Six independent low pass signals of bandwidth 3ω, ω, ω,

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Six independent low pass signals of bandwidth 3ω, ω, ω, 2ω, 3ω, and 2ω Hz are to be time division multiplexed on a common channel using PAM. To achieve time, the minimum transmission bandwidth of the channel should be kHz—

1. 3ω
2. 6ω
3. 12ω
4. 24ω

Correct Option: C

The commutator in TDM (Time Division multiplication) has to be rotated a speed twice that of highest bandwidth i.e. 3_ω × 2 = 6_ω
channel capacity = 2 x highest Bandwidth
= 2 × 6_ω Hz = 12_ω Hz