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Basic signal analysis (system invertible)

  1. Feb 6, 2007 #1
    Ok I have this really simple question that is bugging me.

    Lets say you have the signal:

    y(t) = x(t-4)

    where y(t) corresponds to the output, and x(t) the input.

    I know this system is invertible, but I don't really know how to show that this is the case. I see that the output is x(t) with an independet variable transformation such that the input shifted by 4 units to the right. So if we shift the output four units to the left then we get the input without the independent variable transformation. I just don't know how to express what is going on here mathematically.

    Maybe I don't understand invertibility well enough to apply it.
    From what I gather it can be shown by,

    x(t) --> [system] --> y(t) = T{x(t)}
    y(t) --> [invert] --> T{y(t)} = x(t)

    I'm getting confused since the problem has x(t-4) in this case. I'm guessing I can show it with some type of function composition, but I need some help.

  2. jcsd
  3. Feb 6, 2007 #2


    User Avatar
    Science Advisor
    Gold Member

    You can make the substitution
    t' = t - 4
    so that
    x(t') = y(t'+4)
    The inverted function is non-causal, since you need to know future values of y to find the present value of x.
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