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# Bandwidh of fm signal when squared...

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#### rsashwinkumar

##### Member level 4
Given an FM signal with frequency deviation 90kHz and modulating signal frequency of 5kHz. The B.W. of the FM signal can be found using Carson's rule. Now my problem is what happens to the B.W. when the FM signal is squared and cubed?? Plz help me out...

Generally, each of the generated nth order harmonics will show an n-fold modulation bandwidth.

First you must use the bessel function to determine the center, the minimum and the maximum frecuency of your FM signal.
Second you must use the Modulation Theorem (FOURIER), to determine the new BW

L{f(t) COSωot} = ½ [F(ω-ωo)+F(ω+ωo)]
where ω is the frecuency of f(f), ωo the frecuency of the cos function
F is the fourier transfor of the ft)

In your case f min and fmax and both signals are equal so
new fmin (squared signal) = ωmin - ωmin
new fmax (squared signal) = ωmax + ωmax
BW = new fmax (squared signal) - new fmin (squared signal)

repeat the process for a cubic case

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