## Transfer function and impulse response of a raised cosine filter

#### The raised cosine filter is one of the family of Nyquist filters that satisfy the criteria for zero intersymbol interference.

#### The transfer function H(f) of a raised cosine filter is given by:

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#### where a is the filter roll-off factor and T is the symbol period of the message. An a = 0 corresponds to an ideal brick-wall filter.

#### The impulse response for a raised cosine filter is given by:

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