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:

    The virtue of the camera is not the power it has to transform the photographer into an artist, but the impulse it gives him to keep on looking.
    Brooks Atkinson (1894–1984)

    Eyes seeking the response of eyes
    Bring out the stars, bring out the flowers,
    Thus concentrating earth and skies
    So none need be afraid of size.
    All revelation has been ours.
    Robert Frost (1874–1963)