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:

    “Public administrators would get along better if they would restrain the impulse to butt in or be dragged into trouble. They should remain silent until an issue is reduced to its lowest terms, until it boils down into something like a moral issue.”
    —Calvin Coolidge (1872–1933)

    “Perhaps nothing in all my business has helped me more than faith in my fellow man. From the very first I felt confident that I could trust the great, friendly public. So I told it quite simply what I thought, what I felt, what I was trying to do. And the response was quick, sure, and immediate.”
    —Alice Foote MacDougall (1867–1945)