Frequency Invariance Research Articles

Robust wideband beamforming algorithm based on frequency difference technique

This paper investigates a novel robust wideband beamforming algorithm based on the frequency-difference (FD) technique. While FD technique can maintain good frequency invariance (FI) of the beamformer, it introduces cross terms that can adversely affect performance. To reduce the cross terms, a projection preprocessing is implemented prior to FD operation exploiting the approximate orthogonality between steering vectors (SVs). Then, a robust beamformer is designed based on the estimated cross terms covariance matrix (CTCM) and SV of the signal of interest (SOI). The output of beamformer is an FD SOI. To restore the SOI, we design a filtering system and apply a simple diagonal loading beamforming to obtain the amplitude and phase of SOI, respectively. The simulation results have verified the effectiveness and superiority of the proposed algorithm in the presence of array errors.

Sparse microphone array design for frequency-invariant beamforming via group [formula omitted]-norm optimization

Frequency-invariant (FI) beamforming aims at recovering signals without any distortion and maintaining spatial selectivity over the entire bandwidth. However, most existing FI beamforming (FIB)methods consider the weighted ℓ1-norm or modified ℓ1-norm of the filters as the objective function for sparse FIB design, which cannot assure the optimal sparse solution. To deal with this drawback, an optimization problem for the FIB design of sparse microphone array in terms of ℓp-norm (0<p<1) minimization is formulated, where distortion-less response, mainlobe and sidelobe constraints are considered. Due to the existence of the ℓp-norm objective function, the resultant problem is nonconvex, and therefore, an alternating direction method of multipliers (ADMM) algorithm is devised. Specifically, the corresponding problem is decomposed into multi-block subproblems to determine all unknown variables separately. Then, the most dominant sensor positions for each frequency are determined by using the principal component analysis (PCA) and K-mean clustering algorithm. Numerical examples show that the proposed design achieves good directivity factor, frequency invariance and better sparsity.

Gulls in Porto Coastline as Reservoirs for Salmonella spp.: Findings from 2008 and 2023.

Gulls act as intermediaries in the exchange of microorganisms between the environment and human settlements, including Salmonella spp. This study assessed the antimicrobial resistance and molecular profiles of Salmonella spp. isolates obtained from fecal samples of gulls in the city of Porto, Portugal, in 2008 and 2023 and from water samples in 2023. Antimicrobial susceptibility profiling revealed an improvement in the prevalence (71% to 17%) and antimicrobial resistance between the two collection dates. Two isolate collections from both 2008 and 2023 underwent serotyping and whole-genome sequencing, revealing genotypic changes, including an increased frequency in the monophasic variant of S. Typhimurium. qacE was identified in 2008 and 2023 in both water and fecal samples, with most isolates exhibiting an MDR profile. The most frequently observed plasmid types were IncF in 2008 (23%), while IncQ1 predominated in 2023 (43%). Findings suggest that Salmonella spp. circulate between humans, animals, and the environment. However, the genetic heterogeneity among the isolates from the gulls' feces and the surface water may indicate a complex ecological and evolutionary dynamic shaped by changing conditions. The observed improvements are likely due to measures to reduce biological contamination and antimicrobial resistance. Nevertheless, additional strategies must be implemented to reduce the public health risk modeled by the dissemination of pathogens by gulls.

Interpretation of presynaptic phenotypes of synaptic plasticity in terms of a two-step priming process.

