Latex Layout Control

Margin Placing:
http://help-csli.stanford.edu/tex/latex-margins.shtml
Modify the bottom margin distance:
http://www.latex-community.org/forum/viewtopic.php?f=47&t=9531&start=0

Radioware from Notre Dame

Radioware project from Notre Dame University:
http://radioware.nd.edu/documentation/basic-gnuradio/entering-the-world-of-gnu-software-radio

Introduction to GNURadio

Software radio is the technique of getting the code as close to the antenna as possible. It turns radio hardware problem into software problems. The fundamental characteristic of software radio is that software defines the transmitted waveforms and demodulates the received waveforms. This is in contrast to most radios in which the processing is done with either analog circuitry or analog circuitry combined with digital chips.

Analog to Digital  Converter (ADC)
ADC has two primary characteristics: sampling rate and dynamic range.
Generally speaking, device physics and cost impose trade-offs between the sample rate and dynamic range.

In GNURadio
USRP Board servers as above part which is developed by Matt  Ettus and Eric Blossom.

The RF Front-End
How can we listen to broadcast FM Radio at 92.1 MHz with ADC runs at 20 MHz. The answer is the Radio Frequency (RF) front-end. The receive RF front end translate a range of of frequencies appearing at its input (RF) to a lower range intermediate frequency (IF) range at its output.
For example RF side 90 - 100 MHz range down to 0 - 10 MHz range (IF).

Mostly we can treat the RF front-end as a black box with a single control, the center of the input range that's to be translated.

Center frequency of the output range is called the intermediate frequency, or IF

Typical RF front-end structure:

Antenna -> Low Noise Amplifier (LNA) -> Low Pass Filter (LPF) -> Mixer -> LPF -> ADC 
                                                                   ^
                                              Local Oscillator ----|

In the explaining context of Notre Dame, they use "different frequency" to explain this.
About structure above more information can be found through searching :
direct conversion receiver architecture
More detail information from EE times about RF circuit design.
http://www.eetimes.com/design/microwave-rf-design/4018954/What-s-in-an-RF-Front-End-


FAQ about Hardware Front end :
http://www.ettus.com/faq#norf

Can I create a radio system with just a USRP motherboard and BasicTX/BasicRX, but no RF frontend?

The most direct and easy way to create a complete radio system is to use one of our complete RF frontend daughterboards, the TVRX2, DBSRX2, WBX, SBX, RFX-series, and XCVR2450.




Collaborative Hardware?
MiniCircuits?
GNURadio Introduction Guides Written by Dawei Shen
http://www.snowymtn.ca/gnuradio/gnuradiodoc-1.pdf
Series Documents


Another Hardware introduction Document Created by VT (Virginia Tech)
http://www.ece.vt.edu/swe/chamrad/crdocs/CRTM09_060727_USRP.pdf


ASSA GNU Radio Page
http://www.radio-assa.org.au/sdr/gnu-radio

Cognitive Radio

Some Basic Concepts from wiki:
http://en.wikipedia.org/wiki/Cognitive_radio

Communication effectively, while avoiding interference with licensed and licensed exempt users. This alternation of parameters is based on the active monitoring of several factors in the external and internal radio environment, such as radio frequency spectrum, user behavior and network state.

Virginia Tech guy defines:"a software defined radio with a cognitive engine brain".

A article link talking about more practical and regulatory considerations.

Some reading to keep up with Cognitive Radio\
June 16, 2011
From Spectral Holes (A blog on Cognitive Radio)
http://spectralholes.blogspot.com/

Quasi and Spectrum method

Spectrum Method:
http://en.wikipedia.org/wiki/Spectral_method

Quasi-empiricism in mathematics:
http://en.wikipedia.org/wiki/Quasi-empiricism_in_mathematics

Black Swan Theory &  Nassim Nicholas Taleb & Fooled by Randomness
http://en.wikipedia.org/wiki/Black_swan_theory

When Will We Have Unmanned Commercial Airliners? Unmanned planes dominate the battlefield, yet airliners still have pilots—and copilots

IEEE Spectrum:
http://spectrum.ieee.org/aerospace/aviation/when-will-we-have-unmanned-commercial-airliners/1

Another related article:
http://spectrum.ieee.org/green-tech/advanced-cars/longdistance-car-radar

