Frequency Domain Processing Research Articles

Spectral Hong–Ou–Mandel Interference between Independently Generated Single Photons for Scalable Frequency‐Domain Quantum Processing

AbstractThe photon's frequency degree of freedom, being compatible with mature telecom infrastructure, offers large potential for the stable and controllable realization of photonic quantum processing applications such as the quantum internet. The Hong–Ou–Mandel effect, as a two‐photon interference phenomenon, serves as a central building block for such frameworks. A key element yet missing to enable meaningful frequency‐based implementations as well as scalability in the number of processed photons, is the demonstration of the Hong–Ou–Mandel effect between independently created photons of different frequencies. The experimental implementation of bosonic and fermionic frequency domain Hong–Ou–Mandel interference between independently generated single photons is reported here, with measured visibilities of 74.31% ± 3.56% and 86.44% ± 8.27%, respectively. This is achieved through a scalable photonic frequency circuit that creates two post‐selected pure single photons, which undergo frequency mixing at an electro‐optic phase modulator. The system is on‐the‐fly reconfigurable allowing to probe bosonic and fermionic Hong–Ou–Mandel interference in the same experimental setup. The work demonstrates the versatility of frequency domain processing and its scalability toward higher photon numbers, which enables new quantum gate concepts as well as the establishment of frequency‐based large‐scale quantum networks.

Distributed Nonlinear Polynomial Graph Filter and Its Output Graph Spectrum: Filter Analysis and Design

While frequency-domain algorithms have been demonstrated to be powerful for conventional nonlinear signal processing, there is still not much progress in literature dedicated to nonlinear graph signal processing in frequency domain. The difficulties come from the irregular structure of graph signals and the lack of a straightforward description for the nonlinear relationship between input and output graph signals. In this paper, a distributed nonlinear polynomial graph filter (NPGF) is proposed to characterize the nonlinear input-output relationship by employing polynomial-type nonlinearity based on Hadamard product. Then, the nonlinear output graph signal is reformulated based on the multi-dimensional inverse graph Fourier transform (GFT), where the m-dimensional GFT coefficients are defined as explicit functions of input graph spectrum and filter structural factors (filter parameters, graph shift matrix, nonlinear degree, and graph shift order). The effects of filter structural factors on the output graph spectrum are further evaluated by proposing graph frequency response (GFR) coefficients, which inherently characterize the irregular structural behaviors of a distributed NPGF in frequency domain. The nonlinear output graph spectrum is then developed based on GFR vectors by mapping the GFR coefficients in the tensor formulation to the output GFT coefficients in the vector expression. This can greatly improve the efficiency in calculating the output graph signal if the input signal only involves a few frequency components. Finally, algorithms are proposed to design the filter parameters for the desired output signal. Numerical studies are presented to illustrate and validate the proposed frequency-domain framework for nonlinear graph signal processing.

Fusion Fault Diagnosis Model for Six-Rotor UAVs Based on Conformal Fourier Transform and Improved Self-Organizing Feature Map

If the fault sources can be located in a timely and accurate manner when an unmanned aerial vehicle (UAV) has an early minor fault, a major accident can be avoided. In light of the early fault of the six-rotor UAV motors, this paper proposes a fusion fault diagnosis model based on Conformal Fourier Transform (CFT) and the improved Self-Organizing Feature Map (SOM) neural network. Firstly, to overcome the weakening of UAV fault information caused by external interference and solve the problem that the non-uniform distribution of the collected flight data affects the accuracy of the frequency domain processing, on the basis of changing the processing method of the Fourier integral kernel and using high-order numerical integration, an improved Conformal Fourier Transform (CFT) algorithm optimized by spectrum refinement strategy is proposed. Then this algorithm is used to further intensify the main features and build a clear fault state in a cycle processing method. Secondly, an improved SOM neural network is designed. We use the unweighted average distance (UPGMA) of the agglomerative hierarchical clustering algorithm to detect the clustering areas of each pattern category of the data samples, and the weight vectors of different clustering areas are used to randomly initialize the connection weights of SOM network, thereby improving the clustering speed and convergence effect. On this basis, CFT algorithm is integrated into the improved SOM network to realize the multi-module collaboration strategy and finally form a new fusion fault diagnosis model.

