### Convolution Representation of FIR Filters

Notice that the output of the th delay element in Fig.5.5 is
,
, where is the input signal
amplitude at time . The output signal is therefore

where we have used the

*convolution operator ``''*to denote the convolution of and , as defined in Eq.(5.4). An FIR filter thus operates by convolving the input signal with the filter's

*impulse response*.

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FIR impulse response