# Root-Raised-Cosine-Filter

The root raised cosine filter, abbreviated RRC filter is an applied in the digital signal processing electronic filter which is used for forming signal pulses for transmission over a channel such as a radio channel.

## General

The root raised cosine filter is the square root (English root) from the raised cosine filter and serves to distribute the characteristic of the raised cosine evenly on transmitter and receiver. Then it represents a so-called matched filter in the receiver and maximizing the signal-to -noise ratio. A special feature is that a root raised cosine filter on its own inter-symbol interference (ISI ), which means "flow" the individual transmitter pulses on transmission channel time together. Only the combination of the two RRC filters at the transmitter and receiver together make the entire distance in the ideal case, an ISI - free transmission distance, which allows a temporal distinction of the individual pulses. The individual RRC pulses are mutually orthogonal.

The root raised cosine filter is of the Gaussian filter in addition to one of the most commonly used filter for pulse shaping in digital transmission systems.

## Transfer function

The absolute values of the transfer function Hrrc ( j? ) Of a RRC filter is given by:

Wherein HRC ( j? ) represents the transfer function of the raised cosine filter.

The impulse response h (t) of the RRC filter is β by the roll-off factor, which determines the bandwidth, and in the duration of one transmission symbol Ts and has the following form: