Abstract: Electromagnetic detection signal of wire ropes is a kind of space-time signals relating to time and defect position. Virtual infinite multi-probers technology is adopted to deduce the time-space domain mathematical model of the sensor with aid of Dirac delta function. Spectrum characteristics of the space-time signal are discussed by spectrum analysis principle of discrete periodic signals, and the influence of velocity of the prober on the output signal spectrum is studied using multi-sampling rate theorem. Referring to the sampling theorem of time signal, the sampling theorem of space domain signal is defined and researched, and the natural frequency of space domain signal is determined by the form of defect and the effect region of sensor. With its section centre as the reference point during moving process of sensors, the inherent characteristic of space domain signals is investigated under many kinds of sensor region and defect form. The space domain frequency and the time domain frequency of time-space signals are normalized, sampling frequency is chosen and sampling scheme is determined in several different relationships of time frequency and space frequency. Then a unified sampling theorem on space-time signals is obtained. The effect of prober domain, velocity and time signal on the sampling of time-space signals is illustrated and the sampling theorem of space-time signal is validated. Research results can be extended to applications of related detection system and the sampling of time-space domain signal has certain generalization.

Key words: Electromagnetic testing, Sampling theorem of space-time signal, Space-time signal, Spectral analysis, Virtual infinite multi-probers technology, Wire ropes