# Lysario – by Panagiotis Chatzichrisafis

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

It is possible to load data from a file for plots with PSTricks in TeX. According to the PSTricks manual all that is needed is a file with a list of coordinate pairs delimited by curly braces , parentheses, commas. read the conclusion >
• Filed under: Programming, Scilab
• In [1, p. 94 exercise 4.2] we are asked to consider the estimator $\hat{P}_{AVPER}(0)=\frac{1}{N}\sum\limits_{m=0}^{N-1}\hat{P}_{PER}^{m}(0)$ (1)

where $\hat{P}_{PER}^{m}(0)= x^{2}[m]$ (2)

for the process of Problem 4.1. We are informed that this estimator may be viewed as an averaged periodogram. In this point of view the data record is sectioned into blocks (in this case, of length 1) and the periodograms for each block are averaged. We are asked to find the mean and variance of $\hat{P}_{AVPER}(0)$ and compare the result to that obtained in . read the conclusion >
In problem [1, p. 94 exercise 4.1] we will show that the periodogram is an inconsistent estimator by examining the estimator at $f=0$, or $\hat{P}_{PER}(0)=\frac{1}{N}\left(\sum\limits_{n=0}^{N-1}x[n]\right)^{2}.$ (1)

If $x[n]$ is real white Gaussian noise process with PSD $P_{xx}(f)=\sigma_{x}^{2}$ (2)

we are asked to find the mean an variance of $hat{P}_{PER}(0)$. We are asked if the variance converge to zero as $N \rightarrow \infty$. The hint provided within the exercise is to note that $\hat{P}_{PER}(0)= \sigma_{x}^{2} \left(\sum\limits_{n=0}^{N-1}\frac{x[n]}{\sigma_{x}\sqrt{N}}\right)^{2}$ (3)

where the quantiiy inside the parenthesis is $\sim N(0,1)$ read the conclusion >
I recently wanted to update my OpenCV installation and try to find out why my usb camera – using the macam drivers – was not working with the libraries installed on my system. So this time i had the intention to dig into the code of OpenCV release. That meant using the easy way – mac ports – to install the OpenCV libraries was not an option. read the conclusion > $x[n]=\sum\limits_{i=1}^{P}A_{i}\cos(2\pi f_{i}n+\phi_{i})$
the ensemble ACF and the temporal ACF as $M\rightarrow \infty$, where the $\phi_{i}$‘s are all uniformly distributed random variables on $[0, 2 \pi)$ and independent of each other. We are also asked to determine if this random process is autocorrelation ergodic. read the conclusion >