# Lysario – by Panagiotis Chatzichrisafis

"ούτω γάρ ειδέναι το σύνθετον υπολαμβάνομεν, όταν ειδώμεν εκ τίνων και πόσων εστίν …"

In [1, p. 62 exercise 3.18] we are asked to find the temporal autocorrelation function for the real sinusoidal random process of Problem [1, p. 62 exercise 3.16]:
 $\hat{r}_{xx}[k]=\frac{1}{2M+1}\sum\limits_{n=-M}^{M}x[n]x[n+k]$

as $M\rightarrow \infty$. As a second step we are asked to determine if the random process autocorrelation ergodic. read the conclusion >
Sometimes it is useful to have several scripts (with standard definitions) loaded immediately into scilab.
On MacOsX Scilab executes at startup the first lines of the file .scilab. The file has to be placed (if it does already exist) under the directory:
 /home/$<$User$>$/.Scilab/$<$scilab-version$>$ 
If the file isn’t there just create one and call your scripts with the definitions to be loaded into the scilab workspace.

For example you might want to load definitions of physical constants into the workspace that are defined within ‘physical_constants.sce’. For this purpose add a line like the following into the .scilab file:

exec('Users/$<$User$>$/Development/scilab/Base/physical_constants.sce');
• Filed under: Programming, Scilab
• Last year i got a very different mathematical book as a gift. A comic novel from Doxiadis, Papadimitriou and Papadatos: Logicomix. It is easy to read and provides some insight of the mathematical quest in the area of logic of the last century. You’ll meet people like Bertrand Russel, David Hilbert, Gödel and many more outstanding persons. Some work results of the main actors are presented in that way that is accessible for a wide audience – according to the rules used in popular science media. So even mathematical illiterate persons may enjoy the comic and due to the very nice illustrations i think even kids could enjoy it. The “showdown” is Gödel’s incompleteness theorem and i enjoyed the way the result was presented. The authors admit at the end of the book that the storyline is only loosely based on historical facts but actually this doesn’t reduce the value of the novel. Reading this comic was a nice way to relax during a cold winter’s day. Give it a try !
 $\frac{1}{2M+1}\sum\limits_{n=-M}^{n=M}x[n]$
is given by [1, eq. (3.60), p. 58]. For the case when $x[n]$ is real white noise we are asked to what the variance expression does reduce to. A hint that is given is to use the relationship from [1, eq. (3.64), p. 59]. read the conclusion >
 $x[n]= A \cos(2\pi f_{0}n+\phi)$ (1)
, where $\phi$ is uniformly distributed on $(0,2\pi)$, is WSS by finding its mean and ACF. Using the same assumptions we are asked to repeat the exercise for a single complex sinusoid
 $x[n]=A\exp[j(2\pi f_{0}n+\phi)].$ (2)