Nonlinear Echo Research Articles

On Semi-Blind Source Separation-Based Approaches to Nonlinear Echo Cancellation Based on Bilinear Alternating Optimization

On Semi-Blind Source Separation-Based Approaches to Nonlinear Echo Cancellation Based on Bilinear Alternating Optimization

Nonlinear inviscid damping and shear‐buoyancy instability in the two‐dimensional Boussinesq equations

AbstractWe investigate the long‐time properties of the two‐dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size ε. Under the classical Miles‐Howard stability condition on the Richardson number, we prove that the system experiences a shear‐buoyancy instability: the density variation and velocity undergo an inviscid damping while the vorticity and density gradient grow as . The result holds at least until the natural, nonlinear timescale . Notice that the density behaves very differently from a passive scalar, as can be seen from the inviscid damping and slower gradient growth. The proof relies on several ingredients: (A) a suitable symmetrization that makes the linear terms amenable to energy methods and takes into account the classical Miles‐Howard spectral stability condition; (B) a variation of the Fourier time‐dependent energy method introduced for the inviscid, homogeneous Couette flow problem developed on a toy model adapted to the Boussinesq equations, that is, tracking the potential nonlinear echo chains in the symmetrized variables despite the vorticity growth.

Dynamic Neural Network-based Solutions for Acoustic Echo Suppression

Adaptive filters are widely used as core algorithms in current acoustic echo cancellation (AEC) systems. Echo path estimation is carried out by using different adaptive strategies in the adaptive filter. When nonlinear echo occurs, the performance deteriorates and seriously affects the call quality of both terminals. Taking advantage of the excellent non-linear fitting ability of neural networks in this paper, dynamic neural networks with self-updating parameters work continuously during the inference stage. The algorithm was computed and evaluated using publicly available echo audio data, showing that the dynamic neural network performs approximately as well as the optimal algorithm in the linear echo environment, and outperforms existing algorithms in the non-linear echo environment.

GAN–argcPredNet v1.0: a generative adversarial model for radar echo extrapolation based on convolutional recurrent units

Abstract. Precipitation nowcasting plays a vital role in preventing meteorological disasters, and Doppler radar data act as an important input for nowcasting models. When using the traditional extrapolation method it is difficult to model highly nonlinear echo movements. The key challenge of the nowcasting mission lies in achieving high-precision radar echo extrapolation. In recent years, machine learning has made great progress in the extrapolation of weather radar echoes. However, most of models neglect the multi-modal characteristics of radar echo data, resulting in blurred and unrealistic prediction images. This paper aims to solve this problem by utilizing the features of a generative adversarial network (GAN), which can enhance multi-modal distribution modeling, and design the radar echo extrapolation model GAN–argcPredNet v1.0. The model is composed of an argcPredNet generator and a convolutional neural network discriminator. In the generator, a gate controlling the memory and output is designed in the rgcLSTM component, thereby reducing the loss of spatiotemporal information. In the discriminator, the model uses a dual-channel input method, which enables it to strictly score according to the true echo distribution, and it thus has a more powerful discrimination ability. Through experiments on a radar dataset from Shenzhen, China, the results show that the radar echo hit rate (probability of detection; POD) and critical success index (CSI) have an average increase of 21.4 % and 19 %, respectively, compared with rgcPredNet under different intensity rainfall thresholds, and the false alarm rate (FAR) has decreased by an average of 17.9 %. We also found a problem during the comparison of the result graph and the evaluation index. The recursive prediction method will produce the phenomenon that the prediction result will gradually deviate from the true value over time. In addition, the accuracy of high-intensity echo extrapolation is relatively low. This is a question worthy of further investigation. In the future, we will continue to conduct research from these two directions.

A family of split kernel adaptive filtering algorithms for nonlinear stereophonic acoustic echo cancellation

A family of split kernel adaptive filtering algorithms for nonlinear stereophonic acoustic echo cancellation

Nonlinear stereophonic acoustic echo cancellation using sub-filter based adaptive algorithm

The nonlinear echo path resulting from the unwarranted acoustic echo and nonlinear distortion will degrade the echo cancellation performance of a stereophonic acoustic echo cancellation system. Techniques proposed in the literature rely on the assumption of a linear echo path. In this paper, a nonlinear stereophonic acoustic echo cancellation framework is proposed to address the problem of nonlinear distortion in stereophonic acoustic cancellation systems with a better trade-off between convergence and steady-state performance. The proposed approach uses the functional link-based adaptive filtering to deal with the nonlinear distortion in combination with the sub-filter approach to enhance the convergence performance. In addition to that, the convergence analysis of the proposed algorithm is presented in this paper. Simulations carried out using echo return loss enhancement and magnitude squared coherence as performance metrics using speech and colored noise input demonstrate the proposed framework's ability to improve the echo cancellation performance in the presence of distortion.

