Spectrum Aliasing Research Articles

Dynamic range extension method for sinusoidal phase modulating interferometer based on in-phase component signal reconstruction

Abstract The continuous increase of the amplitude of the measured vibration will cause spectrum aliasing in the interference signal of the sinusoidal phase modulating interferometer (SPMI), thereby constraining its measurement dynamic range (DR). To address this issue, a dynamic range extension method of SPMI based on the reconstruction of in-phase component signal is proposed. On the basis of conventional SPMI, an additional reference signal is introduced for estimating the phase modulation depth (PMD) and the major to minor axis ratio Re of the Lissajous ellipse formed by orthogonal interference signal pair and a phase demodulation algorithm named as PGC-ICR-DCM which integrates PGC-DCM algorithm and the in-phase component signal reconstruction (ICR) is proposed. Initially, the PMD is regulated to approximately 1.8412 rad, ensuring that the quadrature component signal can be accurately extracted from the mixed signal of the interference and carrier signals, even in the presence of spectrum aliasing in the original interference signal. Then, the undistorted quadrature component signal is used to reconstruct an in-phase component signal with the estimated value of Re. Finally, the reconstructed in-phase component signal and quadrature component signal are normalized, and a differential-and-cross-multiplying algorithm (DCM) is applied to obtain the measured vibration. A SPMI measurement system based on Michelson interferometer structure is constructed to experimentally validate the proposed method. The experimental results demonstrate that the proposed method can effectively extend the DR of the SPMI system in the presence of spectrum aliasing. The DR of the system is increased from 97.52 dB @ 55 Hz to 102.6 dB @ 55 Hz, with the maximum measurable amplitude increasing from 7728.75 nm @ 55Hz to 13705.16 nm @ 55 Hz.

Phase Demodulation under Ultra-low sampling rate in heterodyne coherent [formula omitted]-OTDR

Heterodyne coherent phase-sensitive optical time-domain reflectometry(Φ-OTDR) requires a higher data sampling rate to demodulate phase in the “distance” direction effectively. Aiming at the problem of large amount of demodulated data, we propose a phase demodulation method that can effectively recover disturbance information from ultra-low sampling data. This method demodulates the phase of the two-dimensional reconstructed signal in the “time” direction. Thus, the influence of spectrum aliasing in the “distance” direction caused by undersampling is avoided. The undersampling rate is not limited by the spectrum aliasing effect of the detected signal when using this method to demodulate phase. Therefore, accurate phase information can be retrieved under ultra-low sampling rates, significantly reducing the data for phase demodulation in heterodyne coherent Φ-OTDR. In the experiment, three sampling rates (100 MSa/s, 10 MSa/s, 1 MSa/s) within the restricted area of the traditional undersampling demodulation method were selected to acquire data, and the proposed method can also accurately demodulate phase information.

A Novel SAR Imaging Method for GEO Satellite–Ground Bistatic SAR System with Severe Azimuth Spectrum Aliasing and 2-D Spatial Variability

The satellite–ground bistatic configuration, which uses geosynchronous synthetic aperture radar (GEO SAR) for illumination and ground equipment for reception, can achieve wide coverage, high revisit, and continuous illumination of interest areas. Based on the analysis of the signal characteristics of GEO satellite–ground bistatic SAR (GEO SG-BiSAR), it is found that the bistatic echo signal has problems of azimuth spectrum aliasing and 2-D spatial variability. Therefore, to overcome those problems, a novel SAR imaging method for a GEO SG-BiSAR system with severe azimuth spectrum aliasing and 2-D spatial variability is proposed. Firstly, based on the geometric configuration of the GEO SG-BiSAR system, the time-domain and frequency-domain expressions of the signal are derived in detail. Secondly, in order to avoid the increasing cost caused by traditional multi-channel reception technology and the processing burden caused by inter-channel errors, the azimuth deramping is executed to solve the azimuth spectrum aliasing of the signal under the special geometric structure of GEO SG-BiSAR. Thirdly, based on the investigation of azimuth and range spatial variability characteristics of GEO SG-BiSAR in the Range Doppler (RD) domain, the azimuth spatial variability correction strategy is proposed. The signal corrected by the correction strategy has the same migration characteristics as monostatic radar. Therefore, the traditional chirp scaling function (CSF) is also modified to solve the range spatial variability of the signal. Finally, the two-dimensional spectrum of GEO SG-BiSAR with modified chirp scaling processing is derived, followed by the SPECAN operation to obtain the focused SAR image. Furthermore, the completed flowchart is also given to display the main composed parts for GEO SG-BiSAR imaging. Both azimuth spectrum aliasing and 2-D spatial variability are taken into account in the imaging method. The simulated data and the real data obtained by the Beidou navigation satellite are used to verify the effectiveness of the proposed method.