Accurate determination of random pattern phase in structured illumination microscopy with low modulation depth

The initial phase of structured illumination is an important parameter in structured illumination microscopy (SIM). Its estimation accuracy directly affects the reconstruction quality of SIM super-resolution images. However, when the modulation of the system is less than 0.02, the current phase estimation algorithm will cause an estimation error above 0.2 rad. An algorithm based on multi-image correlation processing in frequency domain (MCF) is proposed to solve this problem. Simulation and experimental results show that the MCF algorithm greatly improves both the initial phase estimation accuracy and the reconstruction quality of super-resolution images for low modulation SIM systems with a random phase shift. This means that the MCF algorithm can extend the scope of the SIM technology, especially for low modulation systems or systems lacking precise phase-shifting components.

Using constructed impulse responses to study the influence of sound speed profiles on outdoor acoustic propagation

Time-domain predictions can be accomplished by either explicitly calculating within the time domain, such as with the Finite-Difference, Time-Domain method, or by processing frequency-domain calculations into impulse responses. While the FDTD method has been used extensively in outdoor sound propagation studies, the requirement for extensive computational resources greatly limits the computational domain. The impulse response method, while well-utilized in underwater sound propagation has seen limited use in outdoor sound studies. For a given environmental scenario, the impulse response may be obtained from the inverse Fourier transform of transmission loss simulations in the frequency-domain. When it is convolved with the time variation of the source, the receiver signal may be readily predicted. One may re-use the impulse response for any new source, so long as the sampling criteria are met, and the source and receiver positions and environment match those of the modeled situation. A discussion of the implications of frequency resolution and example comparisons to measurements are presented. [This work was funded by the Assistant Secretary of the Army (Acquisition, Logistics, and Technology) [ASA(ALT)] with portions funded under 0602784/T40/24 and 0602146/AR9/01. Distribution Statement A: Approved for public release; Distribution is unlimited.]

Acoustic analysis of a single-cylinder diesel engine using magnetized biodiesel-diesel fuel blends

Fuels have important effects on the quality parameters of engines such as noise pollution and vibration. Diesel fuel are used in wide range of applications especially in compression ignition engines. The objective of the present research is evaluation of the noise emitted from a single-cylinder diesel engine using magnetized biodiesel-diesel fuel blends. In general, samples were provided with different percentages of the biodiesel-diesel blends as diesel (100, 95, 90, and 80%) and biodiesel (0, 5, 10, and 20%) by applying magnetic field (0, 5300 and 7000 G) to fuel line known as DxByMz. The measurements were done on a power tiller engine at a 10 cm distance from driver ear with three replications. The statistical approach in time domain and signal processing in frequency domain were applied for data analysis. The results of the variance analysis approved significant differences between the studied fuel blends and magnetic levels at 1% probability level. The highest and lowest average value of sound pressure level was corresponded to D100B0M0 and D80B20M5300, respectively. The results in frequency domain showed that the maximum sound pressure level values were in the frequency range of 31.5–200 Hz for all fuel blends and magnetic levels. The frequencies related to the maximum sound values varied by changing biodiesel percent and magnetic level.

Analysis of Human-Land Coupled Bearing Capacity of Qiangtang Meadow in Northern Tibet Based on Fuzzy Clustering Algorithm

Aiming to address the problems of high energy consumption, low efficiency, low correlation between the analyzed and actual results, and poor rationality of research indexes in current methods of analysis of human-land coupled bearing capacity of meadows, a novel method of human-land coupled bearing capacity analysis of Qiangtang meadow in northern Tibet, based on fuzzy clustering algorithm, is proposed. Basic geographic information data in Tibet were acquired, the collected data images were registered by ENVI4.2 software, and the collected data were vectorized by ArcGIS 9.3 software to construct a basic geographic information database in Tibet. Based on the frequency domain processing algorithm, the geographic information image was suppressed by noise and filtered by using a high-pass filter to realize the geographic information data processing in the study area. The human-land coupled bearing capacity analysis of Qiangtang meadow in northern Tibet was evaluated through fuzzy clustering, bearing capacity evaluation, and bearing capacity calculation under the sharing of closure. The experimental results showed that the average running energy consumption of the method was 81 J, and 97% of the analyzed results were consistent with the actual situation. These results indicate that the operation efficiency of the method is high, and the rationality coefficient of the research index is large. The proposed method has superior performance and feasibility.

Frequency-Domain Quantum Interference with Correlated Photons from an Integrated Microresonator.

