Frequency-domain Adaptive Filter Research Articles

Performance analysis of unconstrained partitioned-block frequency-domain adaptive filters in under-modeling scenarios

The unconstrained partitioned-block frequency-domain adaptive filter (PBFDAF) offers superior computational efficiency over its constrained counterpart. However, the correlation matrix governing the natural modes of the unconstrained PBFDAF is not full rank. Consequently, the mean coefficient behavior of the algorithm depends on the initialization of adaptive coefficients and the Wiener solution is non-unique. To address the above problems, a new theoretical model for the deficient-length unconstrained PBFDAF is proposed by constructing a modified filter weight vector within a system identification framework. Specifically, we analyze the transient and steady-state convergence behavior. Our analysis reveals that modified weight vector is independent of its initialization in the steady state. The deficient-length unconstrained PBFDAF converges to a unique Wiener solution, which does not match the true impulse response of the unknown plant. However, the unconstrained PBFDAF can recover more coefficients of the parameter vector of the unknown system than the constrained PBFDAF in certain cases. Also, the modified filter coefficient yields better mean square deviation (MSD) performance than previously assumed. The presented alternative performance analysis provides new insight into convergence properties of the deficient-length unconstrained PBFDAF. Simulations validate the analysis based on the proposed theoretical model.

Multi-domain awareness for compressed deepfake videos detection over social networks guided by common mechanisms between artifacts

The viral spread of massive deepfake videos over social networks has caused serious security problems. Despite the remarkable advancements achieved by existing deepfake detection algorithms, deepfake videos over social networks are inevitably influenced by compression factors. This causes deepfake detection performance to be limited by the following challenging issues: (a) interfering with compression artifacts, (b) loss of feature information, and (c) aliasing of feature distributions. In this paper, we analyze the common mechanism between compression artifacts and deepfake artifacts, revealing the structural similarity between them and providing a reliable theoretical basis for enhancing the robustness of deepfake detection models against compression. Firstly, based on the common mechanism between artifacts, we design a frequency domain adaptive notch filter to eliminate the interference of compression artifacts on specific frequency bands. Secondly, to reduce the sensitivity of deepfake detection models to unknown noise, we propose a spatial residual denoising strategy. Thirdly, to exploit the intrinsic correlation between feature vectors in the frequency domain branch and the spatial domain branch, we enhance deepfake features using an attention-based feature fusion method. Finally, we adopt a multi-task decision approach to enhance the discriminative power of the latent space representation of deepfakes, achieving deepfake detection with robustness against compression. Extensive experiments show that compared with the baseline methods, the detection performance of the proposed algorithm on compressed deepfake videos has been significantly improved. In particular, our model is resistant to various types of noise disturbances and can be easily combined with baseline detection models to improve their robustness.

Frequency-domain adaptive MIMO filter with fractional oversampling using stochastic gradient descent for long-haul transmission over coupled 4-core fibers: erratum.

This erratum corrects errors in Fig. 9(b) and Fig. 14 of our published paper [Opt. Express31, 13104 (2023)10.1364/OE.486032]. Other results, descriptions, and conclusions are not affected by this correction.

Frequency-domain adaptive MIMO filter with fractional oversampling using stochastic gradient descent for long-haul transmission over coupled 4-core fibers.

We propose a fractionally spaced frequency-domain adaptive multi-input multi-output (MIMO) filter architecture in which the sampling rate of input signals is below 2× oversampling with a non-integer oversampling factor for mode demultiplexing in long-haul transmission over coupled multi-core fibers. The frequency-domain sampling rate conversion to the symbol rate, i.e., 1× sampling, is placed after the fractionally spaced frequency-domain MIMO filter. The filter coefficients are adaptively controlled by stochastic gradient descent and gradient calculation with back propagation through the sampling rate conversion from the output signals on the basis of deep unfolding. We evaluated the proposed filter through a long-haul transmission experiment of 16-channel wavelength-division multiplexed and 4-core space-division multiplexed 32-Gbaud polarization-division-multiplexed quadrature phase shift keying signals over coupled 4-core fibers. The fractional oversampling frequency-domain adaptive 8×8 filter with 9/8× oversampling provided little performance penalty after 6240-km transmission compared to the conventional 2× oversampling frequency-domain adaptive 8×8 filter. The computational complexity in terms of the required number of complex-valued multiplications was reduced by 40.7%.

