This paper presents a mathematical analysis of the signal‐to‐noise power ratio degradation incurred when Gaussian signals in Gaussian noise are level‐quantized, time‐sampled, transmitted over a noisy digital channel, and then reconstructed by a low‐pass filter. Application of this analysis occurs when very weak acoustic or seismic signals in strong white noise are collected and transmitted over a digital channel to an analysis location remote from the collection point, and where detectability of the information‐bearing signals at the analysis location depends on the original signal‐to‐noise power ratio in small frequency bands. Therefore, it is important to understand the degradation of the original signal‐to‐noise ratio occurring during transmission. Curves are presented which show bounds on the degradation as a function of the quantizer step size and the channel bit error probability. Also considered is a scheme for transmitting a low‐rate digital sequence by periodically interrupting the level‐and‐time‐quantized analog signal. Three schemes are proposed for doing this, and one scheme is mathematically analyzed. It is shown that this scheme increases the degradation of the reconstructed analog signal by about 0.15 dB over that of the uninterrupted case.