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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?
    Thanks.
     
  2. jcsd
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