The fractional energy spectrum integral of the fractional Fourier transform of chirp signal

Jiangwei Zou; Jinzhen Wang; Shaoying Su; Zengping Chen

doi:10.1117/12.2231540

17 December 2015 The fractional energy spectrum integral of the fractional Fourier transform of chirp signal

Jiangwei Zou, Jinzhen Wang, Shaoying Su, Zengping Chen

Proceedings Volume 9811, MIPPR 2015: Multispectral Image Acquisition, Processing, and Analysis; 98111B (2015) https://doi.org/10.1117/12.2231540
Event: Ninth International Symposium on Multispectral Image Processing and Pattern Recognition (MIPPR2015), 2015, Enshi, China

Abstract

The fractional Fourier transform (FRFT), which is a generalization of the classical Fourier transform (FT), plays an important role in many areas of signal processing and optics. Many properties of this transform are well known. In the field of signal processing, the chirp signal has a good energy concentration in the fractional Fourier domain (FRFD) by choosing an appropriate fractional order, but the study of the fractional energy spectrum integral (FESI) is still missing. The purpose of this paper is to derive the FESI of the FRFT of chirp signal, from which an important property of the chirp signal’s FRFT is discovered that the FESI reaches the valley value at the rotation angle where the FRFT reaches the peak value, and this provides a new approach to detect and estimate the parameter of the chirp signal.

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Jiangwei Zou, Jinzhen Wang, Shaoying Su, and Zengping Chen "The fractional energy spectrum integral of the fractional Fourier transform of chirp signal", Proc. SPIE 9811, MIPPR 2015: Multispectral Image Acquisition, Processing, and Analysis, 98111B (17 December 2015); https://doi.org/10.1117/12.2231540

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KEYWORDS

Commercial off the shelf technology

Signal processing

Fourier transforms

Signal detection

Signal to noise ratio

Fractional fourier transform

Automatic target recognition

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