Studies on synaptic proteins involved in neurotransmitter release often aim at distinguishing between their roles in vesicle priming (the docking of synaptic vesicles to the plasma membrane and the assembly of a release machinery) as opposed to the process of vesicle fusion. This has traditionally been done by estimating two parameters, the size of the pool of fusion-competent vesicles (the readily releasable pool, RRP) and the probability that such vesicles are released by an action potential, with the aim of determining how these parameters are affected by molecular perturbations. Here, it is argued that the assumption of a homogeneous RRP may be too simplistic and may blur the distinction between vesicle priming and fusion. Rather, considering priming as a dynamic and reversible multistep process allows alternative interpretations of mutagenesis-induced changes in synaptic transmission and suggests mechanisms for variability in synaptic strength and short-term plasticity among synapses, as well as for interactions between short- and long-term plasticity. In many cases, assigned roles of proteins or causes for observed phenotypes are shifted from fusion- to priming-related when considering multistep priming. Activity-dependent enhancement of priming is an essential element in this alternative view and its variation among synapse types can explain why some synapses show depression and others show facilitation at low to intermediate stimulation frequencies. Multistep priming also suggests a mechanism for frequency invariance of steady-state release, which can be observed in some synapses involved in sensory processing.

Accurate Spatial-Frequency Response Controllable Frequency Invariant Beampattern Synthesis With Minimum Beamwidth

This communication proposes a new relaxation variable based cost function for the problem of frequency invariant (FI) beampattern synthesis. Two constraints in the spatial and frequency domains are imposed on the optimization problem. The objective of sparsifying the relaxation variable is exploited in constructing the constraint in the spatial domain, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -spatial response variation (SRV) is introduced in the frequency domain constraint to reduce frequency variance. These constraints enable a desirable trade-off between beamwidth and FI properties while achieving accurate spatial-frequency response control. Since the resulting optimization problem is sparse and non-convex, it is then proposed to be solved by exploiting the reweighted- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm in this paper. The remarked feature of the new approach is the improved target detection and anti-interference performance in radar and communication systems without waveform distortion. Simulation results validate the effectiveness of the proposed method.

An optimization method for frequency-invariant beamforming with arbitrary sensor arrays

This paper proposes a beampattern optimization method for frequency-invariant beamforming with arbitrary sensor arrays, which is an extension of the previously proposed method for circular sensor arrays. Based on the criterion of minimizing the mean square error between the synthesized beampatterns at each frequency and the desired beampattern, the relationship between the weighting vectors and the desired weighting vector can be accurately obtained. Then, the relevant performance parameters, such as the directivity factor, error sensitivity function and minimum mean square error, can all be expressed as the accurate closed-form functions of the desired weighting vector. With the above conclusions, a multi-constraint optimization problem is formulated to calculate the optimal desired weighting vector under different constraints. The optimal frequency-invariant beampatterns and their performance parameters can be readily achieved using the derived functions. Thus, the proposed method can not only obtain the optimal desired weighting vector, but also achieve the broadband frequency-invariant beampatterns with only one optimization calculation of the desired weighting vector. Simulations and experimental results show that the proposed method can provide a good trade-off among the directivity, robustness, and frequency invariance.

Synthesis of Wideband Frequency-Invariant Beam Patterns for Nonuniformly Spaced Arrays by Generalized Alternating Projection Approach

This work generalizes the alternating projection approach (APA) to synthesize wideband frequency-invariant (FI) beam patterns for linear nonuniformly spaced arrays (NUSAs). Different from the conventional APA where excitation weights are synthesized for a desired pattern at single frequency, the generalized APA intends to find appropriate finite-impulse response (FIR) filter coefficients for each antenna element to provide the required wideband frequency-dependent excitation for a desired wideband FI pattern, and two modification techniques called mainlobe FI modification and wideband sidelobe control are introduced in each iteration to successively update the FI pattern performance. Several examples for synthesizing wideband FI beam patterns for NUSAs in different applications are conducted to verify the effectiveness and advantages of the proposed generalized APA.