Frequency encoding of quantum information together with fiber and integrated photonic technologies can significantly reduce the complexity and resource requirements for realizing all-photonic quantum networks. The key challenge for such frequency domain processing of single photons is to realize coherent and selective interactions between quantum optical fields of different frequencies over a range of bandwidths. Here, we report frequency-domain Hong-Ou-Mandel interference with spectrally distinct photons generated from a chip-based microresonator. We use four-wave mixing to implement an active "frequency beam splitter" and achieve interference visibilities of 0.95±0.02. Our work establishes four-wave mixing as a tool for selective high-fidelity two-photon operations in the frequency domain which, combined with integrated single-photon sources, provides a building block for frequency-multiplexed photonic quantum networks.

Application of two-dimensional fast Fourier transform algorithm, analog of the Cooley-Tukey algorithm, for 4k fixed format digital image of satellite data in frequency domain processing

Currently, digital images in the format Full HD (1920 * 1080 pixels) and 4K (4096 * 3072) are widespread. This article will consider the option of processing a similar image in the frequency domain. As an example, take a snapshot of the earth's surface. The discrete Fourier transform will be computed using a two-dimensional analogue of the Cooley-Tukey algorithm and in a standard way by rows and columns. Let us compare the required number of operations and the results of a numerical experiment. Consider the examples of image filtering.

User Grouping for the Uplink of Multiuser Hybrid mmWave MIMO

Hybrid analog/digital schemes for precoding/combining have proved to be a low-complexity and/or low-power strategy to obtain reasonable beamforming gains in multiuser millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems. Hybrid precoding/combining performs jointly baseband processing and analog processing in the radio frequency (RF) domain. In these systems, the number of RF chains limits the maximum number of streams simultaneously handled by the transceivers. In the uplink of a multiuser mmWave MIMO system, the hardware reduction based on hybrid transceivers is limited by the number of data streams that must be simultaneously served by the centralized node. Most works approach hybrid transceiver design by considering more RF chains than data streams, an unrealistic assumption when the number of nodes is large. On the other hand, statistically independent information is conventionally assumed in multiuser mmWave systems. This assumption does not hold in scenarios like wireless sensor networks (WSNs), where the sources produce correlated information. In this paper, by enabling inter-user correlation exploitation, we propose a grouping approach to handle a high number of individual sources with a limited number of RF chains through distributed quantizer linear coding (DQLC) mappings. The allocation of the users per group and the hybrid design of the combiner at the common central node to serve the grouped users is also analyzed. We also propose a hybrid minimum mean square error (MMSE) combining design in order to exploit the spatial correlation between the sources in a conventional uncoded mmWave uplink. Simulation results show the performance advantages of the proposed approaches in various hardware-constrained system settings.

Convolutional PCA for Multiple Time Series

We study a fundamental generalization of principal component analysis (PCA) that looks for a small set of common time series, i.e., principal components (PCs), whose filtered versions can explain most of the variances of multiple observed time series. This problem boils down to PCA in the frequency domain, in principle. But, frequency domain processing suffers from aliasing, and brings inconveniences when handling certain time domain properties like nonstationarity, and sparsity. We propose novel time, and $z$ -domain costs for such PCA, and study its properties in detail with setting of either finite or diverging filter lengths. We further discuss its implementations, and possible extensions, and present numerical results for empirical performance study. Convolution is used to extract these PCs, thus the name convolutional PCA.

Downlink Sum-Rates of SC-FDP and OFDM Massive MIMO Systems in Doubly Dispersive Channels

We investigate channel double dispersiveness in downlink of a massive multiple input multiple output system which operates in time division duplex (TDD) mode. We examine single carrier frequency domain processing (SC-FDP) and orthogonal frequency division multiple access (OFDM). In four scenarios. In the first scenario, which is the comprehensive scenario, we consider both the channel aging and channel estimation error effect due to Doppler Frequency. Therefore, we assume to have knowledge of the estimated channel in the previous block which was estimated in presense of Doppler shifts and noise. The other three scenarios are special cases of the first scenario which are studied to have a better insight on the Doppler effects on massive MIMO systems. In the second scenario the system is subject to both channel aging and channel estimation errors, but the channel estimation error is model with Gaussian noise. In the second scenario, we focus only on channel aging effect. In the fourth scenario, to investigate only the impact of channel time variation within the block duration, we assume perfect channel state information (CSI) with no channel aging. The results indicate that in all the scenarios, SC-FDP achieves higher sum-rate than OFDM. For the first scenario the sum-rate of both systems get bounded as the number of BS antennas tends to infinity. However, for the other three cases the sum-rate of SC-FDP, unlike OFDM, increases unboundedly as we increase the number of BS antennas. The results from the block error rate (BLER) studies validate the sum-rate results.

