1. The problem statement, all variables and given/known data Let's say I've got the typical triangular waveform with function x(t) = t, goes from 0 to 1 on the x and y axes. How would I manipulate x(t) and the given X(ω) to, say, 1)Stretch the function on the x axis from 0 to 2, but keep the slope as 1? 2)Flip the function upside down, then shift it up, to get a square? 2. Relevant equations We're given X(ω) = [e^(-jω)+jωe^(-jω)-1]/ ω^2 (standard FT of triangular wave function) Scaling: x(at) = 1/a * X(ω/a) Shifting: x(t-t0) = X(ω)e^(-jωt0) 3. The attempt at a solution For 1, wouldn't it just be x(t/2), and if i wanted to shift it up, let's say Z units, x((t/2 + Z)? But what would the X(ω) look like? For 2, if i just wanted a square I could just do 2X(ω), right? Thanks.