Nonlinear residual echo suppression based on dual-stream DPRNN

The acoustic echo cannot be entirely removed by linear adaptive filters due to the nonlinear relationship between the echo and the far-end signal. Usually, a post-processing module is required to further suppress the echo. In this paper, we propose a residual echo suppression method based on the modification of dual-path recurrent neural network (DPRNN) to improve the quality of speech communication. Both the residual signal and the auxiliary signal, the far-end signal or the output of the adaptive filter, obtained from the linear acoustic echo cancelation are adopted to form a dual-stream for the DPRNN. We validate the efficacy of the proposed method in the notoriously difficult double-talk situations and discuss the impact of different auxiliary signals on performance. We also compare the performance of the time domain and the time-frequency domain processing. Furthermore, we propose an efficient and applicable way to deploy our method to off-the-shelf loudspeakers by fine-tuning the pre-trained model with little recorded-echo data.

Selection on Golay complementary sequences in binary pulse compression for microbubble detection

In medical ultrasound imaging using microbubbles (MBs), the nonlinear echoes from the MBs are used for contrast-specific image construction. Techniques such as pulse inversion, amplitude modulation, and the combined method (PIAM) are employed to increase nonlinear components in the echoes. In addition, employment of pulse compression using binary-coded ultrasound can potentially increase the components. In the case of the nonlinear echo, however, a nonlinear sidelobe occurs around the compressed pulse (correlation peak), and nonlinear components for PIAM in the correlation peak are reduced. The shape of the nonlinear sidelobe and the nonlinear-component reduction in the correlation peak can be estimated from the binary codes used. In this study, the optimal binary codes for PIAM are determined from all patterns of 10, 16, and 20 bit Golay codes. Then, the performance of PIAM with pulse compression using each code is evaluated via computer simulations and experiments using the SonoVue MBs.

A frequency-domain nonlinear echo processing algorithm for high quality hands-free voice communication devices

A frequency-domain nonlinear echo processing algorithm is proposed to improve the audio quality during double-talk periods for hands-free voice communication devices. To achieve acoustic echo cancellation (AEC), a real-time AEC algorithm based on variable step-size partitioned block frequency-domain adaptive filtering (VSS-PBFDAF) and frequency-domain nonlinear echo processing (FNLP) algorithm was employed in the DSP chip of the prototype device. To avoid divergence during double-talk periods, normalized variable step-sizes for each frequency were introduced to adjust the convergence speed. Then, the nonlinear suppression function of FNLP was applied to inhibit the residual nonlinear acoustic echo and ensure the good quality of the near-end voice. The results of the experiment with the prototype device show that the proposed algorithm achieved deeper and more stable convergence during double-talk periods compared to the NLMS, FNLMS and traditional PBFDAF algorithms. Less nonlinear acoustic echo in the output was also obtained due to the use of FNLP. A speech quality assessment based on ITU-T P.563 showed that the Sout of the proposed algorithm achieved higher scores than that of the WebRTC algorithm. In addition, the speech output of the proposed algorithm during the double-talk periods was clear and coherent.

A Collaborative Spline Adaptive Filter for Nonlinear Echo Cancellation

Acoustic echo causes the quality of communication to degenerate and results in loss of clarity. Though conventional linear adaptive filters have been applied successfully to eliminate linear acoustic echo, they can barely deal with the problem of nonlinear acoustic echo. In this paper, a collaborative spline adaptive filter is presented to eliminate nonlinear acoustic echo. The filter is composed of a linear adaptive filter in the upper branch and a nonlinear spline adaptive filter in the lower branch. The nonlinear one is a Hammerstein system consisting of a spline interpolation function and a subsequent linear adaptive filter. The two branches are collaboratively combined and a mixing parameter is adopted, which can be updated to adjust the proportion of the lower branch output signal. Experimental results show that the presented method can achieve a good performance in nonlinear echo cancelation regardless of whether the nonlinear degree of the echo path varies with time or not.

The wavelet transform-domain adaptive filter for nonlinear acoustic echo cancellation

The usage of low-quality components in communicating devices introduces acoustic nonlinearity. The presence of nonlinearity creates challenges in noise cancellation applications, especially the acoustic echo cancellation (AEC) that requires an adaptive filter of a very high order. However, the functional link adaptive filter (FLAF) algorithm models the acoustic nonlinearity efficiently but shows slow convergence performance due to a very high filter order. To improve the convergence performance of the FLAF, the wavelet transform-domain FLAF (WTD-FLAF) is proposed for nonlinear AEC (NAEC) applications. The convergence rate is improved by decomposing a higher-order adaptive filter into smaller-order subfilters. The convergence speed improvement is gained at the expense of increased computational complexity. A low complexity version of the WTD-FLAF, named as selective update WTD-FLAF (SU-WTD-FLAF) algorithm, is also presented. The SU-WTD-FLAF algorithm is based on the selective coefficient update approach. Computer simulations demonstrate that the convergence performance of the proposed algorithms outperforms the standard FLAF.

