1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Time Scaling, Shifting, and Reversal: Fourier Tranfiorm

  1. Nov 15, 2012 #1
    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?
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted