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:

    “If the oarsmen of a fast-moving ship suddenly cease to row, the suspension of the driving force of the oars doesn’t prevent the vessel from continuing to move on its course. And with a speech it is much the same. After he has finished reciting the document, the speaker will still be able to maintain the same tone without a break, borrowing its momentum and impulse from the passage he has just read out.”
    —Marcus Tullius Cicero (106–43 B.C)

    “I’ll never forget my father’s response when I told him I wanted to be a lawyer. He said, “If you do this, no man will ever want you.””
    —Cassandra Dunn (b. c. 1931)