Time-domain Convolution Research Articles

Compression of room impulse responses for compact storage and fast low-latency convolution

Room impulse responses (RIRs) are used in several applications, such as augmented reality and virtual reality. These applications require a large number of RIRs to be convolved with audio, under strict latency constraints. In this paper, we consider the compression of RIRs, in conjunction with fast time-domain convolution. We consider three different methods of RIR approximation for the purpose of RIR compression and compare them to state-of-the-art compression. The methods are evaluated using several standard objective quality measures, both channel-based and signal-based. We also propose a novel low-rank-based algorithm for fast time-domain convolution and show how the convolution can be carried out without the need to decompress the RIR. Numerical simulations are performed using RIRs of different lengths, recorded in three different rooms. It is shown that compression using low-rank approximation is a very compelling option to the state-of-the-art Opus compression, as it performs as well or better than on all but one considered measure, with the added benefit of being amenable to fast time-domain convolution.

Reconstruction of nonstationary sound field based on group sparsity time domain equivalent source method

To improve the accuracy and stability of reconstruction of nonstationary sound field, a novel time domain equivalent source method based on non-convex overlapping group sparsity (NOGS-TESM) is proposed. In the proposed NOGS-TESM, the time-varying pressure in the near field is first modeled by a set of equivalent sources positioned inside the vibrating structure. Then, the NOGS regularization is applied for solving the inverse problem, and a novel algorithm derived on the basis of Majorize-Minimization theory is utilized to obtain the optimal solution of equivalent sources strengths. Finally, the optimal equivalent sources strengths at all times are substituted into a time-domain convolution to calculate the time-varying pressure of reconstruction surface. The proposed NOGS-TESM enriches the prior information by considering the group sparsity of spatial pressure distribution, and enhances the accuracy of estimated equivalent sources strength via its alternative calculation of l0−norm. A vibrating plate to produce a nonstationary sound field, which is designed as a numerical simulation, and the time-varying pressures of measurement surface are input into the proposed NOGS-TESM. The quantitative and qualitative comparisons confirm that the proposed NOGS-TESM can greatly reconstruct the non-stationary sound field in time–space domains, and its reconstruction accuracy is higher than that of TESM with Tikhonov regularization (TR-TESM). Meanwhile, several parameters, for example, the noise and position of equivalent source surface, are discussed in detail, and the superiorities of the proposed NOGS-TESM in terms of stability and robustness are proved by comparing to TR-TESM. The predominance of the proposed NOGS-TESM is further validated by conducting one experiment on the vibrating steel plate.

Gravitational-wave matched filtering on a quantum computer

State-of-the-art quantum computers have very limited applicability for accurate calculations. Here, we report the first experimental demonstration of qubit-based matched filtering for a detection of the gravitational-wave signal from a binary black hole merger. With our implementation on noisy superconducting qubits, we obtained a similar signal-to-noise ratio for the binary black hole merger as achievable with classical computation, providing evidence for the utility of qubits for practically relevant tasks. The algorithm we invented for this application is a Monte Carlo algorithm which uses quantum and classical computation together. It provides a quasi-quadratic speed-up for time-domain convolution, similar to achievable with fast Fourier transform.

Photonic envelope convolver based on time-domain convolution method

A photonic approach of temporal convolver is proposed and experimentally demonstrated. Different from traditional schemes, the photonic envelope convolution can be achieved by time-domain convolution method, which includes three steps of time-domain Fourier transform, multiplication and inverse Fourier transform. The feasibility of the system is verified by theoretical analysis and simulation. The proposed temporal convolution is experimentally evaluated, in which three temporal convolution results between two rectangular signals, between a rectangular signal and a sawtooth signal, and between two sawtooth signals are successfully obtained, which agree with the theoretical analysis well. Because the time-domain Fourier transform and multiplication can be easily implemented through dispersion mediums and modulation devices respectively, the proposed system has advantages of simple configuration, easy operation, reconfigurability and cost-effectiveness. It provides a new access to achieving convolution operation.