Synthesizing Wideband Frequency-Invariant Shaped Patterns by Linear Phase Response-Based Iterative Spatiotemporal Fourier Transform

A new approach for synthesizing wideband frequency-invariant (FI)-shaped patterns is presented. This method is a significant extension of the original iterative spatiotemporal Fourier transform (STFT) method that only deals with wideband FI pencil-beam patterns. Based on the original method, the wideband pattern can be regarded as a spatiotemporal spectral distribution, and the relationship between the spatiotemporal spectral distribution and finite-impulse-response (FIR) filter coefficients can be built as an STFT, which can be efficiently calculated by using 2-D fast Fourier transform (2-D-FFT). To achieve desired FI-shaped pattern performance, the spatiotemporal spectral distribution is iteratively adjusted by two new techniques called wideband pattern shaping and linear phase response (LPR)-based modification. Different from the constant phase response (CPR) processing in the original iterative STFT method, the LPR-based modification uses more relaxed phase requirements, thus releasing much more degrees of freedom. Numerical results show that the proposed method is effective even for very complicated pattern requirements, and it is very efficient in terms of both computation and storage. Besides, the proposed method can take into account the effects of frequency-variant antenna element patterns and mutual coupling in the periodic array structure.

Frequency-invariant beamformer design via ADPM approach

Frequency-invariant (FI) beamformers play an important role in suppressing speech waveform distortions. Due to the perfect FI beampattern (FIB), differential microphone arrays (DMAs) have been widely used in practical applications like voice communication and human-machine interface systems. Superdirective beamforming generated by DMAs have many useful properties but suffer white noise amplification. To address this drawback, we formulate a least squares broadband FI problem, under the white noise output power constraints, to improve robustness of superdirective beamformers. The problem is challenging to solve since FI beamformers are designed on broadband and initialization parameters corresponding to each frequency are different. We devise broadband beampattern synthesis algorithm based on alternating direction penalty method (ADPM), which utilizes the relationship between residuals and penalty terms to reduce the iteration number under the improved framework of alternating direction method of multipliers (ADMM). The proposed ADPM method can decompose the optimization problem into multi-block convex optimization problems and solve them separately. The fast convergence property of our solution is demonstrated via numerical simulations.

Drone Detection and Classification Using Physical-Layer Protocol Statistical Fingerprint

We propose a novel approach for drone detection and classification based on RF communication link analysis. Our approach analyses large signal record including several packets and can be decomposed of two successive steps: signal detection and drone classification. On one hand, the signal detection step is based on Power Spectral Entropy (PSE), a measure of the energy distribution uniformity in the frequency domain. It consists of detecting a structured signal such as a communication signal with a lower PSE than a noise one. On the other hand, the classification step is based on a so-called physical-layer protocol statistical fingerprint (PLSPF). This method extracts the packets at the physical layer using hysteresis thresholding, then computes statistical features for classification based on extracted packets. It consists of performing traffic analysis of communication link between the drone and its controller. Conversely to classic drone traffic analysis working at data link layer (or at upper layers), it performs traffic analysis directly from the corresponding I/Q signal, i.e., at the physical layer. The approach shows interesting properties such as scale invariance, frequency invariance, and noise robustness. Furthermore, the classification method allows us to distinguish WiFi drones from other WiFi devices due to underlying requirement of drone communications such as good reactivity in control. Finally, we propose different experiments to highlight theses properties and performances. The physical-layer protocol statistical fingerprint exploiting communication specificities could also be used in addition of RF fingerprinting method to perform authentication of devices at the physical-layer.

Steering Vector Transformation Technique for the Design of Point Sources Wideband Beamforḿer.(Dept.E)

Steering vector transformation technique for wideband antenna array of point sources is presented. Wideband direction of arrival (DoA) estimation using this technique is illustrated. In the present work, steering vector transformation is applied to the conventional frequency domain beamformer to enhance the frequency invariance of the mainlobe pattern. Several simulation examples are presented to illustrate the advantage of the proposed frequency domain beamformer over the conventional one. As the array size increases or the interelement spacing decreases, the proposed beamformer still has a better frequency invariant property of the mainlobe pattern than the conventional beamformer. Finally, using windows, a better frequency invariant property of the mainlobe patter is obtained by the proposed beamformer than the conventional one.

