I've been given a question like Draw the spectrum of FM signal with modulation index beta = 0, 1 ,2,2.5. I know that it is something related to finding bessels values of the given beta but I don't know what to do after finding the values.My teacher simply posted a solution without any explanation.I've kept the image of solution please tell me how to get those answers.

Here is the solution

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    \$\begingroup\$ Look in any communications textbook. The section describing FM will give the equation for the spectrum in terms of Bessel Functions and the modulation index. Then you can use a table of Bessel Functions to find the levels of each component. \$\endgroup\$ – Barry May 14 '17 at 18:46
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    \$\begingroup\$ I'm voting to close this question as off-topic because it looks like Homework. \$\endgroup\$ – Autistic May 17 '17 at 10:28
  • \$\begingroup\$ @Autistic I'm preparing for final exam and I asked a doubt. On what basis are you saying this as homework question ? I even uploaded the answer and just asked an explanation for it. Whats wrong in this ? Being a senior with 5k reputation can't you even understand the difference between a homework question and a doubt clarification ? \$\endgroup\$ – bharath May 17 '17 at 10:33

From page 8-5 of these class notes from UMD (using Hz instead of radians/sec), the spectrum of an FM tone can be written as

$$s(t) = A_c \sum_{n=-\infty}^{\infty}J_n(\beta)\cos[2\pi(f_c+nf_m)t]$$

where \$A_c\$ is the carrier amplitude, \$f_c\$ is the carrier frequency in Hz, and \$f_m\$ is the frequency of the modulating tone in Hz. Moving this to the frequency domain gives us:

$$S(f) = \frac {A_c} 2 \sum_{n=-\infty}^{\infty} J_n(\beta) [\delta(f - (f_c + n f_m) + \delta(f + (f_c + n f_m)]$$

We can plot this FM spectrum as delta functions with "height" (more accurately, area) \$\frac {A_c} 2 J_n(\beta)\$. Thus, the Bessel function values form the basis of the coefficients of the frequency components.

If you're doing power calculations don't forget to include the negative frequencies as well!


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