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Time invariant Green's function (inpulse response)

  1. Oct 14, 2009 #1
    Hello Forum,

    given a input=delta located at time t=0, the system will respond generating a function h(t).

    If the delta is instead located at t=t0 (delayed by tau), the system will respond with a function g(t)=h(t-tau), just a shifted version of the response for the delta a t=0....

    If this is the case, the system is time invariant and the impulse response is said to be only a function of t-t0........: h(t-t0)

    If the system was time variant instead, it will be a function h(t,t-t0), that is, a function of both time t and t-t0.......it is as if it was a function of two variables.....

    I am not clear on this: isn't the function h, the impulse response, a function of time t also in the case of time invariant system?
    To be time invariant, does the variable t need to always occur with t0 in a subtraction?

  2. jcsd
  3. Oct 21, 2009 #2
    My understanding is that once you have proved that the system is time invariant, i.e. h(t) = h(t-t0), you can safely drop t0 in the expression and simply state the impulse response is h(t).
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