Impulse response of a sequence

Discussion in 'Homework Help' started by TierOne, Feb 5, 2011.

  1. TierOne

    Thread Starter New Member

    Feb 5, 2011
    16
    2
    Hi guys, I need help with finding of impulse response of the following sequence:

    y(n) = x[n] + c

    my answer by substituting x[n] with delta x
    h(k) = delta (x) + c

    correct?
     
  2. narasimhan

    Member

    Dec 3, 2009
    72
    6
    I don't think so. The question looks very simple and your answer looks logical. But if you try to use a simple input say unit step(x(n)=u(n)) the two answers differ(the one got through convolution and one by direct substitution).
    The reason behind this is that unit impulse rule is only applicable for LTI(linear and time-invarient) systems.
    But yours is not linear(its only incrementally linear).
    In simple words a thing called impulse response(like transfer function) does not exist for your system.

    But that said you can just say that your answer will be the output of the system if the input is an impulse.
     
    Last edited: Feb 6, 2011
  3. TierOne

    Thread Starter New Member

    Feb 5, 2011
    16
    2
    @narasimhan

    Thank you, this confirms my observation that I cannot obtain the H(z) using z-transform. Now I have to show it is non-linear or time-variant. Tricky Professor.

    Is this in line with what the rest think?
     
  4. narasimhan

    Member

    Dec 3, 2009
    72
    6
    Its time invariant but certainly non-linear.
    let x1(n) =1 then output y1(n)=1+c
    let x2(n) =2 then output y2(n)=2+c

    let x(3)=x1(n)+x2(n)=3 then y3(n)=3+c
    but y1(n)+y2(n)=3+2c which is not equal to y3(n) hence its non-linear.
     
    TierOne likes this.
  5. TierOne

    Thread Starter New Member

    Feb 5, 2011
    16
    2
    Thank you for the clear steps shown (missed out on scaling property though nevertheless proves the point it is non-linear)

    Is it true that a non-linear system do not have an impulse response? Or does this belong to more advance topics (nonlinear impulse response)
     
  6. narasimhan

    Member

    Dec 3, 2009
    72
    6
    It was not missed. It was intentionally left out. Its only needed if you can't prove non-linearity via the simple additive property.

    There is nothing called nonlinear impulse response. I think it requires state diagram analysis.
     
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