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Prove Time Invariance

  1. Sep 9, 2011 #1
    1. The problem statement, all variables and given/known data
    Prove that the system is either T.I. or is not T.I.


    2. Relevant equations
    y(n) = x(n)*h(n)

    x(n) is the input signal
    y(n) is the output signal
    h(n) is the system


    3. The attempt at a solution
    Inputing x(n-n0) into the system I get out:
    as the output x(n-n0)*h(n)

    Since y(n-n0) = x(n-n0)*h(n-n0) != x(n-n0)*h(n) the system is not T.I.

    I think I am doing this wrong.
     
  2. jcsd
  3. Sep 10, 2011 #2
    how can you get this output for x(n-n0) input ?
     
  4. Sep 10, 2011 #3
    So should it be that an input of x(n-n0) results in x(n-n0)*h(n-n0)?
     
  5. Sep 10, 2011 #4
    no,
    you are telling
    x(n) is input of the system
    y(n) is out put of the system
    h(n) is its transfer function

    in-order to check whether the system is TV or TIV we need the relation between input and output.
    for example if you tell y(t) output =sin times input x(t)
    then we can check whether its TV or TIV
    or we need the impulse response function h(t) to decide whether it is TV or TIV

    you have not given anything
    for every system y(t) is equal to x(t)*h(t)
    but their response depends on the function h(t) which is different for different systems

    P.S.
    I hope you understood
     
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