Efficient Synthesis of Filter-and-Sum Array With Scanned Wideband Frequency-Invariant Beam Pattern and Space-Frequency Notching

This work generalizes the Fourier transform (FT)-based frequency-invariant beamforming (FIB) method to the synthesis of scanned frequency-invariant (FI) beam pattern with space-frequency notching for an array with non-isotropic elements. Wideband FI pattern characteristics are described by using multiple reference sub-band FI patterns. By applying fast Fourier transform (FFT) on the combination of these multiple reference sub-band FI patterns, a wideband excitation distribution can be generated. Based on this excitation distribution, we construct a new wideband excitation distribution that is conjugate-symmetric about zero frequency, so that real-valued finite-impulse-response (FIR) filter coefficients can be obtained by applying FFT on the constructed distribution. Two numerical examples are introduced to show the effectiveness and efficiency of the proposed method.

Differential Beamforming From the Beampattern Factorization Perspective

Differential beamformers have demonstrated a great potential in forming frequency-invariant beampatterns and achieving high directivity factors. Most conventional approaches design differential beamformers in such a way that their beampatterns resemble a desired or target beampattern. In this paper, we show how to design differential beamformers by simply taking advantage of the fact that the beampattern is actually a particular form of an exponential polynomial. Thanks to this quite obvious formulation, a target beampattern is not really needed while the zeros of the exponential polynomial and/or its factorization are fully exploited. The advantage of this factorization is twofold. First, it gives the relation between the beamformer and the roots of the polynomial, so the former can be directly determined from the latter, which seems natural and convenient. Second, based on this factorization, we propose a new formulation of the beamforming filter, which decomposes the filter into shorter ones with the Kronecker product. This formulation is very general, and many well-known beamformers such as the differential and delay-and-sum (DS) ones can be derived from it. Furthermore, the new formulation allows one to combine different kinds of beamformers together, which gives a great flexibility in forming different beampatterns and achieving a compromise among the directivity factor (DF), white noise gain (WNG), and frequency invariance.

Wideband frequency-invariant beamforming with dynamic range ratio constraints

This paper focuses on the optimization design of weighting coefficients of Frost-structural beamformer to obtain a frequency-invariant (FI) beampattern. To ensure the normal operation of beamformer in transmitting links with limited dynamic range, the design is modeled by minimizing the weighted sum of the beampattern matching error and spatial response variation under the constraints of dynamic range ratio (DRR) and linear phase. Next, we propose a novel iterative algorithm to solve the resulting high-dimensional non-convex optimization problems via alternately handling a tractable problem and a multi-constrained convex subproblem. To speed up, we reformulate this multi-constrained subproblem into a new alternating direction method of multipliers form with a series of low-dimensional and less-constrained subproblems, and deduce the closed-form solutions to each subproblem. Numerical results exhibit the good convergence of proposed algorithm and the excellent FI of obtained beampattern under the DRR constraints.

Oscillation-Based Connectivity Architecture Is Dominated by an Intrinsic Spatial Organization, Not Cognitive State or Frequency.

Functional connectivity of neural oscillations (oscillation-based FC) is thought to afford dynamic information exchange across task-relevant neural ensembles. Although oscillation-based FC is classically defined relative to a prestimulus baseline, giving rise to rapid, context-dependent changes in individual connections, studies of distributed spatial patterns show that oscillation-based FC is omnipresent, occurring even in the absence of explicit cognitive demands. Thus, the issue of whether oscillation-based FC is primarily shaped by cognitive state or is intrinsic in nature remains open. Accordingly, we sought to reconcile these observations by interrogating the ECoG recordings of 18 presurgical human patients (8 females) for state dependence of oscillation-based FC in five canonical frequency bands across an array of six task states. FC analysis of phase and amplitude coupling revealed a highly similar, largely state-invariant (i.e., intrinsic) spatial component across cognitive states. This spatial organization was shared across all frequency bands. Crucially, however, each band also exhibited temporally independent FC dynamics capable of supporting frequency-specific information exchange. In conclusion, the spatial organization of oscillation-based FC is largely stable over cognitive states (i.e., primarily intrinsic in nature) and shared across frequency bands. Together, our findings converge with previous observations of spatially invariant patterns of FC derived from extremely slow and aperiodic fluctuations in fMRI signals. Our observations indicate that "background" FC should be accounted for in conceptual frameworks of oscillation-based FC targeting task-related changes.SIGNIFICANCE STATEMENT A fundamental property of neural activity is that it is periodic, enabling functional connectivity (FC) between distant regions through coupling of their oscillations. According to task-based studies, such oscillation-based FC is rapid and malleable to meet cognitive task demands. Studying distributed FC patterns instead of FC in a few individual connections, we found that oscillation-based FC is largely stable across various cognitive states and shares a common layout across oscillation frequencies. This stable spatial organization of FC in fast oscillatory brain signals parallels the known stability of fMRI-based intrinsic FC architecture. Despite the observed spatial state and frequency invariance, FC of individual connections was temporally independent between frequency bands, suggesting a putative mechanism for malleable frequency-specific FC to support cognitive tasks.

