We Know:
Frequency Modulated signal is given by: $$s_{FM} (t)=A_{c} \sin \{ w_c t + 2 \pi k_f \int m(t) \, dt \}$$ Now,
if $ \quad m(t)= A_m \cos(w_m t)$ ,
i.e, its spectrum $M(f)$:
enter image description here
then, $$s_{FM} (t)=A_{c} \sin \{ w_c t + 2 \pi k_f \int A_m \cos(w_m t ) \, dt \}$$ $$= A_{c} \sin \{ w_c t + 2 \pi k_f \frac{ A_m \sin(w_m t ) }{w_m} \}$$ $$= A_{c} \sin \{ w_c t + \frac{ k_f A_m }{f_m} \sin(w_m t ) \}$$ $$=A_{c} \sin \{ w_c t + m_f \sin(w_m t ) \}$$ $$= J_0(m_f) A_c \sin(w_c t) + \sum_{n= 1}^{\infty} [ \{ J_n(m_f) A_c \sin(w_c t + n w_m t) \} + \{ J_{-n}(m_f) A_c\sin(w_c t - n w_m t)\}]$$ $\implies$ the corresponding FM (Frequency Modulation) signal spectrum [$S(f)$] will be: enter image description here

Now, if the spectrum of message signal is triangular,
enter image description here
then, what will be its corresponding WBFM (Wide Band Frequency Modulation) signal spectrum?
i.e, $m_f > 1$

for e.g:
For $m_f \leq 1$ , the corresponding NBFM signal spectrum is:
enter image description here


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