Looking for basic self-study direction
Hi all,
I posted this on the general math forum as well, and I'm sorry for the cross posting but after some thought I figured this thread may be better here. I'm trying to determine the best route for self-study of material relating to communications. I have a very extensive background in communications, however my understanding of the general mathematics is not sufficient to work through many texts and I am seeking to remedy that. Take, for example, the following statement:
![\[r(t) = s(t)*c(\tau ;t) + n(t) = \int_{ - x}^x {c(\tau ;t)s(t - \tau )d\tau + n\left( t \right)} \]](http://latex.codecogs.com/png.latex?\[r(t) = s(t)*c(\tau ;t) + n(t) = \int_{ - x}^x {c(\tau ;t)s(t - \tau )d\tau + n\left( t \right)} \])
At a fundamental level I recognize the components of the above but the syntax is baffling at best for me. Many aspects of texts such as these I can explain exactly what something is and how it works, but I do not possess the proper understanding of the language of mathematics to work through new material or express existing material.
Some other examples:
![\[{h^{\left( l \right)}}\left( t \right)\mathop \Delta \limits_ = \int_{\tau + kT}^{\tau + \left( {k + 1} \right)T} {r\left( t \right){h^{\left( l \right)}}\left( {t - \tau - kT} \right){e^{ - j{\omega _0}t}}dt} \]](http://latex.codecogs.com/png.latex?\[{h^{\left( l \right)}}\left( t \right)\mathop \Delta \limits_ = \int_{\tau + kT}^{\tau + \left( {k + 1} \right)T} {r\left( t \right){h^{\left( l \right)}}\left( {t - \tau - kT} \right){e^{ - j{\omega _0}t}}dt} \])
and
![\[\Lambda \left( {\left. R \right|\mathop \theta \limits^\^ ,\mathop \tau \limits^\^ } \right) = \exp \left\{ {\sum\limits_{k = 0}^{{L_0} - 1} {{\text{Re}}\left[ {{Z_k}\left( {{C_{k,}}{\alpha _k},\mathop \tau \limits^\^ } \right){e^{ - j\left( {\mathop \theta \limits^\^ + {\phi _k}} \right)}}} \right]} } \right.\]](http://latex.codecogs.com/png.latex?\[\Lambda \left( {\left. R \right|\mathop \theta \limits^\^ ,\mathop \tau \limits^\^ } \right) = \exp \left\{ {\sum\limits_{k = 0}^{{L_0} - 1} {{\text{Re}}\left[ {{Z_k}\left( {{C_{k,}}{\alpha _k},\mathop \tau \limits^\^ } \right){e^{ - j\left( {\mathop \theta \limits^\^ + {\phi _k}} \right)}}} \right]} } \right.\])
Do any of you have any suggestions as to where to begin on some of the more general language and form aspects of math, or could identify some of the best areas for me to study to begin to work with things such as the above? My formal background with mathematics has been to the level of calculus 3 and some basic differential equations. I've been pondering starting with discrete mathematics and abstract algebra but I am hoping to work towards this type of content in the most efficient way possible and thought I would check with experts to see if I'm on the right path.
If you have any suggestions it'd be much appreciated, thank you.
Re: Looking for basic self-study direction
In my opinion, you must study analysis, for example, "Real and Complex Analys" by Walter Rudin, downloadable in en.bookfi.org
Re: Looking for basic self-study direction
Thank you very much! I will pick that up.
