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

  1. #1
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    Question Impulse-response coefficients (that represent a differentiation)

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

    Thank you.
    Last edited by courteous; Nov 27th 2011 at 11:44 AM.
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    MHF Contributor chisigma's Avatar
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    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

    $\displaystyle \chi$ $\displaystyle \sigma$
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    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?
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    MHF Contributor chisigma's Avatar
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    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

    $\displaystyle \chi$ $\displaystyle \sigma$
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    Re: Impulse-response coefficients (that represent a differentiation)

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