Search Results (74)

Rolling bearings are prone to failure, meaning that research on intelligent fault diagnosis is crucial in relation to this key transmission component in rotating machinery. The application of deep learning (DL) has significantly advanced the development of intelligent fault diagnosis. This paper proposes a novel method for rolling bearing fault diagnosis based on the fractional constant Q non-stationary Gabor transform (FCO-NSGT) and VMamba-Conv. Firstly, a rolling bearing fault experimental platform is established and the vibration signals of rolling bearings under various working conditions are collected using an acceleration sensor. Secondly, a kurtosis-to-entropy ratio (KER) method and the rotational kernel function of the fractional Fourier transform (FRFT) are proposed and applied to the original CO-NSGT to overcome the limitations of the original CO-NSGT, such as the unsatisfactory time–frequency representation due to manual parameter setting and the energy dispersion problem of frequency-modulated signals that vary with time. A lightweight fault diagnosis model, VMamba-Conv, is proposed, which is a restructured version of VMamba. It integrates an efficient selective scanning mechanism, a state space model, and a convolutional network based on SimAX into a dual-branch architecture and uses inverted residual blocks to achieve a lightweight design while maintaining strong feature extraction capabilities. Finally, the time–frequency graph is inputted into VMamba-Conv to diagnose rolling bearing faults. This approach reduces the number of parameters, as well as the computational complexity, while ensuring high accuracy and excellent noise resistance. The results show that the proposed method has excellent fault diagnosis capabilities, with an average accuracy of 99.81%. By comparing the Adjusted Rand Index, Normalized Mutual Information, F1 Score, and accuracy, it is concluded that the proposed method outperforms other comparison methods, demonstrating its effectiveness and superiority. Full article

Mud pulse telemetry (MPT) systems are a promising approach to transmitting downhole data to the ground. During transmission, the amplitudes of pressure waves decay exponentially with distance, and the channel is often frequency-selective due to reflection and multipath effect. To address these issues, this work proposes a fractional Fourier transform (FrFT)-based channel estimation and equalization method. Leveraging the energy aggregation of linear frequency-modulated signals in the fractional Fourier domain, the time delay and attenuation parameters of the multipath channel can be estimated accurately. Furthermore, a fractional Fourier domain equalizer is proposed to pre-filter the frequency-selective fading channel using fractionally spaced decision feedback equalization. The effectiveness of the proposed method is evaluated through a simulation analysis and field experiments. The simulation results demonstrate that this method can significantly reduce multipath effects, effectively control the impact of noise, and facilitate subsequent demodulation. The field experiment results indicate that the demodulation of real data achieves advanced data rate communication (over 12 bit/s) and a low bit error rate (below 0.5%), which meets engineering requirements in a 3000 m drilling system. Full article

Accurate estimation of Interrupted Sampling Repeater Jamming (ISRJ) sampling duration is essential for effective radar anti-jamming. However, in complex electromagnetic environments, the simultaneous presence of suppressive and deceptive jamming, coupled with significant signal overlap in the time–frequency domain, renders ISRJ separation and parameter estimation considerably challenging. To address this challenge, this paper proposes a method utilizing the Fractional Fourier Transform (FRFT) and a Hybrid Modality Fusion Network (HMFN) for ISRJ signal separation and sampling-duration estimation. The proposed method first employs FRFT and a time–frequency mask to separate the ISRJ and target echo from the mixed signal. This process effectively suppresses interference and extracts the ISRJ signal. Subsequently, an HMFN is employed for high-precision estimation of the ISRJ sampling duration, offering crucial parameter support for active electromagnetic countermeasures. Simulation results validate the performance of the proposed method. Specifically, even under strong interference conditions with a Signal-to-Jamming Ratio (SJR) of −5 dB for deceptive jamming and as low as −10 dB for suppressive jamming, the regression model’s coefficient of determination still reaches 0.91. This result clearly demonstrates the method’s robustness and effectiveness in complex electromagnetic environments. Full article

With the rapid development of drone technology, target detection and estimation of radar parameters for maneuvering targets have become crucial. Drones, with their small radar cross-sections and high maneuverability, cause range migration (RM) and Doppler frequency migration (DFM), which complicate the use of traditional radar methods and reduce detection accuracy. Furthermore, the detection of multiple targets exacerbates the issue, as target interference complicates detection and impedes parameter estimation. To address this issue, this paper presents a method for high-resolution multi-drone target detection and parameter estimation based on the adjacent cross-correlation function (ACCF), fractional Fourier transform (FrFT), and deep learning techniques. The ACCF operation is first utilized to eliminate RM and reduce the higher-order components of DFM. Subsequently, the FrFT is applied to achieve coherent integration and enhance energy concentration. Additionally, a convolutional neural network (CNN) is employed to address issues of spectral overlap in multi-target FrFT processing, further improving resolution and detection performance. Experimental results demonstrate that the proposed method significantly outperforms existing approaches in probability of detection and accuracy of parameter estimation for multiple maneuvering targets, underscoring its strong potential for practical applications. Full article

