Volterra series

About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.

Nonlinear Speech Coding Using Backward Adaptive Variable-Length Quadratic Filters

Abstract: The ADTCM coding technique with nonlinear prediction based on quadratic Volterra filters is examined using backward prediction schemes based on LMS and RLS algorithms. Utilizing backward adaptive quadratic filters in ADTCM based speech coding, by itself, does not result in an overall improvement in the quality of reconstructed signal in comparison with a linear scheme using the same bit rate. However, it is shown that a scheme can be developed in which, for each frame of constant length, a set of quadratic filters with different memory sizes is examined and the nonlinear filter resulting in best improved quality is decided on. The identifying code of the selected filter is sent to the decoder along with the quantized residual signals. The simulation results show that the proposed scheme results in a good improvement (up to 2 dB) in the overall quality of the reconstructed speech signal. This improvement is achieved at the cost of a slight increase in the bit rate and a small delay.

Fast Solution of Induction Heating Problems by Structure-Preserving Nonlinear Model Order Reduction

Abstract: A fast approach to the numerical solution of induction heating problems is proposed. The projection space is efficiently determined by numerically computing a few Volterra kernels of the solution to the problem. Numerical results show that the construction of the reduced nonlinear model is performed at a computational cost that is orders of magnitude less than that for the numerical integration of the full problem. The reduced order model solution then allows accurately reconstructing the whole space-time distribution of magnetic and temperature fields at negligible computational cost.

Power amplifying system and method for generating pre-distortion signals

Abstract: In this invention, a power amplifying system and the method to generate the distorted signal are illustrated. The power amplifying system sends the digital signal and the feedback digital signal to the DSP for computation. The predicted distorted coefficient is sampled to supply for the predicted distorted chip based on the model of the Volterra series or its derivation, the chip applies which to process with the predicted distortion processing, the processed signal is to be sent to power amplifying system through the transmitting channel.

On the Analysis and Emulation of Nonlinear Component Characteristics

Abstract: We present theoretical background and implementation considerations of Volterra series based nonlinear component models. We demonstrate the advantage of combining frequency and time domain representations and present an efficient way to find high-order filter taps.

Adaptive polynomial filtering algorithms

Abstract: This dissertation presents several algorithms for adaptive nonlinear filters equipped with polynomial system models. In particular, truncated Volterra and bilinear system models are considered. These models are capable of representing a wide class of nonlinear systems. A fast, recursive least-squares (RLS) second-order Volterra filter and a fast extended RLS adaptive bilinear filter are introduced. These algorithms exploit the ideas employed for developing fast RLS adaptive multichannel filters and have computational complexity that is an order of magnitude lower than the most efficient previously available RLS algorithms. A theoretical performance analysis of the steady-state behavior of the second-order Volterra filter operating in both stationary and nonstationary environments is presented. The analysis shows that, when the input is zero-mean, Gaussian distributed and the adaptive filter is operating in a stationary environment, the steady-state excess mean-squared error is independent of the statistics of the input signal. The idea of developing fast RLS higher-order Volterra filters is also discussed. Despite the recursive system model employed, the extended RLS adaptive bilinear filter is shown to be stable whenever the desired response signal is bounded. Simulation results that exhibit good parsimony in the use of coefficients of the bilinear filters over the Volterra filters are presented. Mainly motivated by the computational simplicity, gradient-type output-error adaptive bilinear filters are also developed. These algorithms are among a large class of adaptive bilinear filtering algorithms that exhibit stability problems. Several input-dependent stability conditions for the output of a bilinear system to be bounded when the input is bounded are presented. A set of simple sufficient stability conditions of a very general bilinear system model is introduced. The derivation shows that the bilinear system model considered has a unique Volterra series expansion, and then utilizes the convergence concepts associated with the Volterra series expansion. An efficient implementation of the stability test is then introduced. A set of necessary stability conditions for a general bilinear system model and a set of sufficient and necessary stability conditions for a specific bilinear system model are also derived. These conditions are attractive because they are very easy to check. The stability conditions presented in this dissertation are essential for developing a large class of adaptive bilinear filters.