Maritime Moving Target Reconstruction via MBLCFD in Staggered SAR System

Imaging maritime targets requires a high resolution and wide swath (HWRS) in a synthetic aperture radar (SAR). When operated with a variable pulse repetition interval (PRI), a staggered SAR can realize HRWS imaging, which needs to be reconstructed due to echo pulse loss and a nonuniformly sampled signal along the azimuth. The existing reconstruction algorithms are designed for stationary scenes in a staggered SAR mode, and thus, produce evident image defocusing caused by complex target motion for moving targets. Typically, the nonuniform sampling and complex motion of maritime targets aggravate the spectrum aliasing in a staggered SAR mode, causing inevitable ambiguity and degradation in its reconstruction performance. To this end, this study analyzed the spectrum of maritime targets in a staggered SAR system through theoretical derivation. After this, a reconstruction method named MBLCFD (Modified Best Linear Unbaised and Complex-Lag Time-Frequency Distribution) is proposed to refocus the blurred maritime target. First, the signal model of the maritime target with 3D rotation accompanying roll–pitch–yaw movement was established under the curved orbit of the satellite. The best linear unbiased (BLU) method was modified to alleviate the coupling of nonuniform sampling and target motion. A precise SAR algorithm was performed based on the method of inverse reversion to counteract the effect of a curved orbit and wide swath. Based on the hybrid SAR/ISAR technique, the complex-lag time-frequency distribution was exploited to refocus the maritime target images. Simulations and experiments were carried out to verify the effectiveness of the proposed method, providing precise refocusing performance in staggered mode.

A sub-band division algorithm for ultra-wide bandwidth pulsar signals based on RFSoC

In order to realize the real-time processing and analysis of astronomical ultra-wide bandwidth signals, this study proposes a sub-band division algorithm based on RFSoC. The algorithm uses Kaiser window to design FIR prototype low-pass filter, adopts critical sampling polyphase filter bank to decompose ultra-wide bandwidth signal into several sub-bands, and encapsulates each sub-band into VDIF data frame and sends it to GPU server. The algorithm is implemented on RFSoC platform, and its effectiveness is verified by simulation and actual observation. The experimental results show that the algorithm can divide the astronomical ultra-wide bandwidth signal into multiple sub-bands in real time, packetize and transmit them to GPU. This research provides reproducible design and project for ultra-wide bandwidth signal sub-band division with low spectrum leakage and aliasing, high data accuracy, and fast processing speed.

Deep learning-based frequency-multiplexing composite-fringe projection profilometry technique for one-shot 3D shape measurement

The pursuit of precise and efficient 3D shape measurement has long been a focal point within the fringe projection profilometry (FPP) domain. However, achieving precise 3D reconstruction for isolated objects from a single fringe image remains a challenging task in the field. In this paper, a deep learning-based frequency-multiplexing (FM) composite-fringe projection profilometry (DFCP) is proposed, where an end-to-end absolute phase retrieval network (APR-Net) is trained to directly recover the absolute phase map from a FM composite fringe pattern. The obtained absolute phase map exhibits exceptional precision and is devoid of spectrum crosstalk or leakage disturbance typically encountered in traditional FM techniques. APR-Net is intricately crafted, incorporating a nested strategy along with the concept of centralized information interaction. A diverse dataset encompassing various scenarios and free from spectrum aliasing is assembled to guide the training process. A seven-map loss calculation scheme is employed to guide the training process, of which the efficacy is proved through ablation experiments. In the first qualitative experiment, DFCP demonstrates comparable phase accuracy to ground truths with 47 fewer projected images, outperforming other three methods with mean absolute phase errors of 0.0052 rad, 0.1761 rad, 0.0169 rad, and 0.0139 rad. The second qualitative experiment and the quantitative evaluation respectively prove DFCP’s capability in high dynamic range 3D measurement and in precise 3D measurement, with sphere diameter errors of 0.0780 mm and 0.0726 mm, and a spherical centroid distance error of 0.0555 mm.