The paper presents an enhanced numerical framework for computing the one-dimensional fast Fractional Fourier Transform (FRFT) by integrating closed-form Composite Newton-Cotes quadrature rules. We show that a FRFT of a $QN$-length weighted sequence can be decomposed analytically into two mathematically commutative compositions: one involving the composition of a FRFT of an N-length sequence and a FRFT of a Q-length weighted sequence, and the other in reverse order. The composite FRFT approach is applied to the inversion of Fourier and Laplace transforms, with a focus on estimating probability densities for distributions with complex-valued characteristic functions. Numerical experiments on the Variance-Gamma (VG) and Generalized Tempered Stable (GTS) models show that the proposed scheme significantly improves accuracy over standard (non-weighted) fast FRFT and classical Newton-Cotes quadrature, while preserving computational efficiency. The findings suggest that the composite FRFT framework offers a robust and mathematically sound tool for transform-based numerical approximations, particularly in applications involving oscillatory integrals and complex-valued characteristic functions. Full article

Recently, terahertz (THz) radar has been widely researched for its high-resolution in space target imaging. Due to the high rendezvous speed and the short wavelength of THz radar, the traditional stop-and-go model, along with its supporting algorithms, is not applicable. Therefore, a method that jointly compensates the intra- and inter- pulse errors of space targets’ echo is proposed. The algorithm includes the following steps: firstly, a coarse estimation of targets’ translational velocity at part of pulses is conducted through Fractional Fourier transform (FrFT). Then, the improved least square fitting (ILSF) is employed to parameterize the velocity–time dependency of the target. Furthermore, the concept of synthetic waveform entropy (SWE) of a one-dimensional range profile is put forward as the accuracy metric of envelope alignment. Finally, with SWE serving as the fitness function, the Grey Wolf Optimizer (GWO) algorithm is used to search for optimal estimated translation parameters. After several iterations, a fine-grained estimation of target motion parameters is achieved, while simultaneously accomplishing precise joint compensation for intra-pulse and inter-pulse errors. The validity of the proposed method is verified by numerical simulation, electromagnetic calculation data, and field-measured data. Full article

To effectively utilize the rich spectral information of hyperspectral remote sensing images (HRSIs), the fractional Fourier transform (FRFT) feature of HRSIs is proposed to reflect the time-domain and frequency-domain characteristics of a spectral pixel simultaneously, and an FRFT order selection criterion is also proposed based on maximizing separability. Firstly, FRFT is applied to the spectral pixels, and the amplitude spectrum is taken as the FRFT feature of HRSIs. The FRFT feature is mixed with the pixel spectral to form the presented spectral and fractional Fourier transform mixed feature (SF²MF), which contains time–frequency mixing information and spectral information of pixels. K-nearest neighbor, logistic regression, and random forest classifiers are used to verify the superiority of the proposed feature. A 1-dimensional convolutional neural network (1D-CNN) and a two-branch CNN network (Two-CNN_SF²MF-Spa) are designed to extract the depth SF²MF feature and the SF²MF-spatial joint feature, respectively. Moreover, to compensate for the defect that CNN cannot effectively capture the long-range features of spectral pixels, a long short-term memory (LSTM) network is introduced to be combined with CNN to form a two-branch network C-CLSTM_SF²MF for extracting deeper and more efficient fusion features. A 3D-CNN_SF²MF model is designed, which firstly performs the principal component analysis on the spa-SF²MF cube containing spatial information and then feeds it into the 3-dimensional convolutional neural network 3D-CNN_SF²MF to extract the SF²MF-spatial joint feature effectively. The experimental results of three real HRSIs show that the presented mixed feature SF²MF can effectively improve classification accuracy. Full article

