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15 March, 08:51

A communications channel has a bandwidth of 4,000 hz and a signal-to-noise ratio (snr of 30 db. what is the maximum possible data rate?

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  1. 15 March, 09:02
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    Through Shannon's Theorem, we can calculate the capacity of the communications channel using the value of its bandwidth and signal-to-noise ratio. The capacity, C, can be expressed as

    C = B * log₂ (1 + S/N)

    where B is the bandwidth of the channel and S/N is its signal-to-noise ratio.

    Since the given SN ratio is in decibels, we must first express it as a ratio with no units as

    SN (in decibels) = 10 * log (S/N)

    30 = 10log (S/N)

    log (S/N) = 3

    S/N = 10³ = 1000

    Now that we have S/N, we can solve for its capacity (in bits per second) as

    C = 4000 * log₂ (1 + 1000)

    C = 39868.91 bps

    Thus, the maximum capacity of the channel is 39868 bps or 40 kbps.

    Answer: 40 kbps
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