Multi-Scale and Single-Scale Fully Convolutional Networks for Sound Event Detection

Among various Sound Event Detection (SED) systems, Recurrent Neural Networks (RNN), such as long short-term memory unit and gated recurrent unit, is used to capture temporal dependencies, but it is confined in its length of temporal dependencies, resulting in a failure to model sound events with long duration. What’s more, RNN is incapable to process datasets in parallel, leading to low efficiency and low industrial value. Given these shortcomings, we propose to use dilated convolution (and causal dilated convolution) to capture temporal dependencies, as its great ability to ensure high time resolution and obtain longer temporal dependencies under the filter size and the network depth unchanged. In addition, dilated convolution can be parallelized, so it has higher efficiency and industrial value. Based on this, we propose Single-Scale Fully Convolutional Networks (SS-FCN) composed of convolutional neural networks and dilated convolutional networks, with the former to provide frequency invariance and the later to capture temporal dependencies. With the help of dilated convolution to control the length of temporal dependencies, we observe SS-FCN modeling a single length of temporal dependencies achieves superior detection performance for finite kinds of events. For better performance, we propose Multi-Scale Fully Convolutional Networks (MS-FCN), in which the feature fusion module is introduced to capture long short-term dependencies by fusing features with different length of temporal dependencies. The proposed methods achieve competitive performance on three main datasets with higher efficiency. The results show that SED systems based on Fully Convolutional Networks have further research value and potential.

Efficient and Accurate Frequency-Invariant Beam Pattern Synthesis Utilizing Iterative Spatiotemporal Fourier Transform

An iterative spatiotemporal Fourier transform (STFT) method is presented to efficiently design finite-impulse-response (FIR) filter coefficients for generating a desired frequency-invariant (FI) beam pattern of an antenna array. In this method, by introducing the concepts of normalized temporal angular frequency and spatial angular frequency, the broadband pattern is treated as a spatiotemporal spectral distribution. The relationship between the FIR coefficient distribution and the spatiotemporal spectral distribution can be built as an STFT, and consequently the 2-D fast Fourier transform (2D-FFT) and inverse 2D-FFT (2D-IFFT) can be utilized to efficiently accomplish the transformation between the FIR coefficient distribution and the spatiotemporal spectral distribution. Thus, the proposed synthesis method starts from an initial spatiotemporal spectral distribution and then adopt an iterative modification-and-transformation strategy to successively update the obtained spatiotemporal spectral distribution and the corresponding FIR coefficients. Two kinds of pattern modification techniques including the mainlobe FI modification and broadband sidelobe control are adopted in each iteration. Several examples for synthesizing different FI patterns are conducted. Synthesis results show that the proposed method can obtain much better FI pattern performance in terms of both mainlobe FI property and sidelobe control than the original FT method whilst costing less CPU time than the convex optimization method especially for the case of large FI arrays.

A Slow Short-Term Depression at Purkinje to Deep Cerebellar Nuclear Neuron Synapses Supports Gain-Control and Linear Encoding over Second-Long Time Windows.