Faced with increasingly complex electronic jamming environments, intra-pulse agility has become a primary method of anti-interrupted-sampling repeater jamming (ISRJ) for radar systems. However, existing intra-pulse agile signals suffer from high autocorrelation sidelobe levels and limited jamming suppression capabilities. These issues restrict the performance of intra-pulse agile signals in complex electromagnetic environments.This paper proposes an anti-interrupted-sampling repeater jamming method based on Simulated Annealing–2-optimization (SA-2opt) parallel optimization of waveforms and fractional domain extraction. Firstly, the proposed method employs the SA-2opt parallel optimization algorithm to optimize the joint frequency and chirp rate encoding waveform. Then, the received signal is subjected to the fractional Fourier transform (FrFT) and inverse transform to extract the target signal. Finally, jamming detection is conducted based on the multi-dimensional features of the pulse-compressed signal. After this detection, a time-domain filter is constructed to achieve jamming suppression. The optimized waveform exhibits the following advantages: the sub-pulses are orthogonal to each other, and autocorrelation sidelobe levels are as low as -20.7dB. The method proposed in this paper can achieve anti-ISRJ in the case of a high jamming-to-signal ratio (JSR). Simulation experiments validate both the effectiveness of the optimized waveform in achieving low autocorrelation sidelobes and the anti-ISRJ performance of the proposed method. Full article

This study investigated the integration of detection and communication techniques. First, the fractional-order Fourier transform (FRFT) is introduced, and the golden section method, parabolic interpolation, and Brent method are applied to search for the optimal fractional-order domain to accurately estimate the parameters of the linear frequency modulation (LFM) signal. Second, the three search algorithms and the performance of the integrated sensing and communication waveform are simulated. The Brent method improves the parameter searching efficiency by approximately 30% compared with the golden section method; the bit error ratio (BER) of the integrated LFM signal can reach 10⁻⁴ with a signal-to-noise ratio (SNR) of 3 dB. The results show that the integrated waveform can realize the detection function with guaranteed communication performance. An anti-frequency sweeping interference method based on the fractional domain matching order was also carried out to optimize the detection performance of the integrated waveform. Through the analysis of the difference-frequency signal under frequency sweeping interference, two methods, direct filtering, and pairwise cancellation filtering, are used to suppress the interference signal and detect the target distance. The simulation evaluated the detection performance of the two methods under different signal-to-interference ratios (SIR) and filter widths. The simulation results show that the pairwise cancellation filtering suppresses the frequency sweeping interference by 4–6 dB more than the direct filtering with an SIR ≤ −15 dB. Both filtering methods can correctly extract the target position information under frequency sweeping interference with a low signal-to-interference ratio (SIR). In conclusion, this study provides an effective solution for parameter estimation optimization and frequency-sweeping interference suppression for FRFT-based sensing communication systems. Full article

Synthetic aperture radar (SAR) operating mode recognition plays a crucial role in SAR countermeasures and serves as the foundation for effective SAR interference. To address the limitations of current SAR operating mode recognition algorithms, such as low recognition rates, poor generalization, and limited engineering applicability under low signal-to-noise ratio (SNR) conditions, an enhanced algorithm named dual-input feature fusion ShuffleNet (DIFF-ShuffleNet) based on intercepted SAR signal data is proposed. First, the SAR signal is processed by combining pulse compression and time–frequency analysis technology to enhance anti-noise robustness. Then, an improved lightweight ShuffleNet architecture is designed to fuse range pulse compression (RPC) maps and azimuth time–frequency features, significantly improving recognition accuracy in low-SNR environments while maintaining practical deployability. Moreover, an improved coarse-to-fine search fractional Fourier transform (CFS-FRFT) algorithm is proposed to address the chirp rate estimation required for RPC. Simulations demonstrate that the proposed SAR operating mode recognition algorithm achieves over 95.00% recognition accuracy for SAR operating modes (stripmap, spotlight, sliding spotlight, and scan) at an SNR greater than −8 dB. Finally, four sets of measured SAR data are used to validate the algorithm’s effectiveness, with all recognition results being correct, demonstrating the algorithm’s practical applicability. Full article

To address the limitations of traditional tumor diagnostic methods in image feature extraction and model generalization, this study innovatively proposes a synergistic diagnostic model that integrates fractional Fourier transform (FrFT) and error back-propagation (BP) neural networks. The model leverages the time–frequency analysis capability of FrFT and incorporates the fractal characteristics observed during tumor proliferation, effectively enhancing multi-scale feature extraction and representation. Experimental results show that the proposed model achieves an accuracy of 93.177% in classifying benign and malignant tumors, outperforming the support vector machine (SVM) method. The integration of FrFT improves feature distinguishability and reduces dependence on manual extraction. This study not only represents a breakthrough in tumor diagnostic technology but also paves new avenues for the application of fractional calculus and fractal geometry in medical image analysis. The findings show great potential for clinical application and future development. Full article

