- #1
Rick66
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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
Rick66
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
Rick66
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