Raised cosine is a function commonly used in wireless communications.

where

• α ∈
• is the continuous Fourier transform of (note that the normalization of the transform here is slightly inconsistent with the other Wikipedia pages, however)
• ω ∈ radians
• 
• 

For this function, α acts as a spreading parameter in the frequency spectrum of . If α = 0 then becomes the sinc function.

Sample plot

Color	f0	α
Black	2	2
Blue	2	0.75
Red	2	0.5
Green	2	0.25
Purple	2	0

The above table maps the plots shown to the parameters used to generate the plot. Things to notice:

• For α = 0 the function is the sinc function
• As α decreases the more the plot looks like a sinc function
• All plots go through y = 1 at x = 0
• All plots have the same roots, which is a function of f₀
• All of the roots are multiples of