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windsylph

  • 2 years ago

Signals and Systems: Graph Transformations: Suppose a signal x(t) looks like this: https://dl.dropbox.com/u/17638088/Capture.PNG. What does [x(t)+x(-t)]u(t) look like, where u(t) is the unit step function?

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  1. kaushi
    • 2 years ago
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    Unit step function is defined by u(t) = { 0, t<0 and 1, t>=0 } x(t) = { -t+2, 1<t<=2 { 2, 0<t<= 1 { 1, -1<t<=0 { t+1, -2<t<=-1 Now, let's find g(t)= [x(t)+x(-t)]u(t) for each step of x(t) when 1<t<=2 : g(t)= [(-t+2)+(t+1)].1=3 when 0<t<=1 : g(t)= [2 + 1].1 = 3 when -1<t<=0 : g(t) = [1+2].0 =0 when -2<t<=-1 : g(t) = [(t+1)+(-t+2)].0 = 0 which gives g(t) = {0,t<0 and 3, t>=0}

  2. windsylph
    • 2 years ago
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    wait, but isn't x(-t) = -t+1 at 1<t<=2?

  3. kaushi
    • 2 years ago
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    yes, you are correct

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