Are pulse shaping and windowing functions the same in concept? I read a digital communication problem and they interchange terms as windowing function and pulse shaping and refer to it as same entity. For example the following windowing function with Transition time $T_R$ used to smooth transitions between symbols is also refered to as pulse shaping 

$w_T(t)= \left\{ \begin{array}{ll}
         \sin^2(\frac{\pi}{2}(0.5+\frac{t}{T_{TR}})) &amp; \mbox{if $-T_{TR}/2 &lt; t&lt;T_{RT}/2$};\\
        1 &amp; \mbox{if $T_{TR}/2 &lt; t&lt;T-T_{TR}/2$}\\
 \sin^2(\frac{\pi}{2}(0.5-\frac{t-T}{T_{TR}})) &amp; \mbox{if $T-T_{TR}/2 &lt; t&lt;T+T_{TR}/2$};\\
\end{array} \right. $

My understanding is that a pulse shaping function limits signal bandwidth to transmission bandwidth. 

How come the two are refered to as same?

Thanks
Windowing and pulse shaping are very similar, and are implemented in similar ways, but their purposes are different.


Windowing means multiplying a discrete signal by a pulse with certain spectral properties before calculating its Fourier transform. The purpose is reducing the effect of discontinuities at both ends of the discrete signal.
In QAM and related digital signals, the information is transmitted in the amplitudes of a sequence of pulses. Pulse shaping means choosing a pulse with the desired spectral and orthogonality properties.


Note that some digital communications textbooks assume (many times implicitly) a rectangular pulse shape, which is then converted to another pulse shape (using a filter, as in the example in your question). In my opinion, this formulation is unncecessarily complex -- it is better to explicity select  a pulse shape from the start.

Note also that pulse shaping may be understood as the convolution of a stream of deltas with a pulse shape; in that sense, pulse shaping is a sort of "dual" of windowing.