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:

    “It is unfortunately very true that, without leisure and money, love can be no more than an orgy of the common man.... Instead of being a sudden impulse full of ardour and reverie, it becomes a distastefully utilitarian affair.”
    —Charles Baudelaire (1821–1867)

    “[In response to this question from an interviewer: “U. S. News and World Report described you this way: ‘She’s intolerant, preachy, judgmental and overbearing. She’s bright, articulate, passionate and kind.’ Is that an accurate description?”:]
    It’s ... pretty good [ellipsis in original].”
    —Joycelyn Elders (b. 1933)