Quality improvement to holographic microscopy reconstruction based on Kramers-Kronig relations and phase background fitting.

Spectrum aliasing in off-axis digital holography may result in poor image reconstruction quality. This study proposes a method to eliminate the zero-order spectrum and enhance image quality based on Kramers-Kronig relations and phase background fitting. The Kramers-Kronig relations are employed to derive the quotient of the complex wavefront of object and the reference beam, and phase background fitting is performed in a compensatory way to yield the object complex wavefront. The effectiveness of the proposed approach is validated via simulations and experiments. The results show significantly improved off-axis digital holographic microscopy reconstruction quality, making the proposed method a promising option for holographic microscopy imaging.

Partial discharge fault detection method of switchgear based on signal aliasing spectrum separation model

At present, the detection nodes of partial discharge fault in switchgear are generally set in one direction, and the fault detection range is small, which leads to an increase in the false recognition rate of partial discharge fault detection. Therefore, the design and verification analysis of the detection method of partial discharge fault in switchgear is proposed. According to the current measurement requirements and standards, firstly, the characteristics of switchgear discharge faults are extracted, and the fault detection range is expanded by the multi-step method. Multi-step partial discharge fault detection nodes are deployed, and the partial discharge fault detection model with signal aliasing and spectrum separation is constructed. The fault detection is completed by hierarchical fuzzy automatic identification. The test results show that the final detection error rate of partial discharge fault is well controlled below 20% by comparing the seven selected test cycles and combining the signal aliasing spectrum separation model, which shows that the designed detection method of partial discharge fault is more flexible and changeable, and has strong pertinence and reliability. Facing the complex switchgear operating environment, it can also mark the fault position in the shortest time, strengthen the detection results and ensure the detection accuracy.

A method for suppressing spectrum aliasing of off-axis digital holograms based on Kronecker interpolation and backpropagation

The research proposes a new method to solve the spectrum aliasing and improve the resolution of off-axis digital holograms based on Kronecker interpolation and backpropagation algorithms. The method suppresses the direct current (DC) image and increase the low-frequency information with Kronecker interpolation of the hologram. The size of the Fresnel reconstructed image can be controlled with the reconstruction distance, and this feature is used to select the appropriate reconstruction distance for the Fresnel amplitude reconstruction of interpolated holograms to separate the real and imaginary images. To obtain the complete first-order spectral information for the object, the amplitude of the desired image is obtained with spatial domain filtering and then inverted. Finally, the amplitude and phase of the object are reconstructed according to the angular spectrum reconstruction algorithm. The results show that the method can solve the spectrum aliasing problem of the holograms and thus improve the resolution of off-axis holograms. In addition, the background noise of the reconstructed phase is reduced because the influence of the zero-order spectrum can be completely avoided.

EhdNet: Efficient Harmonic Detection Network for All-Phase Processing with Channel Attention Mechanism

The core of harmonic detection is the recognition and extraction of each order harmonic in the signal. The current detection methods are seriously affected by the fence effect and spectrum aliasing, which brings great challenges to the detection of each order harmonic in the signal. This paper proposes an efficient harmonic detection neural network based on all-phase processing. It is based on three crucial designs. First, a harmonic signal-processing module is developed to ensure phase invariance and establish the foundation for subsequent modules. Then, we constructed the backbone network and utilized the feature-extraction module to extract deep abstract harmonic features of the target. Furthermore, a channel attention mechanism is also introduced in the weight-selection module to enhance the energy of the residual convolution stable spectrum feature, which facilitates the accurate and subtle expression of intrinsic characteristics of the target. We evaluate our method based on frequency, phase, and amplitude in two environments with and without noise. Experimental results demonstrate that the proposed EhdNet method can achieve 94% accuracy, which is higher than the compared methods. In comparison experiments with actual data, the RMSE of EhdNet is also lower than that of other recent methods. Moreover, the proposed method outperforms ResNet, BP, and other neural network approaches in data processing across diverse working conditions due to its incorporation of a channel attention mechanism.

