Novel Circuit Implementation Method for Pulse Signal Finite Rate of Innovation Sparse Sampling Based on an Improved Exponential Reproducing Kernel

Finite rate of innovation sampling is a new signal sparse sampling method based on signal information freedom, which can considerably reduce the amount of sampling data. However, the researches on hardware circuit direct implementation of the method are at an initial stage. Therefore, a novel hardware circuit implementation method based on an exponential reproducing kernel (ERK) was developed with an improved ERK sparse sampling theoretical framework, which comprised an analog rational kernel (ARK) and digital rational kernel (DRK). The parameter constraint conditions and selection method for the improved ERK were analyzed. The performance of the ARK hardware circuit and the DRK algorithm were also examined. The designed sparse sampling system was applied to a pipeline flaw ultrasonic inspection by using the sparse sampling data of the ultrasonic signal obtained directly. The experimental results revealed that the proposed method could directly obtain the signal sparse sampling data and accurately reconstruct the initial signal parameters by using a spectrum estimation algorithm. Moreover, the signal sampling rate and the amount of sampling data were reduced considerably.