We show that a quantized large-scale system with unknown parameters and training signals can be analyzed by examining an equivalent system with known parameters by modifying the signal power and noise variance in a prescribed manner. Applications to training in wireless communications and signal processing are shown. In wireless communications, we show that the optimal number of training signals can be significantly smaller than the number of transmitting elements. Similar conclusions can be drawn when considering the symbol error rate in signal processing applications, as long as the number of receiving elements is large enough. We show that a linear analysis of training in a quantized system can be accurate when the thermal noise is high or the system is operating near its saturation rate.