Transmission of an analog signal over a fixed bit-rate channel

The transmission of a nonbandlimited analog signal over a digital channel with a fixed bit-rate is considered. The trade-off between the mean-square error due to quantizing and the mean-square error due to the process of sampling and reconstructing the signal is investigated. Simple approximations to these errors, which are valid in most practical situations, are derived, and simple expressions are obtained from which the optimum sampling interval and number of bits per sample can be calculated. Results for first-, second-, and third-order Butterworth and fiat bandlimited spectra, together with the zero-order hold and the linear point connector, are included. The resulting mean-square error goes to zero with large channel bit-rates in a slower manner than the Shannon limit, which assumes a strictly bandlimited signal and perfect reconstruction.