On the Application of Fractional Derivative Operator Theory to the Electromagnetic Modeling of Frequency Dispersive Media

Fractional derivative operators are finding applications in a wide variety of fields with their ability to better model certain phenomena exhibiting spatial and temporal nonlocality. One area in which these operators are applicable is in the field of electromagnetism, thereby modelling transient wave propagation in complex media. To apply fractional derivative operators to electromagnetic problems, the operator must adhere to certain principles, like the trigonometric functions invariance property. The Grünwald–Letnikov and Marchaud fractional derivative operators comply with these principles and therefore could be applied. The fractional derivative arises when modelling frequency-dispersive dielectric media. The time-domain convolution integral in the relation between the electric displacement and the polarisation density, containing an empirical extension of the Debye model, is approximated directly. A common approach is to recursively update the convolution integral by approximating the time series by a truncated sum of decaying exponentials, with the coefficients found through means of optimisation or fitting. The finite-difference time-domain schemes using this approach have shown to be more computationally efficient compared to other approaches using auxiliary differential equation methods.

High-Precision Joint TDOA and FDOA Location System

Passive location based on TDOA (time difference of arrival) and FDOA (frequency difference of arrival) is the mainstream method for target localization. This paper proposes a fast time–frequency difference positioning method to address issues such as low accuracy, large computational resource utilization, and limited suitability for real-time signal processing in the conventional CAF (cross-ambiguity function)-based approach, aiming to complete the processing of the target radiation source to obtain the target parameters within a short timeframe. In the mixing product operation step of the CAF, a frequency-domain approach replaces the time-domain convolution operation in PW-ZFFT (pre-weighted Zoom-FFT) to reduce the computational load of the CAF. Additionally, a quadratic surface fitting method is used to enhance the accuracy of TDOA and FDOA. The localization solution is obtained using Newton’s method, which can provide more accurate results compared to analytical methods. Next, a signal processing platform is designed with FPGA (field-programmable gate array) and multi-core DSP (digital signal processor), and works by dividing and mapping the algorithm functional modules according to the hardware’s characteristics. We analyze the architectural advantages of multi-core DSP and design methods to improve program performance, such as EDMA transfer optimization, inline function optimization, and cache optimization. Finally, this paper constructs simulation tests in typical positioning scenarios and compares them to hardware measurement results, thus confirming the correctness and real-time capability of the program.

Action capture method of animated characters based on virtual reality technology

Abstract Virtual reality technology is a kind of animation technology that is widely used in the creation of film and television animation art, which makes the technological imprint of film and television animation art creation exceptionally obvious. The article utilizes virtual reality technology to create a virtual scene for character motion capture in film and television animation by combining the video motion capture system. The camera position-solving method is used to map the points in the three-dimensional space to the two-dimensional image plane, and then the high-dimensional image signals are converted to the low-dimensional signals of human body postures through the minimum bounding rectangle of the foreground image to realize the solving of the character’s action posture information. Based on the graph convolution neural network, a time domain graph convolution model is established with the help of layering and cross-frame connection of the null time domain convolution to realize the 3D pose estimation and capture of the character movement in film and television animation. The joints’ confidence smooths the pose sequence of the character’s action. The maximum error of the yaw, pitch, and roll angles in 15 frames does not exceed 0.4° in the pose resolution of the animated character. Real and measured joint flexion and extension angles have errors that are less than 0.3°. The average error of the Euler angle data for character motion capture is between 1.37 and 3.86°, and the MPJVE error of the smoothed data is reduced by 1.15 mm compared to the pre-processing data. The virtual scene constructed by relying on the virtual reality technology can help the video motion capture system to obtain the performance of film and television animated characters, and provide a reference to optimize the film and television animated characters’ movements.

The RFI Fast Mitigation Algorithm Based on Block LMS Filter

The radio telescope possesses high sensitivity and strong signal collection capabilities. While receiving celestial radiation signals, it also captures Radio Frequency Interferences (RFIs) introduced by human activities. RFI, as signals originating from sources other than the astronomical targets, significantly impacts the quality of astronomical data. This paper presents an RFI fast mitigation algorithm based on block Least Mean Square (LMS) algorithm. It enhances the traditional adaptive LMS filter by grouping L adjacent time-sampled points into one block and applying the same filter coefficients for filtering within each block. This transformation reduces multiplication calculations and enhances algorithm efficiency by leveraging the time-domain convolution theorem. The algorithm is tested using baseband data from the Parkes 64 m radio telescope’s pulsar observations and simulated data. The results confirm the algorithm’s effectiveness, as the pulsar profile after RFI mitigation closely matches the original pulsar profile.