Missy Cummings in Engineering Girls:
http://www.engineergirl.org/?id=3113

Research Statement Template Latex

https://www.math.lsu.edu/grad/handbook/hb9

Parallel Numerical Algorithms

Chapter 10 – Iterative Methods for Linear Systems

UIUC
CS 544

Maybe a good book?
http://www.amazon.com/exec/obidos/ASIN/052143064X/ref=nosim/weisstein-20

Kronecker Product

Kronecker Product:
http://www.siam.org/books/textbooks/OT91sample.pdf

KLT
http://fourier.eng.hmc.edu/e161/lectures/klt/node3.html

And their relationships:
http://www-ee.uta.edu/dip/Courses/EE5355/ch3.pdf
(Searching its doc version)

A modification of Classical 2D KLT
ST-KLT carry on spatio-temporal analysis on multi-channel signals

Bi-2DPCA: A Fast Face Coding Method for
Recognition
http://www.intechopen.com/source/pdfs/10663/InTech-Bi_2dpca_a_fast_face_coding_method_for_recognition.pdf

Latex ! Undefined control sequence

A Guide To Latex (H Kopka, P Daly) 4Ed
P402 Appendix C. Error Messages

! Undefined control sequence.
l.3 The last words appear in \txetbf
{bold face}.
?

! Undefined control sequence, meaning that an unknown command name (control sequence) was the cause of the error. Next comes a pair of text lines, the first of which is prefixed with 1.3, meaning that the error occurred in 'line 3' of the input text. The error itself was encountered at the last symbol printed in the upper line. The lower line shows the continuation of the input line being processed when the error was found, here the words {bold face}. Before continuing, TEX waits for a reaction from the user, as indicated by the question mark in the last line of the message.

For my case:

! Undefined control sequence.

l.9 A random vector \underscore

                               {x}:

should be changed to \underline{x}

fixed

Latex Symbols and other resource

Unicode Standard Documents:
http://unicode.org/

Delta Equal
http://unicode.org/charts/PDF/U2200.pdf

Short Math Guide for Latex:
ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf

\triangleq #delta equal to

Consulting The Comprehensive Latex Symbol List (Pakin):

http://www.ctan.org/tex-archive/info/symbols/comprehensive/

How to displaying a formula:
(Useful link for Wikipedia):
http://en.wikipedia.org/wiki/Help:Displaying_a_formula

Kronecker Product
\otimes

FAQ for Latex
http://www.tug.org/pracjourn/2006-1/schmidt/schmidt.pdf

Beamer by Example:
http://tug.org/pracjourn/2005-4/mertz/mertz.pdf

several examples for report:
https://engineering.purdue.edu/ECN/Support/KB/Docs/LaTeXSampleTemplateF
also contains CV example
http://www.tedpavlic.com/post_homework_tex_example.php
http://links.tedpavlic.com/tex/homework.tex
http://maths.dur.ac.uk/Ug/projects/resources/latex/report/

Install Latex in Linux

http://linuxandfriends.com/2009/10/06/install-latex-in-ubuntu-linux/

Setting up Latex
http://www-lmmb.ncifcrf.gov/~toms/latexforbeginners.html

ldd
print shared library dependencies.
Normally, using under /usr/bin /usr/shared /usr/lib path

LaTex Beamer Matrix
http://deic.uab.es/~iblanes/beamer_gallery/index.html
http://www.hartwork.org/beamer-theme-matrix/

Tex Showcase
http://www.tug.org/texshowcase/

LaTex Command Glossary:
http://en.wikibooks.org/wiki/LaTeX/Command_Glossary

Wiki Books:
http://en.wikibooks.org

Other useful resources:
A Guide To Latex and Electronic Publishing

Perturbation Theory

First-order non-singular perturbation theory

This section develops, in simplified terms, the general theory for the perturbative solution to a differential equation to the first order. To keep the exposition simple, a crucial assumption is made: that the solutions to the unperturbed system are not degenerate, so that the perturbation series can be inverted. There are ways of dealing with the degenerate (or singular) case; these require extra care.

Suppose one wants to solve a differential equation of the form

Dg(x) = λg(x)

where D is some specific differential operator, and λ is an eigenvalue. Many problems involving ordinary or partial differential equations can be cast in this form. It is presumed that the differential operator can be written in the form

where  is presumed to be small, and that furthermore, the complete set of solutions for D⁽⁰⁾ are known. That is,one has a set of solutions , labelled by some arbitrary index n, such that

.

Wiki Waves

Wiki Waves
http://www.wikiwaves.org/Main_Page

Trapped modes
http://www.wikiwaves.org/Trapped_Modes
Mathematically, a trapped mode corresponds to an eigenvalue embedded in the continuous spectrum of the relevant operator.

