Question

A certain FM signal is given by: \(s(t)=A_{c} \cos \left[2 \pi f_{c} t+2 \pi k_{f} \int_{0}^{t} m(\tau) d \tau\right]\). Estimate the bandwidth of \(s(t)\) using Carson's rule. Assume the spectrum of m(t) is given by:

$$ \begin{array}{rr} M(f)=\operatorname{rect}(f) \text { and } \operatorname{rect}(f)=1 & -10 \mathrm{kHz} \leq f \leq 10 \mathrm{kHz} \\ \operatorname{rect}(f)=0 & |f| \geq 10 \mathrm{kHz} \end{array} $$

Assume \(k_{f}=2 \mathrm{kHz} /\) volt. Also estimate the bandwidth using Figure 4.9. Compare your results.

(Hint: Consider your response to question 5.) from Short Answers: Chapter 4. above. )

Answer 1