FRI-based sparse sampling for ultrasonic array signals based on pulse-positive sequence delay synthesis

Abstract Ultrasonic transducer arrays have been widely applied to nondestructive testing due to their high testing efficiency and abundant echo information regarding defects. However, the considerable sampling data generated in array testing greatly restricts the performance levels of the subsequent processes, such as data storage, transmission, and processing. An finite rate of innovation- (FRI) based sparse sampling method has been recently developed, which greatly reduces the volume of sampling data, but only for single-transducer signals. If a transducer array is designed to use this sampling framework, a new problem of an overly complex sampling circuit system will appear. Therefore, this paper develops a novel array signal sparse sampling framework based on the pulse-positive sequence delay synthesis technique, which combines the ultrasonic array analog signals into a one-channel analog signal with a low degree of information freedom for sparse sampling. Although the degree of information freedom of the synthetic signal is greater than that of a single transducer signal, it still satisfies the conditions of signal sparse sampling and the volume of sampling data is still much smaller than that obtained using the traditional Nyquist sampling technique. An example of the experiment using a pure shear wave in the oblique incidence mode on a steel sample is provided, which indicates that eight-channel transducer array signals can be synthesized into one-channel signal, and then, the time delay and amplitude of the defect echo signals can be accurately estimated for each array element from the synthetic-signal sparse sampling data.