Fredholm Integral Equation of the First Kind

Equation of the first kind

Integral equations, most generally, are common and take many specific forms (Fourier, Laplace, Hankel, etc.). They each differ in their kernels (defined below). What is distinctive about Fredholm integral equations is that they are integral equations in which the integration limits are constants (they do not include the variable). This is contrast to Volterra integral equations.

A homogeneous Fredholm equation of the first kind is written as:

General theory

The general theory underlying the Fredholm equations is known as Fredholm theory. One of the principal results is that the kernel K is a compact operator, known as the Fredholm operator. Compactness may be shown by invoking equicontinuity. As an operator, it has a spectral theory that can be understood in terms of a discrete spectrum of eigenvalues that tend to 0.

[edit]Applications

Fredholm equations arise naturally in the theory of signal processing, most notably as the famous spectral concentration problem popularized by David Slepian. They also commonly arise in linear forward modeling and inverse problems.

Klein Helmholtz Instability

www.rsmas.miami.edu/users/isavelyev/GFD-2/KH-I.pdf

UHD Start

UHD Wiki

Source code

Note: Users building from source should use the images for the master branch (see binary downloads).
Option 1: Clone the repository:

git clone git://code.ettus.com/ettus/uhd.git

-- Is your corporate or university firewall blocking the git protocol?
-- Try this http mirror instead. The mirror is updated daily.

git clone http://github.com/EttusResearch/UHD-Mirror.git

Option 2: Download an archive here

Build Instruction:
http://files.ettus.com/uhd_docs/manual/html/build.html#boost


Installation information:

Initialized empty Git repository in /home/ian/UHD-Mirror/.git/
remote: Counting objects: 32649, done.
remote: Compressing objects: 100% (7224/7224), done.
remote: Total 32649 (delta 24974), reused 32603 (delta 24939)
Receiving objects: 100% (32649/32649), 16.93 MiB | 830 KiB/s, done.
Resolving deltas: 100% (24974/24974), done.

According build instruction:
Build and Install
Then get into post installation procedures
USB Transport Setting:
http://files.ettus.com/uhd_docs/manual/html/transport.html#usb-transport-libusb

Attention:
On my machine, uhd-usrp.rules file is under ~/uhd/host/utils

http://www.raullen.net/2011/02/20/hello-usrp-n210-how-to-make-usrp-n210-running/
http://gnuradio.microembedded.com/usrpfaqbitstream

Perturbative inversion methods

Perturbative inversion methods for obtaining bottom geoacoustic parameters

Attention is focused primarily on the modal eigenvalue inverse problem for which the theory for determining the compressional  wave speed, compressional wave attenuation, and density is developed in detail. Properties of this technique are studied using synthetic data and include investigations of the dependence of the results on acoustics frequency, number of modes excited, and partial a priori knowledge of the bottom.

Inversion Problem:
The required input data are trapped mode eigenvalues for one or more frequencies, the group velocity dispersion curves for one or more modes, or the cw pressure field versus range (complex field or magnitude only) .

A great explanation of inverse problem:
An inverse problem is a general framework that is used to convert observed measurements into information about a physical object or system that we are interested in. For example, if we have measurements of the Earth's gravity field, then we might ask the question: "given the data that we have available, what can we say about the density distribution of the Earth in that area?" The solution to this problem (i.e. the density distribution that best matches the data) is useful because it generally tells us something about a physical parameter that we cannot directly observe. Thus, inverse problems are one of the most important, and well-studied mathematical problems in science and mathematics. Inverse problems arise in many branches of science and mathematics, including: computer vision, machine learning, statistics, statistical inference, geophysics, medical imaging (such as computed axial tomographyand EEG/ERP), remote sensing, ocean acoustic tomography, nondestructive testing, astronomy, physics and many other fields.


(Linear Inverse Theory)

The objective of an inverse problem is to find the best model, m, such that (at least approximately)

where G is an operator describing the explicit relationship between the observed data, d, and the model parameters. In various contexts, the operator G is called forward operator,observation operator, or observation function. In the most general context, G represents the governing equations that relate the model parameters to the observed data (i.e. the governing physics).

Mathematical

One central example of a linear inverse problem is provided by a Fredholm first kind integral equation.

