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Stuck on proving that this function\signal is not periodic

  1. Dec 2, 2009 #1
    First of all, HI! This is my first post and my first day in this forum. =)

    I am having quite a problem demystifying this function. It's on a book I have and it clearly states that it isn't periodical. I can't reach that conclusion and was hoping you could help me out.

    So, the function in question is [tex]x(t)=sin(\pi t)cos(10t)[/tex]

    What I did was to deconstruct this into
    [tex]\frac{1}{2}\left[ sin(\pi t+10t)-sin(\pi t-10t)\right][/tex]

    Now, I think that the period of the first sin is [tex]\frac{2\pi}{\pi +10}[/tex] and the one from the second sin is [tex]\frac{2\pi}{\pi -10}[/tex].

    I then try to find the fundamental period of the whole function:

    [tex]n\frac{2\pi}{\pi +10}=m\frac{2\pi}{\pi -10}\Rightarrow m=\pi -10[/tex] and [tex]n=\pi+10 \Rightarrow T=2\pi[/tex]


    I know I have to be doing something wrong and possibly it's also really basic, but I got stuck.
    Can anyone help me out? =)
     
  2. jcsd
  3. Dec 3, 2009 #2

    LCKurtz

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    But your m and n aren't integers. Try an indirect argument. Suppose your x(t) has period P, so x(t+P) = x(t). What does that give you? What happens if you put t = 0 in it?
     
  4. Dec 3, 2009 #3

    I had done the substitution before, and noticed it didn't work, but couldn't understand why.
    As soon as you said "integer" however, I just facepalmed myself.

    Thank you so much.
     
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