Convolution Power Ratio Based on Single-Ended Protection Scheme for HVDC Transmission Lines

In order to solve the problems of insufficient abilities to withstand transition resistance under remote faults and difficulties in identifying internal and external faults for HVDC transmission line protection, a new single-ended protection scheme based on time-domain convolutional power was proposed. In this scheme, the ratio of time-domain convolution power at different frequencies is used to detect internal and external faults, and the long window convolution power is used to form the pole selection criteria. Due to the integration of transient power fault characteristics at high and low frequencies, this scheme amplifies the characteristic differences between internal and external faults caused by DC line boundaries and has a strong ability to withstand transition resistance. Based on PSCAD/EMTDC, simulation verification was conducted on the Yunnan–Guangzhou ±800 kV HVDC project. The results show that the proposed single-ended protection scheme can effectively identify fault poles, as well as internal and external faults. It has strong resistance to transition resistance and certain anti-interference ability and has strong adaptability to DC line boundaries, which meets the protection requirements of HVDC transmission systems for high speed, selectivity and reliability.

Difference between Charge–Voltage Relations of Ordinary and Fractional Capacitors

In an ordinary time-varying capacitor, there is debate on whether a time-domain multiplication or a time-domain convolution of capacitance and voltage determines charge. The objective of this work is to resolve this question by experiments on a time-varying capacitor in parallel with a resistor. It was implemented by a motor-driven potentiometer and op-amps. The response matched a power-law function over about two decades of time, and not an exponential, for several sets of parameters. This confirms the time-domain multiplication model. This result is the opposite of that obtained for a constant phase element (CPE) in its common time- and frequency-varying capacitor interpretation. This demonstrates that a CPE is fundamentally different from an ordinary time- and frequency-varying capacitor.

Compressive nonstationary near-field acoustic holography for reconstructing the instantaneous sound field

A compressive nonstationary near-field acoustic holography based on time-domain plane wave superposition method is proposed to precisely reconstruct the instantaneous sound field using the fewer measurement points. In the proposed method, by means of an instantaneous propagation kernel, a time-domain convolution superposition formula is established for relating the time-variant pressure of the hologram plane to the pressure time-wavenumber spectra of the virtual source plane. Next, compressed sensing theory and sparse representation framework are introduced into the time-marching solving inverse process of the established formula, and the smoothed l0 norm and revised Newton optimization algorithm are employed to solve the serious cumulative ill-posed problem over time for acquiring the pressure time-wavenumber spectra. The key is to approximately replace the discontinuous ℓ0 norm by using a suitable continuous function, and the revised Newton algorithm is applied to minimize the continuous function for obtaining the optimal solution. Finally, with the aid of a time-domain convolution formula, the solved pressure time-wavenumber spectra are employed to calculate the time-variant pressure on the reconstruction plane. The proposed method not only can evidently suppress the ill-posed problem of time-marching solving inverse process for improving the reconstruction accuracy, but also can greatly reduce the measurement points and microphone number for drastically decreasing the measurement cost on the premise of ensuring the reconstruction accuracy and spatial resolution. A numerical simulation is conducted, and the simulation effects prove that the proposed method can accurately reconstruct the instantaneous sound field with the fewer measurement points in time–space domains. The reconstruction results are also compared to those of time-domain plane wave superposition method with Tikhonov regularization to verify the superiority of the proposed method with fewer measurement points under different parameter configurations. An experiment of an impaction steel plate is implemented for further validating the competence of the proposed method.

