~Noise}. Briefly, noise generated by
\texttt{Gaussian~White~Noise} has significantly too-small
values of the fourth moment and all higher moments. A
sample of $5\times10^{5}$ points showed:
\[\begin{cases}
\expect{x^{2}} = 1.002 \pm 0.002 & \text{should be 1}\\
\expect{x^{4}} = 2.92 \pm 0.01 & \text{should be 3}\\
\expect{x^{6}} = 13.7 \pm 0.1 & \text{should be 15}\\
\expect{x^{8}} = 86.9 \pm 1.2 & \text{should be 105}
\end{cases}\]
These numerical values strongly suggest that LabView
generates Gaussian variables by the easy-to-program but
highly inaccurate algorithm
$g = \sum_{i=1}^{12}\,(r_{i}-0.5)$,
where $r$ is uniformly distributed on the interval $(0,1)$
and $g$ approximates a normally distibuted variable. With
some help from \emph{Mathematica}, the first four moments of
$g$ can be shown to be $\expect{x^{2}}=1$, $\expect{x^{4}}=29/10
\simeq 2.9$, $\expect{x^{6}} = 569/42 \simeq 13.5$, and
$\expect{x^{8}}=2569/30 \simeq 85.6$, in precise accord with
the LabView numerical results.
Shame on you, National Instruments, for generating Gaussian
variables by such a second-rate algorithm! The
much-superior Box-Muller algorithm (see \emph{Numerical
Recipes}) is implemented in
\texttt{JAS~Gaussian~White~Noise}, which is functionally
equivalent to LabView's \texttt{Gaussian~White~Noise}.}
