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:

    “she drew back a while,
    Then, yielding to the irresistible joy,
    With frantic gesture and short breathless cry
    Folded his frame in her dissolving arms.
    Now blackness veiled his dizzy eyes, and night
    Involved and swallowed up the vision; sleep,
    Like a dark flood suspended in its course,
    Rolled back its impulse on his vacant brain.”
    —Percy Bysshe Shelley (1792–1822)

    “There are situations in life to which the only satisfactory response is a physically violent one. If you don’t make that response, you continually relive the unresolved situation over and over in your life.”
    —Russell Hoban (b. 1925)