A Time-Domain Approach to Channel Estimation and Equalization for the SC-FDM System

Similar to orthogonal frequency division multiplexing receiver, the frequency-domain (FD) channel estimation (CE) and equalization are indispensable parts in the coherent single carrier frequency division multiplexing (SC-FDM) receiver. When the channel varies slowly, the FD processing is cost effective. For the applications with high mobility, the traditional implementation of the SC-FDM receiver causes significant performance degradation. In this paper, we propose to estimate time-varying pieces of channel taps for pilot symbols based on basis expansion model (BEM), and subsequently to reconstruct time-domain (TD) channel response for data symbols by utilizing the Slepian sequences-based piece-wise interpolation. Furthermore, two simplified schemes, i.e., the Slepian sequences-based multiple-point interpolation and the segmented BEM, are developed to reduce the computational complexity of the TD-CE. The Cramer-Rao lower bound (CRLB) of channel impulse response (CIR) estimation is also analyzed. In the light of the sparsity of TD channel gain matrix, we design an iterative least-squares QR decomposition algorithm to equalize the SC-FDM symbols. In the simulated SC-FDM system, when considering the carrier frequency of 5.9 GHz and the velocity of about 510 km/h, we observe that the traditional FD methods cause the demodulation failure, while the proposed TD processing schemes achieve ideal error-probability performance and preserve a relatively low complexity.

Partial FFT Demodulation With IRC in MIMO-SC-FDE Communication Over Doppler Distorted Underwater Acoustic Channels

Multi-input multi-output single carrier frequency domain equalization (MIMO-SC-FDE) has been extensively researched in the past years as a technique to realize high data-rate underwater acoustic (UWA) communication. However, it will suffer from severe inter-symbol interference(ISI), frequency offset and co-channel interference (CoI) over Doppler distorted UWA channels. In order to solve the above problems introduced by UWA channels in MIMO communication scenario, partial FFT demodulation with interference rejection combining (IRC) algorithm is proposed in this letter. Compared with previous works, the proposed algorithm has the ability to simultaneously suppress signal distortion brought by ISI, Doppler shift and CoI by frequency domain processing. Numerical simulation results show that the BER performance of MIMO-SC-FDE in Doppler distorted UWA channel environment is improved with acceptable increase of computational complexity.

High-dimensional feature extraction of sea clutter and target signal for intelligent maritime monitoring network

As one of the source sensors of maritime intelligent traffic network, radar plays an important role in maritime monitoring and early warning. The number of features extracted by the traditional maritime radar target detection method in feature domain is small, and the sea clutter and target echo features are often not linearly separable, so the radar detection performance is seriously affected by sea clutter. To solve this problem, this paper combines the time–frequency domain processing method with the residual neural network, and uses the time–frequency transform method to improve the signal-to-clutter ratio (SCR) and the degree of difference between sea clutter and target echo. On this basis, the high-dimensional time–frequency spectrum features are extracted by using the residual neural network to improve the utilization rate of radar echo information, form a high-dimensional feature space of sea clutter and target echo that are non-linearly separable, and realize the binary classification of sea clutter and target echo. It is verified by the measured data of X-band radar that the proposed target detection method can extract the deep features of the time–frequency spectrum of radar echo, has a high classification accuracy even in the case of low SCR, and has the potential to detect weak targets in the background of strong sea clutter. In addition, the influence of different time–frequency transform methods and polarization modes on target detection performance is further analyzed. The comparative study shows that different time–frequency transform methods and polarization modes have little influence on the classification accuracy of the proposed method. In comparison, under the conditions of fractional Fourier transform and cross-polarization, the proposed method has higher classification accuracy.

Complex and Hypercomplex-Valued Support Vector Machines: A Survey

In recent years, the field of complex, hypercomplex-valued and geometric Support Vector Machines (SVM) has undergone immense progress due to the compatibility of complex and hypercomplex number representations with analytic signals, as well as the power of description that geometric entities provide to object descriptors. Thus, several interesting applications can be developed using these types of data and algorithms, such as signal processing, pattern recognition, classification of electromagnetic signals, light, sonic/ultrasonic and quantum waves, chaos in the complex domain, phase and phase-sensitive signal processing and nonlinear filtering, frequency, time-frequency and spatiotemporal domain processing, quantum computation, robotics, control, time series prediction, and visual servoing, among others. This paper presents and discusses the importance, recent progress, prospective applications, and future directions of complex, hypercomplex-valued and geometric Support Vector Machines.

