In the ideal root raised cosine filter, frequency response consists of unity gain at low frequencies, the square root of raised cosine function in the middle, and total attenuation at high frequencies. The width of the middle frequencies is defined by the roll off factor constant, Alpha, (0<Alpha<1).

In FilterSolutions, the pass band frequency is defined as the .707 half power point.

The root raised cosine filter is generally used in series pairs, so that the total filtering effect is that of a raised cosine filter.

Mathematically, the frequency response may be written as:

The ideal root raised cosine filter frequency response is shown below: