Question

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?

Answer 1

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}

Answer 2

wait, but isn't x(-t) = -t+1 at 1<t<=2?

Answer 3

yes, you are correct