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Highlights • The problems of quadratic range migration and Doppler frequency migration for the maneuvering target are addressed. • A method based on TSS-FrFT is proposed to achieve the coherent integration and it has superior detection performance and low computational complexity. • The acceleration matched filter is presented to remove the DFRC caused by the sudden change of targets acceleration. Abstract This paper considers the detection problem of radar maneuvering target with the range migration (RM) and Doppler frequency migration (DFM) and proposes an coherent integration method based on two steps scaling and fractional Fourier transform, i.e., TSS-FrFT. To be specific, this method corrects the quadratic RM (QRM) and DFM based on FrFT and a scaling processing of the rotation angle firstly. Then, it eliminates the coupling between the range frequency variable and FrFT domain (FrFD) variable via a second scaling processing. In the end, the coherent integration is achieved by the inverse Fourier transform (IFT) with respect to the range frequency variable. Compared with the existing methods, the proposed TSS-FrFT method has superior detection performance and low computational complexity. Moreover, considering the sudden change of the target acceleration within the coherent integration interval, this paper also presents an acceleration matched filter (AMF) to remove the Doppler frequency rate change (DFRC) caused by this acceleration change. Computer simulation results are also given to demonstrate the effectiveness of the proposed method from different aspects, i.e., computational complexity, coherent integration for a single target and multiple targets and detection performance for a uniform acceleration and non-uniform accelerations. [ABSTRACT FROM AUTHOR]

Detection of weak maneuvering target often suffers from the problems of the range migration (RM) and the Doppler frequency migration (DFM) within the coherent pulse interval. In order to eliminate the RM and DFM, a new coherent integration method based on keystone transform (KT) and matched filtering process (MFP), i.e., KT-MFP, is proposed. Specifically, this method firstly corrects the linear RM caused by the unambiguous velocity via KT and then the MFP, which jointly searching in the fold factor and acceleration domain, is carried out to remove the residual RM and compensate the DFM. At last, coherent integration of the target’s energy is achieved through the slow time Fourier transform (FT). The advantage of the proposed method is that it can obtain superior coherent integration and detection performance for both the slow-moving and fast-moving target, in comparison with the existing algorithms. In addition, KT-MFP could avoid the blind speed sidelobe (BSSL) effect. Numerical simulations are performed to assess the performance from different aspects, i.e., computational complexity, coherent integration for a low-speed target, detection performance for a low-speed target, coherent integration for a high-speed target, detection performance for a high-speed target and coherent integration for multi-targets. [ABSTRACT FROM AUTHOR]

The generalized demodulation method based on maximal overlap discrete wavelet packet transform (MODWPT) is well suitable for separating multi-component signals due to the properties of MODWPT such as decomposing a signal into a sum of components and the same time-resolution in all decomposition layers. However, the related separation-method research meets lots of challenges because of multi-component signals whose components are overlapped in frequency at some instants. In this paper, a novel generalized demodulation approach is proposed to separate each component from the multi-component signals. A generalized short time Fourier transform (GSTFT) is introduced to project the multi-component analytic signal onto the time–frequency plane and a varying window function is used to improve the time–frequency concentration of GSTFT. The time–frequency plane is considered as a 2-D time–frequency image, the singular value decomposition (SVD) and the generalized demodulation technique are applied to obtain the component of interest. Simulation results show that, after using the proposed approach, the time domain waveform and the instantaneous frequency of each component are obtained by analyzing multi-component signals whose components may be well separated in frequency at one instant and overlapped at a later instant. [ABSTRACT FROM AUTHOR]

Abstract: A new subsample time delay estimator is proposed in this paper. It is evaluated based on the time delay property of the fractional Fourier transform and is suitable for processing chirp signals. The theoretic derivation of the algorithm is also presented. The validity and superiority to the fractional time delay estimator (FRTDE), the conventional direct correlator (DC) and the average magnitude squared fractional difference function (AMSFDF) estimator of this new time delay estimator are demonstrated via computer simulations. [Copyright &y& Elsevier]

Abstract: Spectral kurtosis (SK) provides a valuable tool for detecting the signal transients buried in noise, which makes it very powerful for designing a filter to extract the signal transients. However, SK requires the selection of a time–frequency frame for decomposition based on Short Time Fourier Transform (STFT). This paper presents an adaptive spectral kurtosis filtering technique to extract the signal transients based on Morlet wavelet. The Morlet wavelet is used as a filter bank whose center frequency is defined by the wavelet correlation filtering. Different bandwidth filter in the filter bank is used to select the optimal filter for extracting the signal transients as the one that maximizes the SK. Effectiveness of the proposed technique is verified through the transient extraction of a simulate signal. For the gear fault feature detection of vehicle transmission gearbox, the proposed technique is applied in the extraction of the signal transients that shows the gear fault, which proves the effectiveness of the proposed technique in extracting the signal transients in the practical application. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce fractional Fourier transforms over finite fields GF(p), where . Such a definition is based on the approach given in [1], which corresponds to a finite field extension of the commuting matrix method for defining discrete fractional Fourier transforms [2]. The transforms we have constructed are then used as the basis of a novel image encryption scheme. Security aspects of such a scheme are analyzed through computer simulations and specific metrics. [Copyright &y& Elsevier]