Check Fredholm first kind integral equation in next several posts
For sufficiently smooth g the operator defined above is compact on reasonable Banach spaces such as L^p spaces. Even if the mapping is injective its inverse will not be continuous. (However, by the bounded inverse theorem, if the mapping is bijective, then the inverse will be bounded (i.e. continuous).) Thus small errors in the data d are greatly amplified in the solution m. In this sense the inverse problem of inferring m from measured d is ill-posed.


Numerical Scheme (quadrature scheme):
Simpson's Rule
http://en.wikipedia.org/wiki/Simpson's_rule
In numerical analysis, Simpson's rule is a method for numerical integration, the numerical approximation of definite integrals. Specifically, it is the following approximation:





2 Regularization Method

Regularization:
http://en.wikipedia.org/wiki/Regularization_(mathematics)
Regularization of Inverse Problem
http://www.springer.com/mathematics/computational+science+%26+engineering/book/978-0-7923-4157-4

The mathematical term well-posed problem stems from a definition given by Jacques Hadamard. He believed that mathematical models of physical phenomena should have the properties that

1. A solution exists
2. The solution is unique
3. The solution depends continuously on the data, in some reasonable topology.

http://en.wikipedia.org/wiki/Ill-posed_problem

In mathematics and statistics, particularly in the fields of machine learning and inverse problems, regularization involves introducing additional information in order to solve an ill-posed problem or to prevent overfitting. This information is usually of the form of a penalty for complexity, such as restrictions for smoothness or bounds on the vector space norm.

Problems that are not well-posed in the sense of Hadamard are termed ill-posed. Inverse problems are often ill-posed.

Such continuum problems must often be discretized in order to obtain a numerical solution. While in terms of functional analysis such problems are typically continuous, they may suffer from numerical instability when solved with finite precision, or with errors in the data. Even if a problem is well-posed, it may still be ill-conditioned, meaning that a small error in the initial data can result in much larger errors in the answers. An ill-conditioned problem is indicated by a large condition number.

If the problem is well-posed, then it stands a good chance of solution on a computer using a stable algorithm. If it is not well-posed, it needs to be re-formulated for numerical treatment. Typically this involves including additional assumptions, such as smoothness of solution. This process is known as regularization and Tikhonov regularization is one of the most commonly used for regularization of linear ill-posed problems.

Other Keywords:
Normed Vector Space/Vector Space
minimum norm solution
A MatLab Program: Least squires with solving minimum norm solution
http://www.mathworks.com/matlabcentral/fileexchange/17474


Smooth Function:
In mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. Higher order differentiability classes correspond to the existence of more derivatives. Functions that have derivatives of all orders are called smooth.

UHD (Universal Hardware Driver)

Build Guide:
http://files.ettus.com/uhd_docs/manual/html/build.html#git

UHD Wiki
http://code.ettus.com/redmine/ettus/projects/uhd/wiki

Install CMake
http://www.geeksww.com/tutorials/operating_systems/linux/installation/downloading_compiling_and_installing_cmake_on_linux.php

GNURadio Installation

GNURadio Ubuntu Installation Guide:

http://gnuradio.org/redmine/projects/gnuradio/wiki/UbuntuInstall

Install Dependencies¶

The following command line scripts will install all the required dependencies. Before running them you should ensure that the Universe repository are enabled in "Software Sources".

To execute the script copy & paste the relevant command line into a terminal.

Maverick (10.10)

sudo apt-get -y install libfontconfig1-dev libxrender-dev libpulse-dev \
swig g++ automake autoconf libtool python-dev libfftw3-dev \
libcppunit-dev libboost-all-dev libusb-dev fort77 sdcc sdcc-libraries \
libsdl1.2-dev python-wxgtk2.8 git guile-1.8-dev \
libqt4-dev python-numpy ccache python-opengl libgsl0-dev \
python-cheetah python-lxml doxygen qt4-dev-tools \
libqwt5-qt4-dev libqwtplot3d-qt4-dev pyqt4-dev-tools python-qwt5-qt4

II. Get the source code

To build and install GNU Radio, you may either download a release tarball, or you may use the git client software to check out code from our git repository. Please refer to the download page for pointers on where to get the code.

To get a handle on what's going on, clone the repository (if you haven't already), then run "qgit" or one of the other git viewers on it. It will show you all of the branching and merging, diffs, etc.

