Increasing the computational efficient of digital cross correlation by a vectorization method

This study presents a vectorization method for use in MATLAB programming aimed at increasing the computational efficiency of digital cross correlation in sound and images, resulting in a speedup of 6.387 and 36.044 times compared with performance values obtained from looped expression. This work bridges the gap between matrix operations and loop iteration, preserving flexibility and efficiency in program testing. This paper uses numerical simulation to verify the speedup of the proposed vectorization method as well as experiments to measure the quantitative transient displacement response subjected to dynamic impact loading. The experiment involved the use of a high speed camera as well as a fiber optic system to measure the transient displacement in a cantilever beam under impact from a steel ball. Experimental measurement data obtained from the two methods are in excellent agreement in both the time and frequency domain, with discrepancies of only 0.68%. Numerical and experiment results demonstrate the efficacy of the proposed vectorization method with regard to computational speed in signal processing and high precision in the correlation algorithm. We also present the source code with which to build MATLAB-executable functions on Windows as well as Linux platforms, and provide a series of examples to demonstrate the application of the proposed vectorization method.