Diffusion Partitioned-Block Frequency-Domain Adaptive Filter Over Multitask Networks

As a generalization of the frequency-domain adaptive filter (FDAF) algorithm, partitioned-block frequency-domain adaptive filter (PBFDAF) results in minimal signal path delay. In this brief, we propose the diffusion normalized PBFDAF algorithm based on an unsupervised clustering strategy to address the low complexity implementation issues in multitask networks. Each node adaptively adjusts the combination weight coefficients by minimizing the instantaneous mean square deviation (MSD) in frequency-domain. The simulation results demonstrate that the proposed algorithm achieves superior performance.

Optimal Step Size Technique for Frequency Domain and Partition Block Adaptive Filters for PEM based Acoustic Feedback Cancellation

The adaptive filtering approach has been commonly used to perform acoustic feedback cancellation (AFC) in digital hearing-aids due to its reliable performance and feasibility. Because the loudspeaker and microphone are close together in hearing aids, the corresponding signals are highly correlated, resulting in biased estimation if adaptive filters are used. This problem can be addressed with the help of the decorrelation prefilter by incorporating the Prediction Error Method (PEM) technique into AFC. Frequency-Domain Adaptive Filters (FDAF) are preferable over the time-domain implementation to achieve better performance in terms of convergence and computational complexity. In addition, Partition-Block Frequency-Domain Adaptive Filters (PBFDAF) offers low processing delay. However, because of their fixed step-size, there is a trade-off between initial convergence and steady-state misalignment in the widely used frequency-domain algorithms. While Variable Step-Size (VSS) algorithms can help with this issue, VSS techniques for frequency-domain algorithms have not been extensively studied in the context of PEM-AFC. Hence, in this paper, we presented an Optimal Step-Size (OSS) technique for both the FDAF-PEM_AFC and PBFDAF-PEM_AFC algorithms to simultaneously accomplish fast convergence and minimal steady-state error. A Feedback Path Change Detector (FPCD) was also incorporated into the proposed algorithms to address the problem of convergence in non-stationary feedback paths. The results of simulations show that the proposed algorithms are clearly superior, and they are encouraging.

Performance Evaluation of Selected Adaptive Filters for Acoustic Echo Cancelation over Voice over Internet Protocol

Advancement of technology has increased the value of the telecommunications industry. One of the services with the rapid growth is Voice over Internet Protocol (VoIP). However, echo is a common disturbing effect in VoIP calls. Instead of suppressing the presence of echo in the VoIP communication channel, echo cancellation works better in full-duplex mode. This paper compares performances of some selected adaptive filters for cancelation of acoustic echo in VoIP channel. The framework for adaptive echo cancellation is built around finite impulse response and fourth-order infinite impulse response Chebyshev type II filters for the modeling of echo and acoustic environment, respectively. Selected adaptive algorithms for analysis are least mean square, recursive least square and frequency domain adaptive filter. The analysis is carried out in MATLAB 2018a environment. Echo return loss enhancement, error estimate and convergence rate are the performance indices employed for performance comparison of selected adaptive algorithms. It was found that the FDAF algorithm performed best based on computed error return loss enhancement and error estimate figures. In addition, FDAF converges faster than LMS and RLS with average time of 0.026431 s over 2048 filter lengths. Thus, FDAF shows a better promise over the two variants of time domain adaptive algorithm (LMS and RLS) analyzed in this paper.

Analysis of Deficient-Length Partitioned-Block Frequency-Domain Adaptive Filters

This paper studies the convergence behavior of the partitioned-block frequency-domain adaptive filters (PBFDAF) for under-modeling scenarios. We focus on a family of the overlap-save PBFDAF algorithms with 50% overlap, including both of the constrained and unconstrained versions. The stochastic analysis of the constrained and unconstrained algorithms is carried out individually due to their convergence differences. For each algorithm, the frequency-domain error vector and the update equations are transformed into the time-domain counterparts, so we can analyze their convergence behavior completely in the time domain. We present the mean and mean-square convergence behavior of the augmented weight-error vector, and we obtain the closed-form expressions for the learning curve and the steady-state solutions. Based on the solution of the steady-state weight-error vector, we analyze if each version of the PBFDAF algorithm converges to the true solution and the Wiener solution. The theoretical model gains new insights into the convergence behavior of the deficient-length PBFDAF algorithms. The computer simulations support the theoretical model very well.

