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Four independent messages have bandwidths of 100Hz, 100Hz, 200Hz, 400Hz respectively, each one is sampled at the Nyquist rate and the samples are time division multiplexed (TDM) and transmitted. The transmitted sample rate (in Hz) is    
    Correct answer is '1600'. Can you explain this answer?
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    Four independent messages have bandwidths of 100Hz, 100Hz, 200Hz, 400H...
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    Four independent messages have bandwidths of 100Hz, 100Hz, 200Hz, 400H...
    Solution:

    Given:

    Bandwidth of message 1 (B1) = 100 Hz
    Bandwidth of message 2 (B2) = 100 Hz
    Bandwidth of message 3 (B3) = 200 Hz
    Bandwidth of message 4 (B4) = 400 Hz

    Sampling rate = 2 * maximum bandwidth

    Sample rate for message 1 (Fs1) = 2 * B1 = 200 Hz
    Sample rate for message 2 (Fs2) = 2 * B2 = 200 Hz
    Sample rate for message 3 (Fs3) = 2 * B3 = 400 Hz
    Sample rate for message 4 (Fs4) = 2 * B4 = 800 Hz

    The transmitted sample rate is the sum of the sample rates of all the messages.

    Transmitted sample rate = Fs1 + Fs2 + Fs3 + Fs4
    Transmitted sample rate = 200 + 200 + 400 + 800
    Transmitted sample rate = 1600 Hz

    Therefore, the transmitted sample rate is 1600 Hz.

    Conclusion:

    The transmitted sample rate is the sum of the sample rates of all the messages. In this case, the transmitted sample rate is 1600 Hz.
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