Wheel-bearing fault diagnosis of trains using empirical wavelet transform

We deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform (LCT) of a function, from the samples of the original function. Two approaches are presented and compared. The first is based on decomposition of the LCT into chirp multiplication, Fourier transformation, and scaling operations. The second is based on decomposition of the LCT into a fractional Fourier transform followed by scaling and chirp multiplication. Both algorithms take ~ N log N time, where N is the time-bandwidth product of the signals. The only essential deviation from exactness arises from the approximation of a continuous Fourier transform with the discrete Fourier transform. Thus, the algorithms compute LCTs with a performance similar to that of the fast Fourier transform algorithm in computing the Fourier transform, both in terms of speed and accuracy.

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Digital Computation of Linear Canonical Transforms

Partly ensemble empirical mode decomposition: An improved noise-assisted method for eliminating mode mixing

An adaptively fast ensemble empirical mode decomposition method and its applications to rolling element bearing fault diagnosis

As the fractional Fourier transform has attracted a considerable amount of attention in the area of optics and signal processing, the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier transform. Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain, the discretization of the fractional Fourier transform has been investigated recently. A summary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper. The discretizations include sampling in the fractional Fourier domain, discrete-time fractional Fourier transform, fractional Fourier series, discrete fractional Fourier transform (including 3 main types: linear combination-type; sampling-type; and eigen decomposition-type), and other discrete fractional signal transform. It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.

Research progress on discretization of fractional Fourier transform

The complex bidimensional empirical mode decomposition

Angular decompositions for the discrete fractional signal transforms

In this paper, a generalized angular decomposition algorithm for the discrete fractional signal transforms is proposed. By the angular decomposition algorithm, the discrete fractional signal transforms can be computed by a weighted summation of the transform evaluated at special angles. Also the weighting coefficients are just equal to the inverse discrete Fourier transform of the eigenvalues of the fractional signal transform kernels.

Min-Hung Yeh

Papers

The complex bidimensional empirical mode decomposition

Angular decompositions for the discrete fractional signal transforms

Angular decompositions for the discrete fractional signal transforms