Does a raised-cosine filter have infinite support?
An ideal raised cosine impulse is band-limited with cut-off frequency $f_c=(1+\beta)/(2T)$, where $\beta$ ($0\le\beta\le 1$) is the roll-off factor. Since it is band-limited, it must have infinite support in the time domain. The important difference with a sinc impulse is that its envelope decays much faster (for $\beta&gt;0$, of course).

Note that even though an ideal raised cosine filter has infinite support, in a practical implementation you would use a filter with finite support (implemented as an FIR filter) that approximates the ideal raised cosine impulse in some interval around its maximum.