Modeling the connection between oil painting creation and university students’ inspiration in the context of “Internet+”

Abstract In the Internet era, oil painting creation requires constant observation and learning before it can be inspired, and the inspiration for oil painting creation is like a godsend. This paper constructs a fast Fourier transform convolutional model based on fast Fourier transform and convolutional neural network to study the connection between oil painting creation and university students’ inspiration in the context of “Internet+”. The model was evaluated algorithmically, and a dataset of oil paintings was built to investigate the influence of the hue and brushwork technique on students’ inspiration. From the algorithm evaluation, the algorithm of this paper’s model reduces the floating-point computation from 34.76G to 20.08G than the traditional time-domain convolution algorithm, which reduces the floating-point computation by nearly 15G and greatly improves the running speed of this paper’s model. From the hue examples, the percentage of blue-gray, pale white, and light blue oil paintings are 34.95%, 18.59%, and 10.73%, respectively. Various hues will bring students different emotional expressions and induce their creative inspiration. In terms of brushwork techniques, the average percentages of the six brushwork techniques are 16.53%, 22.21%, 15.68%, 11.73%, 14.69%, and 19.16%, respectively. The fast Fourier transform convolution model established under the background of “Internet+” can effectively analyze the different tones and brushstroke techniques in oil paintings so that students can feel the emotion and vitality of the works in the process of observation and thus promote the generation of inspiration for oil painting creation of college students.

Acceleration-to-displacement conversion as a single time-domain convolution operation

In this paper, we derive a computationally simple and efficient formulation to convert an acceleration signal to a displacement signal. We show that a previously derived approach based on Least Square Support Vector Machine can be recast as a single time-domain convolution between the acceleration signal and a windowing function. An explicit equation is derived for the windowing function, which only takes the window length as its argument. This paper reveals previously unknown insights into how input is processed in the original approach by expressing the Least Square Support Vector Machine approach as a convolution operation between the acceleration signal and an explicitly defined windowing function. The new formulation inherits all the benefits of the original method, such as the numerical stability and intrinsic robustness to noise, and gives the same result as the original method at a significantly reduced computational effort. It does not require any matrix inversion and computes the displacement values without discarding any calculated values.

Reconstruction of transient acoustic field using sparse real-time near-field acoustic holography

A sparse real-time near-field acoustic holography method is proposed to precisely and stably reconstruct a transient sound field. By a time-domain impulse response function, a time domain convolution equation between the pressure time-wavenumber spectra on the hologram and reconstruction planes is first established. Then, a smoothed ℓ0-norm optimization algorithm is applied to solve the serious ill-conditioned problem of the inverse process to get the pressure time-wavenumber spectrum of the reconstruction plane. The key part of solving this problem is to approximate replace the discontinuous ℓ0-norm by using a suitable continuous Gaussian function family, and a steepest ascent algorithm is introduced to minimize the continuous function for obtaining the optimal solution. Finally, the pressure time-wavenumber spectra of the reconstruction plane for all wavenumbers at all times are solved, and the corresponding time-dependent pressures are gained by the two-dimensional space inverse Fourier transform. A numerical simulation is conducted to observe the reconstruction capacity of the proposed method. The simulation effect prove that the proposed method can accurately reconstruct the transient sound field, and its reconstruction results are compared to those of the real-time near-field acoustic holography (RTNAH) with Tikhonov regularization and YALL1 modal for verifying the superiority of the proposed method. The YALL1 module utilizes an alternating direction algorithm for solving the ℓ1 minimization problems. Several parameters including the noise, position of the holograph plane and two initialization values are discussed in the simulation. The comparison and discussion results show that the reconstruction effect of the proposed method is much better than those of RTNAH with Tikhonov regularization and YALL1 modal under different parameter configurations. An experiment with a percussive steel plate is implemented for further validating the effectivity of the proposed method.

Research on Processing the Feature Model of Converter Station Based on Machine Learning

The current traditional converter station feature model processing method uses switching functions to model converter station equipment, which leads to poor processing results because it ignores the dynamic coupling characteristics between the second harmonics inside the converter station. In this regard, a machine-learning-based switching station feature model processing method is proposed. By combining different terminals to determine their port parameters, constructing the characteristic impedance model of the converter station, using time-domain recursive convolution to calculate the voltage levels at each key point of the AC system, and finally calculating the magnitude as well as the phase angle constants, the time-varying model of the multi-harmonic converter can be fixed. In the experiments, the computational accuracy of the proposed method is verified. The analysis of the experimental results shows that the proposed method has a high component amplitude and excellent computational performance when the characteristic model of the converter station is processed.

