The raised-cosine filter is a filter frequently used for pulse-shaping in digital modulation due to its ability to minimise intersymbol interference (ISI). Its name stems from the fact that the non-zero portion of the frequency spectrum of its simplest form (${\displaystyle \beta =1}$) is a cosine function, 'raised' up to sit above the ${\displaystyle f}$ (horizontal) axis.

The raised-cosine filter is an implementation of a low-pass Nyquist filter, i.e., one that has the property of vestigial symmetry. This means that its spectrum exhibits odd symmetry about ${\displaystyle {\frac {1}{2T}}}$, where ${\displaystyle T}$ is the symbol-period of the communications system.

Its frequency-domain description is a piecewise-defined function, given by:

or in terms of havercosines:

for

and characterised by two values; ${\displaystyle \beta }$, the roll-off factor, and ${\displaystyle T}$, the reciprocal of the symbol-rate.

The impulse response of such a filter is given by:

in terms of the normalised sinc function. Here, this is the "communications sinc" ${\displaystyle \sin(\pi x)/(\pi x)}$ rather than the mathematical one.