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Finding the times when one cycle occurs for FM wave

  1. May 24, 2013 #1
    Hello everyone,

    I'm trying to find the times when one cycle occurs for a FM wave. For instance, given

    y(t) = sin(2∏f[itex]_{c}[/itex]*t[itex]_{1}[/itex] + sin(2∏f[itex]_{m}[/itex]*t[itex]_{1}[/itex]))

    at an arbitrary time t[itex]_{1}[/itex], I wish to find the time t[itex]_{2}[/itex] such that

    (f[itex]_{c}[/itex]* t[itex]_{2}[/itex] + sin(2∏f[itex]_{m}[/itex]* t[itex]_{2}[/itex]) – (f[itex]_{c}[/itex]*t[itex]_{1}[/itex] + sin(2∏f[itex]_{m}[/itex]*t[itex]_{1}[/itex]) = 1 (cycle).

    Now I've tried plotting the wave argument in n-t "space" (i.e. n is cycles),

    n = f[itex]_{c}[/itex]*t + sin(2∏f[itex]_{m}[/itex]*t)

    to see if some solution presents itself. For instance, we can see that it gives oscillations about the regularly increasing line n = f[itex]_{c}[/itex]*t so that t[itex]_{2}[/itex] ≈1/f[itex]_{c}[/itex] + t[itex]_{1}[/itex] gives an approximate solution. But as to an exact solution, I've hit a brick wall. So if somebody could point me in the right direction it would be greatly appreciated.
    Thank you
    Last edited: May 24, 2013
  2. jcsd
  3. May 25, 2013 #2
    PS: I have made the correction to y(t) above.
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