## Implementation of digital Nyquist filters

#### Traditionally it has been difficult to construct a filter having a Nyquist response using analogue components, and it has taken the development of the digital signal processor (DSP) to bring Nyquist and raised cosine filters into everyday use.

#### Using a class of filters known as digital non-recursive linear phase or finite impulse response (FIR) filters, it is possible to approximate to any required degree of accuracy a perfect raised cosine filter. The 'length' of the filter (equivalent to filter order in analogue terminology) is greater for filters that have sharp transition bands, corresponding to filters with small a. |

#### Long filters incur the greatest processing overhead and also introduce the largest propagation delay through the filter. High filter delay is particularly disadvantageous in applications such as full-duplex speech transmission, where the subjective effect of time delay in a conversation can be very disturbing. (Note: significant delay is also introduced by the speech vocoders and other aspects of the data modulation and demodulation process such as interleaving and error correction).

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