Question

(a) Estimate $B_{FM}$ and $B_{PM}$ for the modulating signal $m(t)$ in Fig. 5.4a for $k_f = 2 imes 10^5$ and $k_p = 5pi$. Assume the essential bandwidth of the periodic $m(t)$ as the frequency of its third harmonic. (b) Repeat the problem if the amplitude of $m(t)$ is doubled [if $m(t)$ is multiplied by 2]. (a) The peak amplitude of $m(t)$ is unity. Hence, $m_p = 1$. We now determine the essential bandwidth $B$ of $m(t)$. It is left as an exercise for the reader to show that the Fourier series for this periodic signal is given by $m(t) = sum_n C_n cos nomega_0 t$ $omega_0 = frac{2pi}{2 imes 10^{-4}} = 10^4 pi$

          (a) Estimate $B_{FM}$ and $B_{PM}$ for the modulating signal $m(t)$ in Fig. 5.4a for $k_f = 2 	imes 10^5$ and $k_p = 5pi$. Assume the essential bandwidth of the periodic $m(t)$ as the frequency of its third harmonic.
(b) Repeat the problem if the amplitude of $m(t)$ is doubled [if $m(t)$ is multiplied by 2].
(a) The peak amplitude of $m(t)$ is unity. Hence, $m_p = 1$. We now determine the essential bandwidth $B$ of $m(t)$. It is left as an exercise for the reader to show that the Fourier series for this periodic signal is given by
$m(t) = sum_n C_n cos nomega_0 t$
$omega_0 = frac{2pi}{2 	imes 10^{-4}} = 10^4 pi$

$(a) Estimate BFM and BPM for the modulating signal m(t) in Fig. 5.4a for kf = 2 imes 10^5 and kp = 5pi. Assume the essential bandwidth of the periodic m(t) as the frequency of its third harmonic. (b) Repeat the problem if the amplitude of m(t) is doubled [if m(t) is multiplied by 2]. (a) The peak amplitude of m(t) is unity. Hence, mp = 1. We now determine the essential bandwidth B of m(t). It is left as an exercise for the reader to show that the Fourier series for this periodic signal is given by m(t) = sumn Cn cos nomega0 t omega0 = frac2pi2 imes 10^-4 = 10^4 pi$

Added by David S.

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