Analysis of Unconstrained Partitioned-Block Frequency-Domain Adaptive Filters

Previously, we have presented a performance analysis of the unconstrained partitioned-block frequency-domain adaptive filter (PBFDAF) with 50% overlap. It was found that the unconstrained PBFDAF always converges to a biased solution, and hence the mean-square deviation (MSD) learning curve does not match the mean-square error (MSE) learning curve. To deal with this problem, we present an alternative theoretical model of the unconstrained PBFDAF by introducing a modified time-domain weight vector. We show that the new weight vector can converge to the true system impulse response in the mean sense. We also derive the analytical expressions for the MSD and the MSE. The analysis here is equivalent to that in our previous work, but the former is much simpler and easier to handle. Also, the MSD learning curve calculated from the new weight vector is in good agreement with the MSE learning curve. Computer simulations support the analytical results well.

Comb-partitioned frequency-domain constraint adaptive algorithm for active noise control

Active noise control (ANC) is gaining credence as an effective approach in mitigating low-frequency urban noise. Current ANC algorithms that attenuate noise across the full audio frequency band, often exert control effort excessively at higher frequencies. Moreover, such unrestrained control unavoidably attenuates some critical sounds, such as alarms and warning signals. In practice, excessive control effort in ANC usually results in output-saturation distortion, which affects the adaptive system stability and degrades the residual audio quality. To provide greater flexibility of control in frequency bands of interest without incurring output saturation, this paper proposes two variants of the filtered reference comb-partitioned frequency-domain adaptive filter (FxCFDAF) algorithm, namely the leaky FxCFDAF and drop-out FxCFDAF algorithms, which exert output-effort constraint at the control filter in the frequency domain. In addition, the comb-partitioning approach in the proposed FxCFDAF algorithms is delayless and computationally-efficient, which are essential for practical implementation, unlike the conventional frequency-domain adaptive algorithm. Experimental simulations carried out on measured primary and secondary paths validate the proposed algorithms’ advantage over the conventional FxLMS algorithm in mitigating large-amplitude noise without output saturation.

On the Convergence Behavior of Partitioned-Block Frequency-Domain Adaptive Filters

Partitioned-block frequency-domain adaptive filter (PBFDAF) algorithms have become very popular, in particular, for acoustic signal processing. However, the stochastic behavior of PBFDAFs has not been extensively examined. This paper presents a comprehensive statistical analysis for a family of the overlap-save PBFDAF algorithms with 50% overlap, including the transient and steady-state performance. The frequency-domain equations of the PBFDAFs are transformed into the time-domain counterparts, which allows us to carry out the analysis completely in the time domain. By means of the independence assumption and vectorization operation, theoretical models for the mean and mean-square behavior of the PBFDAF algorithms are established without restricting the distribution of the inputs to being Gaussian. Specifically, the mean weight behavior and corresponding steady-state solution are provided. Closed-form expressions for the mean-square deviation (MSD) and mean-square error (MSE) are derived. The upper bound on the step size for the mean and mean-square stability of the PBFDAFs is specified. The theoretical model presents new insights into the convergence properties of the PBFDAFs with a sufficient number of coefficients. It was revealed that both the constrained and unconstrained PBFDAFs converge to the Wiener solution. However, the mean weight vector of the unconstrained PBFDAF algorithms cannot converge to the true solution for any inputs, while that of the constrained version can. The presented theory explains why the steady-state MSD of the unconstrained PBFDAF algorithm is larger than that of the constrained version but their minimum MSE is the same. Monte Carlo simulations provide very good support for our theory.

Multichannel speaker interference reduction using frequency domain adaptive filtering

Microphone leakage or crosstalk is a common problem in multichannel close-talk audio recordings (e.g., meetings or live music performances), which occurs when a target signal does not only couple into its dedicated microphone, but also in all other microphone channels. For further signal processing such as automatic transcription of a meeting, a multichannel speaker interference reduction is required in order to eliminate the interfering speech signals in the microphone channels. The contribution of this paper is twofold: First, we consider multichannel close-talk recordings of a three-person meeting scenario with various different crosstalk levels. In order to eliminate the crosstalk in the target microphone channel, we extend a multichannel Wiener filter approach, which considers all individual microphone channels. Therefore, we integrate an adaptive filter method, which was originally proposed for acoustic echo cancellation (AEC), in order to obtain a well-performing interferer (noise) component estimation. This results in an improved speech-to-interferer ratio by up to 2.7 dB at constant or even better speech component quality. Second, since an AEC method requires typically clean reference channels, we investigate and report findings why the AEC algorithm is able to successfully estimate the interfering signals and the room impulse responses between the microphones of the interferer and the target speakers even though the reference signals are themselves disturbed by crosstalk in the considered meeting scenario.

