In the field of time domain measurement, with increasing complexity of measured signals, the periodic stationarity of signals is destroyed and the transient non-stationarity starts to stand out, specifically manifested as frequent presence of transient abnormal signals, such as burrs, harmonics, noises, and modulating waves in the periodic signals. By applying the entropy estimation of signals to the field of time domain measurement, this paper designs a transient abnormal signal acquisition system based on approximate entropy (ApEn) and sample entropy (SampEn). In the process of data acquisition, the ApEn and SampEn of sampled data are computed in real time and the complexities of measured signals are differentiated, thus realizing abnormal signal detection. The experimental results demonstrate that SampEn generally has a higher sensitivity and wider application than ApEn in the detection process of transient abnormal signals. The study can provide a new method for the design of a time-domain measuring instrument with abnormal signal detection ability.