Nonlinear Acoustic Echo Canceller to Combat Sigmoid-Type Nonlinearities Under Noisy Environment

This paper presents a nonlinear-acoustic-echo-cancellation (NAEC) technique to tackle sigmoid-type nonlinearities under noisy environment. The nonlinear echo in acoustic systems is inevitable due to the inherent nonlinear characteristics of amplifiers and/or loudspeakers, which deteriorates the quality of speech as well as audio signal reception. Here, the sigmoid-type nonlinearity is modelled by incorporating two control parameters, which determine the shaping- and clipping-parameter values of the saturation curve at a particular room temperature. These control parameters are adjusted by utilizing the variable-step-size (VSS) least-mean-square (LMS) algorithm to enhance the convergence rate and tracking capability of presented NAEC. Furthermore, the impulse response of a room (indoor channel) in the acoustic echo path is modelled as a tap-delay-line finite-impulse-response filter, whose tap-coefficients are estimated by utilizing a modified recursive-least-squares (RLS) algorithm (involving the noise statistics) at the different values of signal-to-noise-ratio (SNR), when correlated as well as uncorrelated input signals are processed. Simulation results demonstrate the efficiency and efficacy of above mentioned adaptive NAEC technique using the VSS-LMS and modified RLS algorithms in terms of the high convergence rate as well as high value of echo-return-loss-enhancement (ERLE) factor. Both the elevating value of shaping-parameter (i.e., increasing nonlinearity level) and the alleviating value of SNR adversely affect the performance of all NAECs. However, the VSS-LMS and modified RLS algorithm based presented adaptive NAEC outperforms the traditional VSS-LMS and normalized-least-mean-square (NLMS) algorithm based NAEC under similar conditions.

Nonlinear acoustic echo cancellation with kernelized adaptive filters

A well-known problem in speech communication is the occurrence of acoustic echo in hands-free telephony. There are several classical adaptive filters that have been used as a stand alone approach for linear acoustic echo cancellation(AEC). A common assumption in most AEC techniques is that the echo path is linear. However, in real scenarios, owing to distortions introduced by other acoustic artefacts in handheld devices, the echo path is nonlinear. Therefore, there is a need to employ a nonlinear echo canceller. In this paper, a kernel expansion on a family of adaptive filtering algorithms based on least mean square filter is proposed. Kernel methods help model the nonlinear echo path and attain global minimum easily by finding the optimal set of filter weights. The simulations are carried out for speech signal with and without noise under different signal-to-noise ratio values. The results show that the proposed method achieves a significant improvement in a nonlinear acoustic echo cancellation environment in terms of echo return loss enhancement.

Channel Sparsity Aware Function Expansion Filters Using the RLS Algorithm for Nonlinear Acoustic Echo Cancellation

In this paper, we propose a channel sparsity aware sequential recursive least squares (sparse SEQ-RLS) algorithm for function expansion filters with applications in nonlinear echo cancellation. The algorithm is developed based on a diagonal channel structure from the Volterra filter and updating dominant coefficients taking into consideration of sparse elements in the diagonal channel. The third-order Volterra, third-order even mirror Fourier nonlinear (EMFN), and functional link artificial neural network (FLANN) filters are developed according to the sparse SEQ-RLS algorithm. The computation complexity for the upper bound is analyzed to validate the efficiency for each proposed filter. Computer simulation results demonstrate that all proposed function expansion filters with the sparse SEQ-RLS algorithm are effective for nonlinear echo cancellation. In general, the EMFN filter provides better performance compared to the Volterra and FLANN filters.

Long-Lived Coherence Originating from Electronic-Vibrational Couplings in Light-Harvesting Complexes

We theoretically investigate the evolutions of two-dimensional, third-order, nonlinear photon echo rephasing spectra with population time by using an exact numerical path integral method. It is shown that for the same system, the coherence time and relaxation time of excitonic states are short, however, if the couplings of electronic and intra-pigment vibrational modes are considered, the coherence time and relaxation time of this vibronic states are greatly extended. It means that the couplings between electronic and vibrational modes play important roles in keeping long-lived coherence in light-harvesting complexes. Particularly, by using the method we can fix the transition path of the energy transfer in bio-molecular systems.