New Insights into Convergence Theory of Constrained Frequency-Domain Adaptive Filters

Two kinds of update equations are commonly used for the constrained frequency-domain adaptive filter (FDAF), namely the gradient-constrained version and the weight-constrained version. The constraint is imposed only on the stochastic gradient vector in the first version, while it is imposed on the whole weight vector in the second version. It was already found that the two versions have different convergence behaviors, but a rigors analysis of the convergence behavior of the gradient-constrained FDAF is still lacking so far. This paper presents a comprehensive statistical analysis of the gradient-constrained FDAF. We set up an equivalent update equation of the gradient-constrained FDAF, which provides a close link with that of the weight-constrained version. Then, the mean and mean-square convergence behaviors of the gradient-constrained FDAF are analyzed using the new update equation, and the corresponding steady-state solutions are provided. Theoretical results confirm that the gradient-constrained FDAF will converge to a biased solution and exhibits a larger mean-square error than the weight-constrained version when, for instance, the weight vector is not initialized properly. Simulation results agree with our theoretical predictions very well.

Optimum step-size control for a variable step-size stereo acoustic echo canceller in the frequency domain

The frequency-domain adaptive filter (FDAF) is a competitive candidate for stereo acoustic echo cancellation (SAEC) because of its good convergence and computational efficiency. However, there is a conflict between the convergence rate and the steady-state misalignment when using a constant step size. In this paper, a variable step-size approach is proposed for the stereo echo canceller in the frequency domain. The proposed method uses a first-order Markov model to describe the time-varying echo paths between the loudspeakers and the microphone. Following a statistical convergence analysis of the two-channel FDAF algorithm, the state recursion of the system distance in each frequency bin is given. The optimal step size is then derived by minimizing the system distance. Several practical problems, including noise power spectral density estimation and echo paths change detection, are discussed in details. Moreover, a close link between the proposed optimum step-size control method and the multichannel state–space frequency-domain adaptive filter is established. We show that the proposed variable step-size approach can also be incorporated into the block extended least-mean-square algorithm to fully exploit their benefits. Finally, computer simulations demonstrate that the proposed algorithm exhibits an excellent convergence performance and is very robust to the double talk.

Fractional Fourier Transform Based Adaptive Filtering Techniques for Acoustic Emission Signal Enhancement

Acoustic emission technique (AET) is a well-known non-destructive testing method used for the detection of crack growth and monitoring structural integrity of components. The main limitation in the application of AET is the fact that acoustic emission (AE) signal is often affected by background noise. A new approach is proposed in this paper to reduce the background noise and to improve the accuracy of AE signal detection. Various noise reduction methods have been applied and studied for AE signal enhancement so far. Some of the studies proved that self-adaptive noise cancellation (SANC) and adaptive noise cancellation (ANC) are better techniques for denoising the AE signal. This paper proposes the use of ANC and SANC schemes based on Fractional Fourier Transform (FrFT) for AE signal enhancement. FrFT is the generalization of the classical Fourier Transform (FT). The use of FrFT gives an advantage of an additional degree of freedom (angle of rotation in time–frequency plane) over the traditional Fourier transform and could provide improved performance. In this method, the noisy signal is rotated in time- frequency plane to extract the signal in Fractional Fourier domain (FrFD). Two adaptive filters viz. least mean squares and normalized least mean squares are studied for FrFD based ANC approach. The performance of the proposed method is validated using real AE signals acquired from three different experiments: pencil lead break test, composite drilling test and concrete compression test. Results are compared with the time and frequency domain adaptations. Moreover, the results have also been compared with the frequency domain adaptation techniques. Results have demonstrated that FrFD based ANC approach outperforms the conventional time domain and frequency domain adaptive filtering with an improved signal to noise ratio and significantly reduces mean square error.

Convergence Analysis of Deficient-Length Frequency-Domain Adaptive Filters

The frequency-domain adaptive filter (FDAF) has been utilized in various applications where the length of the modeling filter is very long. The convergence behavior of the FDAF in the full-modeling case has been well analyzed. However, because the length of the true filter may be rather long and is unknown in practice, the length of the adaptive filter is usually less than that of the true system. In this paper, only the statistical behavior of the deficient-length constrained FDAF was analyzed for Gaussian inputs. This paper presents a unified approach to the stochastic analysis of a family of the FDAF in an under-modeling situation and for arbitrary input distributions. Specifically, the mean and mean-square convergence behaviors of FDAFs are presented, and the closed-form expression of the steady-state misalignment is given. Our theoretical results provide some new insights into the convergence property of deficient-length FDAFs. In addition, the analysis is carried out in the frequency domain directly. Computer simulations indicate an excellent agreement with our theoretical predictions.

