Simple MATLAB code to show the zero-correlation between sample of white Gaussian noise

Let be a Nx1 vector that contains pseudorandom samples drawn from standard normal distribution. This represents N samples taken from a standard normal distribution at time ‘t’.

The correlation of the sequence is given by E[xH]

This means, we need to compute the matrix xH M (M is a very large number) times, sum up all the matrices, and divide the resultant matrix by M. We can see that as M tends to infinity, we get a diagonal matrix as output. If the variance of the noise distribution is 1, then we get an identity matrix.

Z=10;
N=1000000
Y=zeros(Z,Z);
for i=0:N-1
    x=randn(Z,1);
    X=x*x';
    Y=Y+X;
end
Y./N
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Post workout pancake; a healthy alternative to protein shakes!

Here is a healthy solid-food alternative to the shaky protein you’ve been using as your post workout recovery. Egg-whites, oats, banana pancake.

You’ll need (to serve: 1)

  • Egg whites (5-6)      
  • 1 banana
  • 1/2 cup oats
  • 2 tsp sugar or 1 sachet of splenda

Get it done:

  • Blend all the ingredients well in a blender until a smooth consistency is achieved.
  • Pour it into a pre-heated non-stick pan and cook in medium heat (closed).
  • Flip it when the top turns golden-brown in color.
  • Once cooked, allow it to cool; ReAdY to Be serVed!!
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Free Online Courses that help, really!

It’s being a long time since I sat down to blog. No! I did sit down a few times to blog about this topic, but aah, it didn’t happen. Now I felt I shouldn’t be late any more with this.

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Prof. Gilbert Strang

The Open Course Ware by MIT offers hell lot of courses online spread over a wide variety of subjects and fields. It’s absolutely FREE! I personally have taken the 34 videos Linear Algebra lecture series by Prof. Gilbert Strang. Was an amazing experience!

Here you get the complete list of courses offered by MIT OCW http://ocw.mit.edu/courses/

MIT OCW has also developed a high-school level course ware which can be found here http://ocw.mit.edu/high-school/

 

 

 

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Actually, SEE (Stanford Engineering Everywhere) was my stepping stone to online education. Professor Andrew Ng, Director of the Stanford Artificial Intelligence Lab gave me a great experience through his Machine Learning class which helped to gain in-depth knowledge of the applications of Machine Learning in real world problems, apart from what I have learned in my under-graduate course in Neural Networks. You get the complete list of courses offered by SEE here, http://see.stanford.edu/see/courses.aspx.

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Prof. Andrew NG & Prof. Daphne Koller

Co-founded by Prof. Andrew Ng and Prof. Daphne Koller of the Stanford, Coursera is a place where online courses from professors of various universities meet, to give us a great learning experience. Here is the course list, https://www.coursera.org/courses.

Most of the classes listed above offers its takers a classroom like experience with assignment, tests and exams; it’s FUN + knowledge!! Prof. Gilbert Strang in his introduction video to ‘Highlights of calculus‘ says, ‘ I think the textbooks as often so large and so many exercises that it’s totally easy to lose the key point…’

 

Happy Learning!!

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Home-made Cappuccino…

2012-01-17 18.00.10

An empty glass bottle of Nutella was the only ‘special’ thing used to create this lovely cup of Cappuccino at home.

Some LaTeX Tweaks…

Here are some \LaTeX tweaks I used to prepare a template for one of our lab reports recently. Most of the help was received from http://tex.stackexchange.com/.

Adding more columns to the index page than the default ‘Chapter No.- Chapter Name- Page’

\documentclass[10pt,letterpaper]{article}
\usepackage{lipsum,titletoc}

\titlecontents{section}
[0em]
{}
{}
{}
{\titlerule*[0.5em]{.}\contentspage}

\begin{document}

 \noindent\begin{minipage}[c]{0.7\textwidth}
\renewcommand{\contentsname}{\Large \centerline{CONTENTS}}
\tableofcontents

\addtocontents{toc}{\textbf{No.}\hspace{2cm}\textbf{Experiment}~\hfill\textbf{Page}\par}

\end{minipage}
%
\hspace{0.05\textwidth}
%
\begin{minipage}[c]{0.2\textwidth}
\begin{tabular}{lr}
\textbf{Date} & \textbf{Signature} \\[1em]

\end{tabular}
\vspace{3.02in}  %adjust this to align date & sign in the contents page
\end{minipage}$

Putting a Border Around Each Page

\begin{document}
\fancypage{%
\setlength{\fboxsep}{10pt}\doublebox}{}

Preventing \chapter{} from beginning on a new page

\makeatletter
 \patchcmd{\chapter}{\if@openright\cleardoublepage\else\clearpage\fi}{}{}{}
 \makeatother

\begin{document}
.......................
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