A brief summary of nonlinear echoes and Landau damping

In this expository note we review some recent results on Landau damping in the nonlinear Vlasov equations, focusing specifically on the recent construction of nonlinear echo solutions by the author [arXiv:1605.06841] and the associated background. These solutions show that a straightforward extension of Mouhot and Villani's theorem on Landau damping to Sobolev spaces on $\mathbb T^n_x \times \mathbb R^n_v $ is impossible and hence emphasize the subtle dependence on regularity of phase mixing problems. This expository note is specifically aimed at mathematicians who study the analysis of PDEs, but not necessarily those who work specifically on kinetic theory. However, for the sake of brevity, this review is certainly not comprehensive.

Identifying the nonlinear mechanical behaviour of micro-speakers from their quasi-linear electrical response

In this study model identification of the nonlinear dynamics of a micro-speaker is carried out by purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker, which takes into account the nonlinear damping characteristic of the device, can be identified by measuring the response between the voltage input and the current flowing into the coil. An analytical formulation of the quasi-linear model of the micro-speaker is first derived and an optimisation method is then used to identify a polynomial function which describes the mechanical damping behaviour of the micro-speaker. The analytical results of the quasi-linear model are compared with numerical results. This study potentially opens up the possibility of efficiently implementing nonlinear echo cancellers.

Significance-aware filtering for nonlinear acoustic echo cancellation

This article summarizes and extends the recently proposed concept of Significance-Aware (SA) filtering for nonlinear acoustic echo cancellation. The core idea of SA filtering is to decompose the estimation of the nonlinear echo path into beneficially interacting subsystems, each of which can be adapted with high computational efficiency. The previously proposed SA Hammerstein Group Models (SA-HGMs) decompose the nonlinear acoustic echo path into a direct-path part, modeled by a Hammerstein Group Model (HGM) and a complementary part, modeled by a very efficient Hammerstein model. In this article, we furthermore propose a novel Equalization-based SA (ESA) structure, where the echo path is equalized by a linear filter to allow for an estimation of the loudspeaker nonlinearities by very small and efficient models. Additionally, we provide a novel in-depth analysis of the computational complexity of the previously proposed SA and the novel ESA filters and compare both SA filtering approaches to each other, to adaptive HGMs, and to linear filters, where fast partitioned-block frequency-domain realizations of the competing filter structures are considered. Finally, the echo reduction performance of the proposed SA filtering approaches is verified using real recordings from a commercially available smartphone. Beyond the scope of previous publications on SA-HGMs, the ability of the SA filters to generalize for double-talk situations is explicitly considered as well. The low complexity as well as the good echo reduction performance of both SA filters illustrate the potential of SA filtering in practice.

Phase and Amplitude Modulation Methods for Nonlinear Ultrasound Imaging With CMUTs.

Conventional amplitude and phase modulated pulse sequences for selective imaging of nonlinear tissue and ultrasound contrast agents are designed for piezoelectric transducers that behave linearly. Inherent nonlinearity of capacitive micromachined ultrasonic transducers (CMUTs), especially during large-signal operation, renders these methods inapplicable. In this paper, we present different pulse sequences for nonlinear imaging that are valid for small- and large-signal CMUT operations. For small-signal operation, two-pulse amplitude and phase modulation methods for microbubble and tissue harmonic imaging are presented, where CMUT nonlinearity is compensated via subharmonic excitation. In the large-signal regime, using a nonlinear model, we first show that there is a simple linear relationship between the phases of each harmonic distortion component generated and the input drive signal. Based on this observation, we demonstrate a pulse sequence using N+1 consecutive phase modulated transmit events to extract N harmonics of the nonlinear contrast agent echo content uncorrupted by CMUT nonlinearity. The proposed methods assume no apriori information about the transducer and, therefore, are applicable to any CMUT. The phase modulation method is also valid for piezoelectric transducers and systems with nonlinearities described by Taylor series where the same phase relationship between the input signal and the harmonic content is valid. The proof of principle experiments using a commercial contrast agent validates the phase modulated pulse sequences for CMUTs, operating in a highly nonlinear collapse-snapback mode and for piezoelectric transducers.

Suppression of remnant nonlinear echo due to harmonic distortions in intelligent communication networks

Voice communication today has become an important and an integral part of human kind in which speech quality is an important concern. The issue of speech degradation due to end user devices can be tackled when efficient devices and algorithms are used to cancel acoustic echo. Acoustic echo canceller AEC is used to eliminate unwanted echo which dampens speech signal and reduces the efficiency of signal transmission. With advent of sophisticated technology low cost loudspeakers and power amplifiers are devised which bring nonlinearity into communication channel. In this paper, an improved solution for the cancellation of the nonlinear echo to restore the speech quality in a communication channel is designed. The conceived algorithm deals with nonlinear AEC with moderately low computational complexity and faster convergence. The whole process starts with linear AEC and then the proposed harmonic distortion nonlinear remnant echo suppressor comes into action after passing through linear AEC.