Results 1 to 5 of 5

Math Help - Impulse-response coefficients (that represent a differentiation)

  1. #1
    Member courteous's Avatar
    Joined
    Aug 2008
    From
    big slice of heaven
    Posts
    206

    Question Impulse-response coefficients (that represent a differentiation)

    These weighted-impulse-response h coefficients (should) represent a differentiator:
    h = \frac{1}{3}(-1, -2, 0, 2, 1)
    If x[n] is the input sample, what is then the output y[n]?

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

    Thank you.
    Last edited by courteous; November 27th 2011 at 12:44 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5

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

    courteous wrote...

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

    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...

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

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member courteous's Avatar
    Joined
    Aug 2008
    From
    big slice of heaven
    Posts
    206

    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?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5

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

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

    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

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member courteous's Avatar
    Joined
    Aug 2008
    From
    big slice of heaven
    Posts
    206

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

    Thank you! What is the (1) thing at the end? Just a reference mistakenly copied along?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Stability of an impulse response (image processing -Wavelets)?
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: December 3rd 2010, 06:26 PM
  2. Mechanics-----Impulse
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: May 26th 2010, 10:10 AM
  3. Impulse question.
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 23rd 2009, 02:29 PM
  4. sinosoidal->impulse
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: April 15th 2008, 03:43 PM
  5. Impulse
    Posted in the Advanced Applied Math Forum
    Replies: 8
    Last Post: April 8th 2008, 07:22 PM

/mathhelpforum @mathhelpforum