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A Comprehensive Survey on Fractional Fourier Transform

Zhang Y., Wang S., Yang J.-F., Zhang Z., Phillips P., Sun P., Yan J.

Fundamenta Informaticae

2017

Vol. 151, nr 1/4

1--48

The Fractional Fourier transform (FRFT) is a relatively novel linear transforms that is a generalization of conventional Fourier transform (FT). FRFT can transform a particular signal to a unified time-frequency domain. In this survey, we try to present a comprehensive investigation of FRFT. Firstly, we provided definition of FRFT and its three discrete versions (weighted-type, sampling-type, and eigendecomposition-type). Secondly, we offered a comprehensive theoretical research and technological studies that consisted of hardware implementation, software implementation, and optimal order selection. Thirdly, we presented a survey on applications of FRFT to following fields: communication, encryption, optimal engineering, radiology, remote sensing, fractional calculus, fractional wavelet transform, pseudo-differential operator, pattern recognition, and image processing. It is hoped that this survey would be beneficial for the researchers studying on FRFT.

Vibrator Data Denoising Based on Fractional Wavelet Transform

Zheng J., Zhu G., Liu M.

Acta Geophysica

2015

Vol. 63, no. 3

776--788

In this paper, a novel data denoising method is proposed for seismic exploration with a vibrator which produces a chirp-like signal. The method is based on fractional wavelet transform (FRWT), which is similar to the fractional Fourier transform (FRFT). It can represent signals in the fractional domain, and has the advantages of multi-resolution analysis as the wavelet transform (WT). The fractional wavelet transform can process the reflective chirp signal as pulse seismic signal and decompose it into multi-resolution domain to denoise. Compared with other methods, FRWT can offer wavelet transform for signal analysis in the timefractional- frequency plane which is suitable for processing vibratory seismic data. It can not only achieve better denoising performance, but also improve the quality and continuity of the reflection syncphase axis.