An iteratively reweighted time-domain acoustic method for reconstructing the transient acoustic field

An improved iterative reweighted least-squares based on real-time near-field acoustic hologram method (RTNAH) is proposed to reconstruct the transient acoustic field. First, time-domain convolution relation formula between the pressure time-wavenumber spectra on the hologram and reconstruction planes is first established by an impulse response function, and the corresponding matrix equation is obtained. Then, for solving the pressure spectra on the reconstruction plane, an improved iterative reweighted least-squares algorithm is applied for solving the minimization problem of the sum of 2-norm residual and 2-norm weighted solution under the weighted and sparse representation framework. By controlling the iteratively updated weighting matrix, the sparsity of the solution is promoted. Finally, the pressure spectra of the reconstruction plane are estimated, and the corresponding time-varying pressures are acquired by the two-dimensional inverse Fourier transform. A numerical simulation is conducted to observe the reconstruction capacity of the proposed method. The simulation results demonstrate that the proposed method can reconstruct the transient acoustic field in time-space domains very well. Meanwhile, several vital parameters are discussed, and the superiorities of the proposed method are testified by comparing to RTNAH with Tikhonov regularization and YALL1 model. An experiment is implemented for further validating the effectivity of the proposed method.

Leak Location for Urban Elbowed Water Pipe Based on Complex-Optimized FastICA Blind Deconvolution

Previous research has primarily focused on leak diagnosis algorithms under the interference of outside environment noise. However, the former algorithms in leak detection are easily affected by noise from the pipe, especially the one that contains elbow noise. This article was mainly concerned with the effective and reliable approach to precisely locate leaks in the buried elbow pipeline system. To overcome the drawback of elbow noise interference and extract the leak source from the mixing signal in the greatest extent, this article proposes a novel frequency-domain-independent component analysis (ICA) blind deconvolution algorithm, which is based on a popular optimized FastICA (O-FICA) called complex-optimized FastICA (CO-FICA) algorithm. In comparison, CO-FICA differs from the time-domain blind convolution separation (T-BCS) algorithm, which transforms complicated time-domain convolution into a simple frequency-domain product problem. Compared with the conventional complex FastICA (C-FICA), the proposed CO-FICA method does not need to estimate signal statistics at each step, but it displays more excellent performance in convergent speed and separated precision. Altogether, the results from this study demonstrate that the localization precision of the proposed method is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 87\%$ </tex-math></inline-formula> under the interference of elbow noise.

Sampling Rate Offset Estimation and Compensation for Distributed Adaptive Node-Specific Signal Estimation in Wireless Acoustic Sensor Networks

Sampling rate offsets (SROs) between devices in a heterogeneous wireless acoustic sensor network (WASN) can hinder the ability of distributed adaptive algorithms to perform as intended when they rely on coherent signal processing. In this paper, we present an SRO estimation and compensation method to allow the deployment of the distributed adaptive node-specific signal estimation (DANSE) algorithm in WASNs composed of asynchronous devices. The signals available at each node are first utilised in a coherence-drift-based method to blindly estimate SROs which are then compensated for via phase shifts in the frequency domain. A modification of the weighted overlap-add (WOLA) implementation of DANSE is introduced to account for SRO-induced full-sample drifts, permitting per-sample signal transmission via an approximation of the WOLA process as a time-domain convolution. The performance of the proposed algorithm is evaluated in the context of distributed noise reduction for the estimation of a target speech signal in an asynchronous WASN.

Fault Diagnosis Based on Optimized Wavelet Packet Transform and Time Domain Convolution Network

Fault Diagnosis Based on Optimized Wavelet Packet Transform and Time Domain Convolution Network

Time-domain convolution model for studying oscillation dynamics in an injection-locked optoelectronic oscillator.

A time-domain convolution model is proposed to study the oscillation dynamics in the injection-locked optoelectronic oscillator (OEO). The model has the ability to calculate multiple characteristics of the oscillation signal, such as the spectrum and the phase noise. Based on the model, the injection locking, the frequency pulling and the asymmetrical spectrum generation phenomena are numerically simulated in success. The simulation results fit in with the experimental results, indicating that the proposed model accurately describes the oscillation dynamics in the injection-locked OEO. In addition, the building-up process of the oscillation signal in the OEO is simulated. Alternating appearance of the sidebands on both sides of the primary oscillation mode is observed for the first time in the asymmetrical spectrum generation. This model is a powerful tool to study the oscillation dynamics in the injection-locked OEO.