Journal ArticleDOI
Short-Time Fractional Fourier Transform and Its Applications
Ran Tao,Yan-Lei Li,Yue Wang +2 more
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TLDR
The short-time fractional Fourier transform (STFRFT) is proposed to solve the problem of locating the fractional fourier domain (FRFD)-frequency contents which is required in some applications and its inverse transform, properties and computational complexity are presented.Abstract:
The fractional Fourier transform (FRFT) is a potent tool to analyze the chirp signal. However, it fails in locating the fractional Fourier domain (FRFD)-frequency contents which is required in some applications. The short-time fractional Fourier transform (STFRFT) is proposed to solve this problem. It displays the time and FRFD-frequency information jointly in the short-time fractional Fourier domain (STFRFD). Two aspects of its performance are considered: the 2-D resolution and the STFRFD support. The time-FRFD-bandwidth product (TFBP) is defined to measure the resolvable area and the STFRFD support. The optimal STFRFT is obtained with the criteria that maximize the 2-D resolution and minimize the STFRFD support. Its inverse transform, properties and computational complexity are presented. Two applications are discussed: the estimations of the time-of-arrival (TOA) and pulsewidth (PW) of chirp signals, and the STFRFD filtering. Simulations verify the validity of the proposed algorithms.read more
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Journal ArticleDOI
Lv's Distribution: Principle, Implementation, Properties, and Performance
TL;DR: The distribution is demonstrated to be a CFCR representation that is computed without using any searching operation and to generate a new TF representation, called inverse LVD (ILVD), and a new ambiguity function, called Lv's ambiguity function (LVAF), both of which may break through the tradeoff between resolution and cross terms.
Journal ArticleDOI
Linear and synchrosqueezed time-frequency representations revisited
TL;DR: It is shown that the higher concentration of the synchrosqueezed transforms does not seem to imply better resolution properties, so that the SWFT and SWT do not appear to provide any significant advantages over the original WFT and WT apart from a more visually appealing pictures.
Journal ArticleDOI
Detection and Extraction of Target With Micromotion in Spiky Sea Clutter Via Short-Time Fractional Fourier Transform
TL;DR: The results demonstrate that the proposed method not only achieves high detection probability in a low-SCR environment but also outperforms the short-time Fourier transform-based method.
Journal ArticleDOI
Optical image encryption algorithm based on phase-truncated short-time fractional Fourier transform and hyper-chaotic system
TL;DR: The simulation results demonstrate that the proposed image encryption algorithm based on the PTSTFrFT is secure and robust enough against the common attacks.
Journal ArticleDOI
A novel fractional wavelet transform and its applications
TL;DR: In this paper, a novel fractional wavelet transform (FRWT) is proposed in order to rectify the limitations of the WT and the FRFT in the time-frequency domain.
References
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Journal ArticleDOI
Matching pursuits with time-frequency dictionaries
Stéphane Mallat,Zhifeng Zhang +1 more
TL;DR: The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions, chosen in order to best match the signal structures.
Journal ArticleDOI
Time-frequency distributions-a review
TL;DR: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented with emphasis on the diversity of concepts and motivations that have gone into the formation of the field.
Journal ArticleDOI
The fractional Fourier transform and time-frequency representations
TL;DR: The authors briefly introduce the functional Fourier transform and a number of its properties and present some new results: the interpretation as a rotation in the time-frequency plane, and the FRFT's relationships with time- frequencies such as the Wigner distribution, the ambiguity function, the short-time Fouriertransform and the spectrogram.
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The Fractional Order Fourier Transform and its Application to Quantum Mechanics
TL;DR: In this article, a generalized operational calculus is developed, paralleling the familiar one for the ordinary transform, which provides a convenient technique for solving certain classes of ordinary and partial differential equations which arise in quantum mechanics from classical quadratic hamiltonians.
Journal ArticleDOI
Digital computation of the fractional Fourier transform
TL;DR: An algorithm for efficient and accurate computation of the fractional Fourier transform for signals with time-bandwidth product N, which computes the fractionsal transform in O(NlogN) time.