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A convolutional encoder is called so because it performs a ''[[convolution]]'' of the input stream with the encoder's ''impulse responses'':
:<math>y_i^j=\sum_{k=0}^{\infty} h^j_k x_{i-k} = (x * h^j)[i],</math>
where {{mvar|x}} is an input sequence, {{mvar|y<sup>j</sup>}} is a sequence from output {{mvar|j}}
A convolutional encoder is a discrete [[LTI system|linear time-invariant system]]. Every output of an encoder can be described by its own [[transfer function]], which is closely related to the generator polynomial. An impulse response is connected with a transfer function through [[Z-transform]].
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