A wide-beam NCS algorithm for multi-receiver SAS based on azimuth spectrum superposition

The existing multi-receiver synthetic aperture sonar (SAS) imaging algorithms are suitable for narrow-beam width, which will lead to a decrease in imaging quality under wide-beam condition and are not in line with the development needs of SAS. We propose a non-linear chirp scaling algorithm (NCSA) for wide beam multi-receiver SAS. Firstly, the point target reference spectrum (PTRS) of each receiver is obtained by the Lagrange inversion theorem (LIT), and then the under-sampled signal in the azimuth frequency domain is obtained through azimuth spectrum extension; Then, considering the cubic term of range frequency in the PTRS and the linear variation of equivalent frequency modulation slope with range, each receiver is imaged using the NCSA, and coherent superposition is performed in the azimuth frequency domain to eliminate spectrum aliasing caused by azimuth spectrum extension; Finally, the azimuth inverse transform is performed on the superimposed signal to obtain the focusing imaging. Computer simulation experiments and field data verify that this method is superior to the existing SAS imaging algorithm, improving the quality of wide-beam imaging, avoiding the interpolation operation of the traditional range-Doppler algorithm, and saving computation cost.

MosReformer: Reconstruction and Separation of Multiple Moving Targets for Staggered SAR Imaging

Maritime moving target imaging using synthetic aperture radar (SAR) demands high resolution and wide swath (HRWS). Using the variable pulse repetition interval (PRI), staggered SAR can achieve seamless HRWS imaging. The reconstruction should be performed since the variable PRI causes echo pulse loss and nonuniformly sampled signals in azimuth, both of which result in spectrum aliasing. The existing reconstruction methods are designed for stationary scenes and have achieved impressive results. However, for moving targets, these methods inevitably introduce reconstruction errors. The target motion coupled with non-uniform sampling aggravates the spectral aliasing and degrades the reconstruction performance. This phenomenon becomes more severe, particularly in scenes involving multiple moving targets, since the distinct motion parameter has its unique effect on spectrum aliasing, resulting in the overlapping of various aliasing effects. Consequently, it becomes difficult to reconstruct and separate the echoes of the multiple moving targets with high precision in staggered mode. To this end, motivated by deep learning, this paper proposes a novel Transformer-based algorithm to image multiple moving targets in a staggered SAR system. The reconstruction and the separation of the multiple moving targets are achieved through a proposed network named MosReFormer (Multiple moving target separation and reconstruction Transformer). Adopting a gated single-head Transformer network with convolution-augmented joint self-attention, the proposed MosReFormer network can mitigate the reconstruction errors and separate the signals of multiple moving targets simultaneously. Simulations and experiments on raw data show that the reconstructed and separated results are close to ideal imaging results which are sampled uniformly in azimuth with constant PRI, verifying the feasibility and effectiveness of the proposed algorithm.

Spectral De-Aliasing Method of Micro-Motion Signals Based on a Complex-Valued U-Net Network

Spectrum aliasing occurs in signal echoes when the sampling frequency does not comply with the Nyquist Sampling Theorem. In this scenario, the extraction of micro-motion parameters becomes challenging. This paper proposes a spectral de-aliasing method for micro-motion signals based on a complex-valued U-Net network. Zero interpolation is employed to insert zeros into the echo, effectively increasing the sampling frequency. After zero interpolation, the micro-motion signal contains both real micro-motion signal frequency components and new frequency components. Short-Time Fourier Transform (STFT) is then applied to transform the zero-interpolated echo from the time domain to the time–frequency domain. Furthermore, a complex-valued U-Net training model is utilized to eliminate redundant frequency components generated by zero interpolation, thereby achieving the frequency reconstruction of micro-motion signal echoes. Finally, the training models are employed to process the measured data. The theoretical analysis, simulations, and experimental results demonstrate that this method is robust and feasible, and is capable of addressing the problem of micro-motion signal echo spectrum aliasing in narrowband radar.

