I was going over some review problems and came across an interesting one.
Using the techniques of (linearity, time shifting, and time scaling) what are some approaches I could use to turn the fourier transform from the left graph to the right?
X(ω) = 4* (sin w)^2 / w^2
My understanding so far:
- Using the time shift property for fourier transforms I know the we can use
x(t -1) to move the graph to start at t=1
- We can use x(t/3) to extend or "stretch" the base to the to t=7
What is eluding me is how to form that "middle" or clipped top of the z(t) graph. Any insight?