In the corner reflector jamming scenario, the ship target and the corner reflector array have different degrees of defocusing in the synthetic aperture radar (SAR) image due to their complex motions, which is unfavorable to the subsequent target recognition. In this manuscript, we propose an imaging method for marine targets based on time–frequency analysis with the modified Clean technique. Firstly, the motion models of the ship target and the corner reflector array are established, and the characteristics of their Doppler parameter distribution are analyzed. Then, the Chirp Rate–Quadratic Chirp Rate Distribution (CR-QCRD) algorithm is utilized to estimate the Doppler parameters. To address the challenges posed by the aggregated scattering points of the ship target and the overlapping Doppler histories of the corner reflector array, the Clean technique is modified by short-time Fourier transform (STFT) filtering and amplitude–phase distortion correction using fractional Fourier transform (FrFT) filtering. This modification aims to improve the accuracy and efficiency of extracting scattering point components. Thirdly, in response to the poor universality of the traditional Clean iterative termination condition, the kurtosis of the residual signal spectrum amplitude is adopted as the new iterative termination condition. Compared with the existing imaging methods, the proposed method can adapt to the different Doppler distribution characteristics of the ship target and the corner reflector array, thus realizing better robustness in obtaining a well-focused target image. Finally, simulation experiments verify the effectiveness of the algorithm. Full article

As a generalization of the short-time Fourier transform (STFT), the novel short-time fractional Fourier transform (NSTFRFT) has been introduced recently. In order to improve the concentration of the time–frequency representation (TFR) generated by the NSTFRFT, two post-processing time–frequency analysis methods, two synchroextracting transforms based on the NSTFRFT with two different fractional Fourier transform (FRFT) angles, are proposed in this paper. One is achieved via an equation where the instantaneous frequency satisfies the condition where the FRFT angle takes ${\displaystyle \frac{\pi }{2}}$, and the other one is obtained using the instantaneous frequency estimator in the case that the FRFT angle takes a value related to the chirp rate of the signal. Although the conditions of the two synchroextracting transforms are different, their implementation can be unified into the same algorithm. The proposed synchroextracting transforms supplement existing post-processing time–frequency analysis methods which are based on the NSTFRFT. Experiments are conducted to verify the performance and superiority of the proposed methods. Full article

In indoor visible light communication (VLC) and visible light positioning (VLP) systems, the performance of conventional orthogonal frequency-division multiplexing (OFDM) schemes is often compromised due to the nonlinear characteristics and limited modulation bandwidth of light-emitting diodes, the multipath effect in enclosed indoor environments, and the relative positions of transmitters and receivers. This paper proposes an OFDM scheme based on the fractional Fourier transform (FRFT) to address these issues, demonstrating promising results when applied to indoor VLC and VLP systems. The FRFT, a generalization of the conventional Fourier transform (FT) in the fractional domain, captures information in both the time and frequency domains, offering greater flexibility than the FT. In this paper, we first introduce the computation method of the reality-preserving FRFT for an intensity modulation/direct detection VLC system and integrate it with OFDM to optimize system performance. By adopting FRFT-OFDM under the optimal fractional order, we enhance both the bit error ratio (BER) performance and positioning accuracy. Simulation results reveal that the FRFT-OFDM scheme with an optimized fractional order significantly improves the BER and positioning accuracy compared to the FT-OFDM scheme across most receiver positions within the indoor observation plane. For communication, the FRFT-OFDM scheme achieves over 6 dB $E_b/N_0$ gain compared to the FT-OFDM scheme at a BER of $3\times {10}^{-4}$ when the receiver is positioned at most locations in the room. For positioning, the FRFT-OFDM scheme enhances positioning accuracy by more than 1 cm relative to the FT-OFDM scheme at most locations in the room. Notably, both systems maintain the same computational complexity and spectral efficiency. Full article

Addressing the issue of linear frequency modulation (LFM) interference in GNSS positioning, this paper proposes an interference suppression method based on energy residual searching, incorporating the fractional Fourier transform (FrFT) for improved performance. In GNSS systems, LFM interference can severely impair positioning accuracy and system robustness, potentially rendering the receiver incapable of performing accurate localization. To address this issue, an energy residual function is introduced to quantitatively assess the impact of interference on the original signal. This function combines differences in signal energy with signal quality after spectral line removal to achieve effective interference evaluation. By optimizing the parameters of the fractional Fourier transform to maximize the value of the energy residual function the proposed method significantly enhances interference suppression. Our experimental results demonstrate that the method performs exceptionally well on practical datasets, effectively removing interference and restoring relevant peaks. This approach mitigates the negative effects of LFM interference on GNSS positioning performance, substantially improving both positioning accuracy and system robustness. Full article