III. Start the build process

To compile, there are 5 steps. Start by cd'ing to the gnuradio directory, then complete the following commands:

$ ./bootstrap         # Do NOT perform this step if you are building from a tarball.
$ ./configure
$ make
$ make check
$ sudo make install

For my configuration:


*********************************************************************
The following components were skipped either because you asked not
to build them or they didn't pass configuration checks:


gcell
gr-gcell
gr-comedi
gr-qtgui
gr-uhd
gr-shd


These components will not be built.


Configured GNU Radio release 3.4.2 for build.

Answer From FAQ:

How come not all the components are getting installed?

When you run ./configure, it might say that some components are not being installed. It might look like this:

*********************************************************************
The following components were skipped either because you asked not
to build them or they didn't pass configuration checks:

gcell
gr-gcell
gr-comedi
gr-radar-mono

These components will not be built.

This is not a problem per se. It is not usual to install all the components of GNU Radio. However, if a component is listed here which you actually need, you're probably lacking some dependencies. Check the build guide again, or try the automatic build script.

Error:

ImportError: libgnuradio-core-3.4.2.so.0: cannot open shared object file: No such file or directory

Path Setting?

add /usr/local/bin to etc/ld.so.conf

Common Problems

Bad LD_LIBRARY_PATH

You get

dburgess@localhost:~/r2.5Lacassine/apps$ ./OpenBTS 
./OpenBTS: error while loading shared libraries: libosip2.so.4: cannot open shared object file: No such file or directory

The problem is that your LD_LIBRARY_PATH does not include a path to the named library, libosip2.so.4 in this example. You need to define your LD_LIBRARY_PATH in your .bashrc or your .cshrc, depending on which shell type you use.

Fix LD_LIBRARY_PATH

Then (sudo) ldconfig

Fixed!

Installing NumPy/SciPy/Linux

http://www.scipy.org/Installing_SciPy/Linux

Installing Yum

sudo apt-get install yum

Installing SIP (Required by PyQt4 Version4.12 or later)

http://www.riverbankcomputing.com/software/sip/download
SIP A Tool for Generating Python Bindings for C & C++ Libraries

http://www.ics.uci.edu/~dock/manuals/sip/sipref.html#installing-sip

Installing Qt 4.7.4 (Required by PyQt4)

http://doc.qt.nokia.com/4.7/install-x11.html

Installing PyQt4

http://www.riverbankcomputing.co.uk/software/pyqt/download

http://www.riverbankcomputing.co.uk/static/Docs/PyQt4/html/installation.html

Error Msg:

$ python ./configure.py 
Determining the layout of your Qt installation...
Error: Unable to find the qmake configuration file
/usr/local/Trolltech/Qt-4.5.2/mkspecs/default/qmake.conf. Use the QMAKESPEC
environment variable to specify the correct platform.

How to fix?

A possible explanation:

http://www.riverbankcomputing.com/pipermail/pyqt/2011-April/029547.html

According to above two installation guides, change environment variable settings.

Installing PyQw5

http://pyqwt.sourceforge.net/download.html

Installing Matplotlib

http://matplotlib.sourceforge.net/

sudo apt-get install python-matplotlib

Installing iPython(Suggested)

http://ipython.org/download.html

Real-Time Convex Optimization in Signal Processing

http://www.stanford.edu/~boyd/papers/rt_cvx_sig_proc.html

CVXMOD installation

http://cvxmod.net/install.html

Some CVXOPT Installation Issue

Following last post, python version 2.6.
During CVXOPT installation,
fatal error: Python.h: No such file or directory
Solution: sudo apt-get install python-dev


http://stackoverflow.com/questions/4097339/missing-python-h-while-trying-to-compile-a-c-extension-module

CVXOPT Python Installation Instructions

http://courses.csail.mit.edu/6.867/wiki/index.php?title=Python_Installation_Instructions

Including how to install Lapack

Convex Optimization

http://web.njit.edu/~simeone/ece788.htm

Fundamental theorem of linear algebra

In mathematics, the fundamental theorem of linear algebra makes several statements regarding vector spaces. These may be stated concretely in terms of the rank r of an m×nmatrix A and its singular value decomposition:

First, each matrix  (A has m rows and n columns) induces four fundamental subspaces. These fundamental subspaces are:

name of subspace	definition	containing space	dimension	basis
column space, range or image	im(A) or range(A)		r (rank)	The first r columns of
nullspace or kernel	ker(A) or null(A)		n − r (nullity)	The last (n − r) columns of
row space or coimage	im(AT) or range(AT)		r	The first r rows of
left nullspace or cokernel	ker(AT) or null(AT)		m − r	The last (m − r) rows of