Fourier Transform Signals - Time Transformations 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?
HINT:

Note that $x(t)+x(t-1)$ has the required shape. Now it's only a matter of shifting, time scaling, and amplitude scaling to arrive at the exact expression for $z(t)$.