Finite Impulse Response - Impulse Response

Impulse Response

The impulse response can be calculated if we set in the above relation, where is the Kronecker delta impulse. The impulse response for an FIR filter then becomes the set of coefficients, as follows

for to .

The Z-transform of the impulse response yields the transfer function of the FIR filter

\begin{align} H(z) &= Z\{h\} \\ &= \sum_{n=-\infty}^{\infty} h z^{-n} \\ &= \sum_{n=0}^{N}b_n\,z^{-n} \end{align}

FIR filters are clearly bounded-input bounded-output (BIBO) stable, since the output is a sum of a finite number of finite multiples of the input values, so can be no greater than times the largest value appearing in the input.

Read more about this topic:  Finite Impulse Response

Famous quotes containing the words impulse and/or response:

    “There is only one honest impulse at the bottom of Puritanism, and that is the impulse to punish the man with a superior capacity for happiness—to bring him down to the miserable level of “good” men i.e., of stupid, cowardly and chronically unhappy men.”
    —H.L. (Henry Lewis)

    “Women had to deal with the men’s response when the women wanted more time “out” of the home; men now must deal with the women’s response as men want more time “in.””
    —Kyle D. Pruett (20th century)