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Six independent low pass signals of bandwidth $3$ $\mathrm{W}, \mathrm{W}, \mathrm{W}, 2 \mathrm{~W}, 3 \mathrm{~W}$, and $2 \mathrm{~W} \mathrm{~Hz}$ are to be timedivision-multiplexer on a common channel using PAM. To achieve this, the minimum transmission bandwidth of the channel should be ...... $\mathrm{Hz}$.