Modifications in the sensitivity of neural elements allow the brain to adapt its functions to varying demands. Frequency-dependent short-term synaptic depression (STD) provides a dynamic gain-control mechanism enabling adaptation to different background conditions alongside enhanced sensitivity to input-driven changes in activity. In contrast, synapses displaying frequency-invariant transmission can faithfully transfer ongoing presynaptic rates enabling linear processing, deemed critical for many functions. However, rigid frequency-invariant transmission may lead to runaway dynamics and low sensitivity to changes in rate. Here, I investigated the Purkinje cell to deep cerebellar nuclei neuron synapses (PC_DCNs), which display frequency invariance, and yet, PCs maintain background activity at disparate rates, even at rest. Using protracted PC_DCN activation (120 s) to mimic background activity in cerebellar slices from mature mice of both sexes, I identified a previously unrecognized, frequency-dependent, slow STD (S-STD), adapting IPSC amplitudes in tens of seconds to minutes. However, after changes in activation rates, over a behavior-relevant second-long time window, S-STD enabled scaled linear encoding of PC rates in synaptic charge transfer and DCN spiking activity. Combined electrophysiology, optogenetics, and statistical analysis suggested that S-STD mechanism is input-specific, involving decreased ready-to-release quanta, and distinct from faster short-term plasticity (f-STP). Accordingly, an S-STD component with a scaling effect (i.e., activity-dependent release sites inactivation), extending a model explaining PC_DCN release on shorter timescales using balanced f-STP, reproduced the experimental results. Thus, these results elucidates a novel slow gain-control mechanism able to support linear transfer of behavior-driven/learned PC rates concurrently with background activity adaptation, and furthermore, provides an alternative pathway to refine PC output.SIGNIFICANCE STATEMENT The brain can adapt to varying demands by dynamically changing the gain of its synapses; however, some tasks require ongoing linear transfer of presynaptic rates, seemingly incompatible with nonlinear gain adaptation. Here, I report a novel slow gain-control mechanism enabling scaled linear encoding of presynaptic rates over behavior-relevant time windows, and adaptation to background activity at the Purkinje to deep cerebellar nuclear neurons synapses (PC_DCNs). A previously unrecognized PC_DCNs slow and frequency-dependent short-term synaptic depression (S-STD) mediates this process. Experimental evidence and simulations suggested that scaled linear encoding emerges from the combination of S-STD slow dynamics and frequency-invariant transmission at faster timescales. These results demonstrate a mechanism reconciling rate code with background activity adaptation and suitable for flexibly tuning PCs output via background activity modulation.

Time-domain frequency-invariant beampattern synthesis via alternating direction method of multipliers.

This paper addresses time-domain frequency-invariant beampattern synthesis under multiple constraints. Mainlobe spatial response variation is introduced to characterize the frequency invariance. Peak constraints and norm constraints are imposed to control the sidelobe response and robustness of the beamformer, respectively. Such constraints are separated with the help of the alternating direction method of multipliers (ADMM), and an iterative solution is derived. Unlike the traditional interior-point approach with cubic complexity, the proposed algorithm shows quadratic complexity in a single iteration. Simulation results demonstrate that the proposed algorithm can achieve satisfactory performance in less time.

Measurement of Principal Modes in Few-Mode Fibers by S2 Method

Using principal modes (PMs) can avoid the inter-mode crosstalk in fiber-optic communication and reduce the complexity of digital signal processing. In this paper, a new detection method for PMs based on spatially and spectrally resolved imaging (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) is used to recover their intensity distributions and inter-mode dispersion parameters. This method collects the optical interference information on a two-dimensional plane at different frequencies. The collected data can be used to characterize the principal modes, including their patterns and differential mode group delays. Due to the frequency invariance of PMs even in mode coupling state, which is studied carefully, this proposed method is shown to be robust. Analyses based on a four-mode fiber show that the distributed fluctuation of the coupling coefficients break the frequency invariance of PMs. We experimentally measure the mode characteristics of a four-mode fiber with S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> method. The results show that the mode group delays of degenerate modes can be separated in mode coupling state, which is exactly appropriate for the modified measurement method.