Abstract: The local polynomial Fourier transform (LPFT), as a high-order generalization of the short-time Fourier transform (STFT), has been developed and used for many different applications in recent years. This paper attempts to review previous research work on the following issues of the LPFT. Firstly, the definition, the properties of the LPFT and its relationships with other transforms are reviewed. The LPFT for multicomponent signal is then presented. The polynomial time frequency transform (PTFT), which is the maximum likelihood estimator to estimate the parameters in the LPFT, as well as its properties and fast algorithms are discussed. By comparing with the Fourier transform (FT), the STFT and the Wigner–Ville distribution (WVD), the LPFT has its superiority in obtaining improved SNRs, which can be supported by theoretical analysis and computer simulations. Furthermore, the reassignment method is combined with the LPFT and the robust LPFT to improve the concentration of the signal representation in the time–frequency domain. Performances obtained by using various LPP-related methods are compared for signals in different noise environments, such as the additive white Gaussian noise (AGWN), impulsive noise, and the mixture of AGWN and impulsive noise. [Copyright &y& Elsevier]

Abstract: This paper presents a new method to detect linear frequency modulated (LFM) signals by jointly using the local polynomial periodogram (LPP) and the Hough transform. Theoretical comparison is made on the 3dB signal-to-noise ratios (SNRs), achieved by the pseudo-Wigner–Ville distribution (PWVD) and the LPP, to show that the latter is important to achieve significant increase of noise margins in the Hough transform domain. The results of computer simulations are presented for the detection of mono- and multi-component LFM signals corrupted by additive white Gaussian noise and impulsive noise. It is also found that by using the time–frequency filtering, the computational complexity of the detection can be substantially reduced. Both the theoretical analysis and the simulation results show that the proposed method achieves significant performance improvement on detecting the LFM signals in very low signal-to-noise ratio environments. [Copyright &y& Elsevier]

Abstract: We introduce a new discrete fractional Fourier transform (DFrFT) based on only the DFT matrix and its powers. Eigenvectors of the DFT matrix are obtained in a simple-yet-elegant and straightforward manner. We show that this DFrFT definition based on the eigentransforms of the DFT matrix mimics the properties of continuous fractional Fourier transform (FrFT) by approximating the samples of the continuous FrFT. By appropriately combining existing commuting matrices we obtain a new commuting matrix which performs better. We show the validity of the proposed algorithms by computer simulations comparing DFrFT points and continuous FrFT samples for various signals. [ABSTRACT FROM AUTHOR]

Abstract: The fractional convolution and correlation of two functions, as usually defined, exhibit only partial invariance properties which prevent their actual use in many applications of signal processing. Indeed, an effective translation invariance is obtained by slightly modifying the former definitions and by introducing fractional translation operators. The translation invariances of the so-defined fractional convolution and correlation are expressed by integrals which are shown to be the exact counterparts, in the fractional domain, of the integrals that are used to express the well-known translation invariances of the usual convolution and correlation. The former theoretical results are applied to proving a fractional sampling theorem and are illustrated by numerical simulations. They are also compared to those obtained by some authors on the basis of alternative definitions. [Copyright &y& Elsevier]

Abstract: Grigoryan [Fourier transform representation by frequency-time wavelets, IEEE Trans. Signal Process. 53 (7) (2005) 2489–2497] has proposed an alternative representation of the Fourier transform, called A-wavelet transform. In that paper, the Cosine and Sine signals defined over one period have been used to develop the Cosine- and Sine-wavelet transforms and using those wavelet transforms the Fourier transform has been represented. For computing the Fourier transform at a given frequency, one does not require to compute the Cosine- and Sine-wavelet transforms at all time points in the time-frequency plane, but at specific time points that are separated out by 2π/ω, ω is the frequency variable. In this paper, we propose SC- and SS-wavelet transforms that help representing the Fourier transform of a signal in a better way. The SC- and SS-wavelet transforms use the Cosine and Sine signals defined over the smaller intervals (of length 2π/(mω), m⩾1) than that (of length 2π/ω) used in the A-wavelet transform. The SC- and SS-wavelet transforms not only give sharper time-frequency localization but also much more information in a better localized form than the A-wavelet transform. [Copyright &y& Elsevier]