Efficient method for the field‐programmable gate arrays calculation of Wigner‐Ville distribution

Abstract

Various signals of finite length are often analysed by the Wigner-Ville distribution (WVD). Thus, this article deals with the implementation of their discrete WVDs on field-programmable gate arrays (FPGAs). For the discrete WVD, its calculation procedures are composed of the autocorrelation function and Fourier transform. Since the autocorrelation procedure is the most time-consuming step in the entire computation process, the authors analyse the calculation procedure of autocorrelation function in detail. Here the proposed efficient method just calculates partial non-zero elements of the autocorrelation matrices in order to reduce the computation complexity. The FFT (built-in FPGAs) is then utilised to acquire the discrete WVD. In addition, the idea of the fully-pipelined and parallelism is borrowed to reduce the running time but at the cost of recourses. Finally, the authors provide implementations of both authors proposed method and two other algorithms on different FPGAs. The experimental results show that the Intel Arria-10 FPGA families are the better choice in the floating point arithmetic and that authors method has the best performance.

Identification of wind turbine gearbox weak compound fault based on optimal empirical wavelet transform

“…Traditional analysis methods have been widely used in the processing of non-stationary signals, e.g. short-time Fourier transform (STFT) [11,12], continuous wavelet transform (CWT) [13,14] and Wigner-Ville distribution (WVD) [15,16] etc. The time-frequency resolution of STFT and CWT is not ideal due to pre-defined basis functions and window functions.…”