Real-time optical properties and oxygenation imaging using custom parallel processing in the spatial frequency domain.

The development of real-time, wide-field and quantitative diffuse optical imaging methods is becoming increasingly popular for biological and medical applications. Recent developments introduced a novel approach for real-time multispectral acquisition in the spatial frequency domain using spatio-temporal modulation of light. Using this method, optical properties maps (absorption and reduced scattering) could be obtained for two wavelengths (665 nm and 860 nm). These maps, in turn, are used to deduce oxygen saturation levels in tissues. However, while the acquisition was performed in real-time, processing was performed post-acquisition and was not in real-time. In the present article, we present CPU and GPU processing implementations for this method with special emphasis on processing time. The obtained results show that the proposed custom direct method using a General Purpose Graphic Processing Unit (GPGPU) and C CUDA (Compute Unified Device Architecture) implementation enables 1.6 milliseconds processing time for a 1 Mega-pixel image with a maximum average error of 0.1% in extracting optical properties.

Method for pests detecting in stored grain based on spectral residual saliency edge detection

Abstract Pests detecting is an important research subject in grain storage field. In the past decades, many edge detection methods have been applied to the edge detection of stored grain pests. Although some of them can realize the stored grain pests detecting, precision and robustness are not good enough. Spectral residual (SR) saliency edge detection defines the logarithmic spectrum of image as novelty part of the image information. The remaining spectrum is converted to the airspace to obtain edge detection results. SR algorithm is completely based on frequency domain processing. It not only can effectively simplify the target detection algorithm, but also can improve the effectiveness of target recognition. The experimental results show that the edge results of stored grain pests detected by SR method are effective and stable.

Iterated extended Kalman filter for airborne electromagnetic data inversion

ABSTRACTThe iterated extended Kalman filter (IEKF) is a tool within the theory of optimal estimation used for nonlinear problems. The IEKF minimises variance in the estimation error in terms of a probabilistic approach. Despite the special terminology, the Kalman filter algorithm minimises the objective function, representing the normalised squared difference between the measured and calculated vectors for the parameters of a selected model. It works like the weighted least squares method – a conventional method for airborne electromagnetic data inversion. In this article, I describe the essence of the Kalman approach to solving inverse problems. I show how one-dimensional inversion with lateral constraints can be performed in terms of the Kalman filter. The described algorithm takes account of the measurement noise, which is specified as the dispersion of signals in the corresponding measurement channels at high altitude. A specific covariance matrix representation allows use of the corresponding Kalman filter calculation methods. They provide numerical stability of the algorithm. The Kalman approach makes it possible to combine modern techniques used in airborne survey data processing. Some examples of Kalman filter use in frequency-domain airborne data processing are given.

Evaluation of Acoustic Emission Source Location in Long Steel Pipes for Continuous and Semi-continuous Sources

Acoustic emission (AE) is a commercially-available technique used for structural health monitoring in large structures such as pipeline systems. It is a passive technique that relies on AE and can be generated in continuous and/or burst form (semi-continuous), recorded at one or more sensors with known positions. In truly continuous emission, the source has little or no temporal structure, making it difficult to identify the departure time of a source. In this research, the focus of the analysis was to evaluate distortions of AE continuous and semi-continuous sources in time and frequency domains and to examine how attenuation compares with a discontinuous on long steel pipe. Two different methods have generated artificial, relatively white, sources; continuous AE from a compressed air jet, and semi-continuous signals using a solenoid valve to modulate the air jet. Several arrays have been used to study axial and circumferential propagation, and a combination of time (energy-based) and frequency (time-based) domain processing has been used to develop generic approaches for source location. It is concluded that an energy-based technique combining a digital filter applied to the more heavily attenuated spectral component is more effective in location continuous emission, while semi-continuous signals are more effectively dealt with using cross-correlation applied to a less heavily attenuated spectral component to determine the arrival time of a recognizable time segment. Moreover, it has been observed that the distinction between axial and circumferential propagation of AE is less significant in long pipes.