Categories: Special functions | Trigonometry
Raised cosine is a function commonly used in wireless communications.
where
For this function, α acts as a spreading parameter in the frequency spectrum of . If α = 0 then becomes the sinc function.
The above table maps the plots shown to the parameters used to generate the plot. Things to notice:
![\mathbf{x}(t) = \frac{\sin\left(\pi f_0 t\right)\cos\left(\pi \alpha f_0 t\right)}{\pi f_0 t\left[1 - \left(2 \alpha f_0 t\right)^2\right]}](a/../upload/math/92a7de5ff6ed6b1736e91fe1e999cd5d.png)
![\mathbf{X}(\omega) = \left \{ \begin{matrix} 1/f_0, & \left|\omega\right| \le \omega_1 \\ \\ \frac{0.5}{f_0} \left[1 + \cos\left(\frac{\left|\omega\right| - \omega_1}{2 \alpha f_0}\right)\right], & \omega_1 < \left|\omega\right| < \omega_2 \\ \\ 0, & \left|\omega\right| > \omega_2 \end{matrix} \right.](a/../upload/math/f40fead66600a373e0266d8788cfb36f.png)
![\left[0, 1\right]](a/../upload/math/078c04b251da1da2aee75daa308d0945.png)
is the 
(note that the normalization of the transform here is slightly inconsistent with the other Wikipedia pages, however)
radians