Accuracy Improvement of High-Resolution Wide-Swath Spaceborne Synthetic Aperture Radar Imaging with Low Pule Repetition Frequency

For a single-channel spaceborne synthetic aperture radar (SAR), the usage of a low pulse repetition frequency (PRF) is an effective technical way to extend the range swath. The sub-aperture imaging strategy is usually used to solve the problem of azimuth spectrum aliasing under the condition of a low PRF. However, the required up-sampling processing before the coherent synthesis of sub-images will lead to spectrum discontinuity between adjacent sub-images, which leads to an obvious grating lobe phenomenon after the process of sub-image synthesis, resulting in a significant decrease in image quality. For this issue, a high-resolution wide-swath (HRWS) imaging algorithm for a spaceborne SAR with a low PRF is proposed in this paper based on optimal spectrum shift processing. First, each sub-aperture is imaged using the typical range migration algorithm (RMA), and then all sub-images are up-sampled at the same time. Then, based on the criterion of the minimum grating lobe, the optimal spectrum shift is estimated. Finally, the spectrum of all sub-images is shifted and then all the shifted sub-images are synthesized coherently. The simulation data processing results verify the effectiveness of the proposed method.

Air gap eccentric analysis and fault detection of traction motor

To solve the problem of air gap eccentric fault of traction motor, the fault characteristic frequency is close to the fundamental frequency, and the decomposed frequency affects each other, which is easy to cause spectrum aliasing. A reconstruction of variational mode decomposition method is proposed (reconstructed variational mode decomposition, RVMD); first of all, to construct and solve the variational stator current signal problem, to find the best decomposition number, and to obtain multiple modal functions, and to realize the effective separation and frequency profile of each component of the signal. Then, the decomposed modal function components with different frequencies and different amplitude can keep the decomposed positions unchanged and be reconstructed to form a new frequency spectrum. Experimental results show that the proposed RVMD method can detect weak faults timely and effectively, and has good application value.

An improved range-interpolation-free PFA for bistatic synthetic aperture radar based on the principle of chirp scaling

In this paper, an improved range-interpolation-free polar format algorithm (PFA) is proposed for the bistatic synthetic aperture radar (SAR). As an alternative solution to the range spatial frequency resampling of the classic bistatic PFA, the conventional range-frequency scaling transformation (CRST) provides a further explanation of the range resampling of the bistatic PFA from the perspective of range-azimuth decoupling. Nevertheless, CRST cannot be taken as the perfect equivalence to the range resampling of the PFA for its inalterable output spacing of the range spatial frequency. Besides, CRST can be implemented by the principle of chirp scaling (PCS). The scaled range frequency may exceed the observed frequency band, which will cause range spectrum aliasing. To solve the above problems, we propose an improved range-frequency scaling transformation (IRST), which has the same alterable range spatial frequency output spacing as the classic PFA. Further, the PCS-based IRST is also given. The aliased spectrum localization criterion is defined to avoid spectrum aliasing according to the relation between the range frequency and the observed frequency band after IRST. Analyses and simulations are executed to demonstrate the effects of the proposed algorithm.

Target Measurement in Radio Frequency Simulation Using Code-Interrupted Transmitting and Receiving of Pulse Signals

The interrupted transmitting and receiving (ITR) has been utilized in radio frequency simulation to conduct target measurement with pulse signal. Because the ITR results in partly missing of pulse signal, the spectrum aliasing occurs and the target range profile is difficult to be obtained. Therefore, frequency domain filtering and sparse reconstruction are proposed to recover the target range profile. However, frequency domain filtering is ineffective when wideband signal is utilized. The calculation of sparse reconstruction is complex and the reconstruction performance may be poor for some cases of ITR parameters. To solve this problem, the code-interrupted transmitting and receiving (code-ITR) of pulse signal is proposed in this paper. Firstly, the ITR sequences is coded according the duty ratio of each sub-pulse. Secondly, the echo combination and cancellation are processed to eliminate the false peaks in the range profile of ITR echo. By using the code-ITR and echo processing method, the range profile can be obtained for target measurement. Simulations and experiments are performed to verify the effectiveness of the proposed method.

Impact of resampling interpolation FIR filter in the practical Kramers-Kronig receiver.

