FIR impulse response
The impulse response 
is obtained at the output when the
input signal is the impulse signal
![$ \delta = [1,0,0,0,\ldots]$](http://www.dsprelated.com/josimages_new/filters/img594.png){kind=small}
(§5.6). If the 
th tap is denoted 
, then it is
obvious from Fig.5.5 that the impulse response signal is
given by
![$\displaystyle h(n)\isdef \left\{\begin{array}{ll} 0, & n<0 \\ [5pt] b_n, & 0\leq n\leq M \\ [5pt] 0, & n> M \\ \end{array} \right. \protect$](http://www.dsprelated.com/josimages_new/filters/img596.png)
In other words, the impulse response simply consists of the tap coefficients, prepended and appended by zeros.
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Convolution Representation Summary