Quality improvement and performance analysis of High Efficiency Video Coding under high quantization parameters and rain streaks

High Efficiency Video Coding standard is an advanced and widely used video coding standard in recent high-definition (HD) video application. This video codec faces many challenges during the video transmission over lower bandwidth channel. One of the main challenges is the noise removal from HD video sequences. For noise removal, this video codec has in-loop filters specifically. Although these loop filters are efficient, they are not effective in removing rain pattern from the video sequences. To overcome this problem, a denoising filter has to be added to the loop filters. For denoising, an optimized multi-delay block frequency domain (OMBFD) adaptive filter is presented in this paper. Based on the intensity of raindrop, it is identified from the successive video frames. Then, these predicted raindrops are removed using the existing loop filters. Nevertheless, still, noises present in the frame are removed using the proposed OMBFD filter. To control the process of filtering, the exponential forgetting factor which is used in the proposed denoising filter is optimized using firefly optimization algorithm. Simulation results show the proposed denoising algorithm affords promising performance improvement compared to other denoising filters.

Analysis of the Unconstrained Frequency-Domain Block LMS for Second-Order Noncircular Inputs

The unconstrained frequency-domain block least mean square (UFBLMS) algorithm is a de facto standard in frequency-domain adaptive filtering, owing to its fast convergence for correlated input signals. However, although many complex-valued signals in real-world applications are second-order noncircular (improper), for computational convenience, existing mean square analyses of UFBLMS assume second-order circular (proper) input data. This, in turn, makes conventional mean square evaluations of UFBLMS inadequate. To address this issue, we propose a novel performance evaluation framework of UFBLMS, which makes it possible to investigate how the full second-order statistics of second-order noncircular correlated input signals, i.e., both their covariance and complementary covariance, influence the output error and the weight error of UFBLMS. A unified stability bound on the step-size of UFBLMS is next provided, enabling intuitive closed-form relations, in the steady-state stage, between the terms within full second-order error statistics, namely, the mean square error (MSE) and complementary MSE, and the input noncircularity. Furthermore, this proposed full second-order statistical framework is shown to enable more physical insight into the underlying physics of the contribution of the real and imaginary channels of UFBLMS, which cannot be achieved using the standard MSE analysis due to its insufficient degrees of freedom. Simulations and real-world experiments in the system identification setting support the analysis.

A Unified Approach to the Statistical Convergence Analysis of Frequency-Domain Adaptive Filters

The frequency-domain adaptive filter (FDAF) algorithms are used in many applications due to their computational efficiency and good convergence performance. Many efforts have been made to analyze the convergence behavior of FDAF in the past. However, the previous analyses are based on coarse approximations of overlap-save procedures or small step-size assumptions and hence came to inaccurate predictions of the transient and steady-state performance. Moreover, the rigorous step-size bound in the mean-square sense has not been provided so far. To address these problems, we carry out an extensive analysis of the convergence behaviors for a family of FDAFs based on the overlap-save structure. Using a unified update equation of four FDAFs, the state recursions of the mean weight-error vector and the weight-error covariance matrix are worked out rigorously in the frequency domain, which are then used to investigate the mean-square deviation (MSD) and mean-square error (MSE) during the transient phase. In addition, we obtain the analytical results on the steady-state MSD and MSE, and the bound on the step size for both the mean and mean-square stabilities. Specifically, the analysis presented here does not restrict the regression data to being Gaussian or white. Computer simulations in a system identification scenario confirmed that the proposed theoretical results are much more accurate than the previous approaches.

Application of adaptive line spectrum enhancer in adaptive matched filter

The most classical detector of active sonar and radar is the matched filter (MF), which is the optimal processor under ideal conditions. Aiming at the problem of active sonar detection, we propose a frequency-domain adaptive matched filter (FDAMF) with the use of a frequency-domain adaptive line enhancer (ALE). The FDAMF is an improved MF. In the simulations in this paper, the signal to noise ratio (SNR) gain of the FDAMF is about 18.6 dB higher than that of the classical MF when the input SNR is -10 dB. In order to improve the performance of the FDAMF with a low input SNR, we propose a pre-processing method, which is called frequency-domain time reversal convolution and interference suppression (TRC-IS). Compared with the classical MF, the FDAMF combined with the TRC-IS method obtains higher SNR gain, a lower detection threshold, and a better receiver operating characteristic (ROC) in the simulations in this paper. The simulation results show that the FDAMF has higher processing gain and better detection performance than the classical MF under ideal conditions. The experimental results indicate that the FDAMF does improve the performance of the MF, and can adapt to actual interference in a way. In addition, the TRC-IS preprocessing method works well in an actual noisy ocean environment.