Q$12$: A certain sinusoid at a frequency of $f_{m}Hz$ is used at the modulating signal in both an AM $($DSB $-$ LC$)$ and an FM system. The unmodulated carrier powers are equal in both systems. When modulated, the peak frequency deviation of FM system is set to four times the bandwidth of the AM system. The magnitude of those sidebands spaced $fmHz$ from carrier in both systems are equal, determine:

$($a$)$The modulation index of FM system.

$($b$)$ The modulation index of AM system.

$133$

$($CH $5)$ Angle Modulation

By Dr$.$ Hikmat Al$-$Shamary & Dr$.$ Tariq M$.$ Salman