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 $M(f)$:
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:
Now, if the spectrum of message signal is triangular,
i.e,
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:
