The present disclosure shows new mechanisms for sampling an input signal. In particular, some embodiments of the present disclosure include a new type of a level-crossing sampling mechanism called a derivative level-crossing sampling (D-LCS). At a high level, D-LCS involves quantizing the derivative of an input signal when the derivative of the input signal crosses one of the quantization thresholds. For certain class of signals, the derivative of the input signal can vary at a slower speed compared to the amplitude of the input signal. Therefore, by sampling the derivative of the input signal, instead of the input signal itself, the number of samples per unit time can be reduced.