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Root Raised Cosine Filter

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 Alpha, (0<Alpha<1). In FilterSolutions, the passband frequency is defined as the .707 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. The advantage of this use is that, if the transmit side filter is stimulated by an impulse, then the receive side filter is forced to filter an input pulse shape that is identical to its own impulse response. This configuration thereby sets up a Matched Filter, maximizing Signal to Noise (S/N) ratio while simultaneously minimizing Inter-Symbol Interference (ISI).