Impulse-response coefficients (that represent a differentiation)

Quote:

These weighted-impulse-response $\displaystyle h$ coefficients (should) represent a differentiator:

$\displaystyle h = \frac{1}{3}(-1, -2, 0, 2, 1)$

**If $\displaystyle x[n]$ is the input sample, what is then the output $\displaystyle y[n]$? **

Is it this: $\displaystyle y[n] = \frac{1}{3}\big(-x[n-4] - 2x[n-3] + x[n-1] + 2x[n]\big)$ ? (Wondering)

Thank you.

Re: Impulse-response coefficients (that represent a differentiation)

courteous wrote...

... these weighted impulse response h coefficients should represent a differentiator:

$\displaystyle h= \frac{1}{3}\ (-1,-2,0,1,2)$

A differentiator has typically *linear phase* and that means that its impulse response must be *antysimmetrical*, so that [probably] the impulse response is...

$\displaystyle h= \frac{1}{3}\ (-1,-2,0,2,1)$

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

Re: Impulse-response coefficients (that represent a differentiation)

chisigma, you're (of course) correct ... that was a typo (fixed it in OP)

Can you help me out?

Re: Impulse-response coefficients (that represent a differentiation)

The response to an imput sequence x(n) is...

$\displaystyle y(n)= \sum_{k=0}^{4} h(k)\ x(n-k) = \frac{1}{3}\ \{- x(n) -2\ x(n-1) +2\ x(n-3) + x(n-4)\} $ (1)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

Re: Impulse-response coefficients (that represent a differentiation)

Thank you! What is the (1) thing at the end? Just a reference mistakenly copied along?