The Volterra filter is one of the digital filters that can describe nonlinearity. In this paper, we analyze the dynamic behaviors of an adaptive signal processing system with the Volterra filter for nonwhite input signals by a statistical-mechanical method. Assuming the self-averaging property with an infinitely long tapped-delay line, we derive simultaneous differential equations that describe the behaviors of macroscopic variables in a deterministic and closed form. We analytically solve the derived equations to reveal the effect of the nonwhiteness of the input signal on the adaptation process. The results for the second-order Volterra filter show that the nonwhiteness decreases the mean-square error (MSE) in the early stages of the adaptation process and increases the MSE in the later stages.

The Volterra filter is one of the digital filters that can describe nonlinearity. In this paper, we analyze the dynamic behaviors of an adaptive signal-processing system including the Volterra filter by a statistical-mechanical method. On the basis of the self-averaging property that holds when the tapped delay line is assumed to be infinitely long, we derive simultaneous differential equations in a deterministic and closed form, which describe the behaviors of macroscopic variables. We obtain the exact solution by solving the equations analytically. In addition, the validity of the theory derived is confirmed by comparison with numerical simulations.

Adaptive Volterra filters (AVFs) are usually used to identify nonlinear systems, such as loudspeaker systems, and ordinary adaptive algorithms can be used to update the filter coefficients of AVFs. However, AVFs require huge computational complexity even if the order of the AVF is constrained to the second order. Improving calculation efficiency is therefore an important issue for the real-time implementation of AVFs. In this paper, we propose a novel sub-band AVF with high calculation efficiency for second-order AVFs. The proposed sub-band AVF consists of four parts: input signal transformation for a single sub-band AVF, tap length determination to improve calculation efficiency, switching the number of sub-bands while maintaining the estimation accuracy, and an automatic search for an appropriate number of sub-bands. The proposed sub-band AVF can improve calculation efficiency for which the dominant nonlinear components are concentrated in any frequency band, such as loudspeakers. A simulation result demonstrates that the proposed sub-band AVF can realize higher estimation accuracy than conventional efficient AVFs.

Extreme learning machine (ELM) has recently attracted many researchers' interest due to its very fast learning speed, good generalization ability, and ease of implementation. However, it has a linear output layer which may limit the capability of exploring the available information, since higher-order statistics of the signals are not taken into account. To address this, we propose a novel ELM architecture in which the linear output layer is replaced by a Volterra filter structure. Additionally, the principal component analysis (PCA) technique is used to reduce the number of effective signals transmitted to the output layer. This idea not only improves the processing capability of the network, but also preserves the simplicity of the training process. Then we carry out performance evaluation and application analysis for the proposed architecture in the context of supervised classification and unsupervised equalization respectively, and the obtained results either on publicly available datasets or various channels, when compared to those produced by already proposed ELM versions and a state-of-the-art algorithm: support vector machine (SVM), highlight the adequacy and the advantages of the proposed architecture and characterize it as a promising tool to deal with signal processing tasks.

In this paper, we propose a parameter estimation method using Volterra kernels for the nonlinear IIR filters, which are used for the linearization of closed-box loudspeaker systems. The nonlinear IIR filter, which originates from a mirror filter, employs nonlinear parameters of the loudspeaker system. Hence, it is very important to realize an appropriate estimation method for the nonlinear parameters to increase the compensation ability of nonlinear distortions. However, it is difficult to obtain exact nonlinear parameters using the conventional parameter estimation method for nonlinear IIR filter, which uses the displacement characteristic of the diaphragm. The conventional method has two problems. First, it requires the displacement characteristic of the diaphragm but it is difficult to measure such tiny displacements. Moreover, a laser displacement gauge is required as an extra measurement instrument. Second, it has a limitation in the excitation signal used to measure the displacement of the diaphragm. On the other hand, in the proposed estimation method for nonlinear IIR filter, the parameters are updated using simulated annealing (SA) according to the cost function that represents the amount of compensation and these procedures are repeated until a given iteration count. The amount of compensation is calculated through computer simulation in which Volterra kernels of a target loudspeaker system is utilized as the loudspeaker model and then the loudspeaker model is compensated by the nonlinear IIR filter with the present parameters. Hence, the proposed method requires only an ordinary microphone and can utilize any excitation signal to estimate the nonlinear parameters. Some experimental results demonstrate that the proposed method can estimate the parameters more accurately than the conventional estimation method.

In this paper, we propose a use of the group sparsity in adaptive learning of second-order Volterra filters for the nonlinear acoustic echo cancellation problem. The group sparsity indicates sparsity across the groups, i.e., a vector is separated into some groups, and most of groups only contain approximately zero-valued entries. First, we provide a theoretical evidence that the second-order Volterra systems tend to have the group sparsity under natural assumptions. Next, we propose an algorithm by applying the adaptive proximal forward-backward splitting method to a carefully designed cost function to exploit the group sparsity effectively. The designed cost function is the sum of the weighted group l1 norm which promotes the group sparsity and a weighted sum of squared distances to data-fidelity sets used in adaptive filtering algorithms. Finally, Numerical examples show that the proposed method outperforms a sparsity-aware algorithm in both the system-mismatch and the echo return loss enhancement.

In this letter, the compensation ability of nonlinear distortions for loudspeaker systems is demonstrated using dynamic distortion measurement. Two linearization methods using a Volterra filter and a Mirror filter are compared. The conventional evaluation utilizes swept multi-sinusoidal waves. However, it is unsatisfactory because wideband signals such as those of music and voices are usually applied to loudspeaker systems. Hence, the authours use dynamic distortion measurement employing a white noise. Experimental results show that the two linearization methods can effectively reduce nonlinear distortions for wideband signals.

In this letter, we propose a blind adaptive receiver with nonlinear structure for DS/CDMA communication systems. The proposed receiver requires the signature waveform and timing for only the desired user. It is shown that the blind adaptation is equivalent to the adaptation with the training signal and the function to be minimized has no local minima.