The practical Kramers-Kronig (KK) receiver has been a competitive receiving technique in the data-center, medium reach, and even long-haul metropolitan networks. Nevertheless, an extra digital resampling operation is required at both ends of the KK field reconstruction algorithm due to the spectrum broadening caused by adopting the nonlinear function. Generally, the digital resampling function can be implemented by using linear interpolation (LI-ITP), the Lagrange cubic interpolation (LC-ITP), the spline cubic interpolation (SC-ITP), time-domain anti-aliasing finite impulse response (FIR) filter method (TD-FRM) scheme, and fast Fourier transform (FFT)-based scheme. However, the performance and the computational complexity analysis of different resampling interpolation schemes in the KK receiver have not been thoroughly investigated yet. Different from the interpolation schemes of conventional coherent detection, the interpolation function of the KK system is followed by the nonlinear operation, which will broaden the spectrum significantly. Due to the frequency-domain transfer function of different interpolation schemes, the broadened spectrum will have a potential spectrum aliasing, which will cause serious inter-symbol interference (ISI) and further impair the KK phase retrieval performance. We experimentally investigate the performance of different interpolation schemes under different digital up-sampling rates (i.e. the computational complexity) as well as the cut-off frequency, the tap number of the anti-aliasing filter, and the shape factor of the TD-FRM scheme in a 112-Gbit/s SSB DD 16-QAM system over 1920-km Raman amplification (RFA)-based standard single-mode fiber (SSMF). The experimental results involve that the TD-FRM scheme outperforms other interpolation schemes and the complexity is reduced by at least 49.6%. In fiber transmission results, take 20% soft decision-forward error correction (SD-FEC) of 2×10-2 as the threshold, the LI-ITP and LC-ITP schemes only reach 720-km while others can reach up to 1440-km.

Scattering characteristics of electrically large arbitrarily shaped targets illuminated by an off-axis vortex electromagnetic beam

For the application of vortex electromagnetic (EM) beams in practical detection scenes, the scattering characteristics of electrically large arbitrarily shaped targets illuminated by an off-axis Laguerre–Gaussian (LG) vortex beam are investigated and compared to the on-axis incidence case. The vector potential method is used to extract the electric and magnetic field components of the LG beam in different polarization states. The physical optics algorithm is adopted to calculate the scattering fields of four typical targets with the shape of a sphere, NASA almond, blunt cone, and blade model. The results revealed that as the beam center offset and the topological charge of the incident vortex beam increase, the scattering field distorts, and the obvious orbital angular momentum (OAM) spectrum mixing occurs. In addition, OAM spectrum aliasing occurs for asymmetric targets, even at on-axis incidence. These results elucidate the mechanism of vortex EM scattering and provide a reference for applying vortex beams for target detection and recognition.

An Efficient Digital Channelized Receiver for Low SNR and Wideband Chirp Signals Detection

Synthetic aperture radar (SAR) is essential for obtaining intelligence in modern information warfare. Wideband chirp signals with a low signal-to-noise ratio (SNR) are widely used in SAR. Intercepting low-SNR wideband chirp signals is of great significance for anti-SAR reconnaissance. Digital channelization technology is an effective means to intercept wideband signals. The existing digital channelization methods have the following problems: the contradiction of reception blind zone and signal spectrum aliasing, high computational complexity, and low estimating accuracy for chirp signals with a low SNR. This paper proposes a non-critical sampling digital channelized receiver architecture to intercept chirp signals. The receiver architecture has no blind zone in channel division and no aliasing of signal spectrum in the channel, which can provide reliable instantaneous frequency measurements. An adaptive threshold generation algorithm is proposed to detect signals without prior information. In addition, an improved instantaneous frequency measurement (IFM) algorithm is proposed, improving low SNR chirp signals’ frequency estimation accuracy. Moreover, a simple channel arbitration logic is proposed to complete the cross-channel combination of wideband signals. Simulations show that the proposed receiver architecture is reliable and robust for low SNR and wideband chirp signal detection. When the input SNR is 0 dB, the absolute frequency root-mean-square error (RMSE) of bandwidth and the center frequency is 0.57 MHz and 1.05 MHz, respectively. This frequency accuracy is great for radio frequency (RF) wideband systems.