## The root raised cosine filter |
In-depth

#### Given that the Nyquist filter response must apply to the whole transmission link including TX and RX sections to achieve zero ISI performance, it is necessary to consider where best to place the filtering within the transmission system. Filtering is almost always mandatory in the transmission unit, particularly in the case of wireless communications, to constrain the 'on-air bandwidth' of the signal to that dictated by regulation or by the practical necessity to co-habit with users on adjacent channel frequencies. Good receiver filtering is also vital (again especially in wireless applications), in order to remove strong signal interferers from overloading the demodulator circuitry, and also to reject as much noise as possible that does not fall within the modulation passband. For these reasons, it is necessary for the Nyquist filter function to be shared between TX and RX units (assuming that the channel response itself is flat or has been equalized in some way).

#### It is common practice to split the filtering function of a raised cosine filter equally between transmitter and receiver so that each unit ends up with what is termed a root raised cosine transfer characteristic. Under these circumstances, the peak to mean ratio of the transmitted signal must be evaluated for a root raised cosine response, not a raised cosine response as is often mistakenly thought. |

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