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Maximum tolerable signal-to-noise ratio on the channel

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Suppose that an analog communications channel has an intended capacity of 10 Mbps. The bandwidth is 4 MHz. According to Shannon's law, what is the maximum signal-to-noise ratio (in dB) that can be tolerated on this channel?

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Solution Summary

Stepwise calculations shown, along with the formula used. Final answer also given in decibels.

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As per Shannon's law, the theoretical maximum rate at which data can be transmitted error-free over a bandwidth-limited channel in the presence of Gaussian noise is expressed as:

C = ...

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