Topic
Volterra series
About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.
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21 May 2001
TL;DR: A new method is presented for the identification of frequency-domain Volterra kernels based on the assumption that frequency- domain kernels are focally smooth, the kernel surface can be approximated by interpolation techniques, thus reducing the complexity of the model.
Abstract: The paper presents a new method for the identification of frequency-domain Volterra kernels. Based on the assumption that frequency-domain kernels are focally smooth, the kernel surface can be approximated by interpolation techniques, thus reducing the complexity of the model. Similarly to the unreduced (Volterra) model, this smaller model is also (i) linear in the unknowns, (ii) only locally sensitive to its parameters and (iii) free of structural assumptions about the system. The parameter estimation boils down to solving a linear system of equations in the least-squares (LS) sense. The design of the interpolation scheme is described, and the performance of the approximation is analyzed, and illustrated by simulation. The algorithm allows a significant saving in measurement time compared to other kernel estimation methods.
11 citations
TL;DR: The autocorrelation function is derived and it is shown that it does not provide sufficient information necessary for estimating the parameters of the proposed model and the third-order moment sequence provides additional information that can be used in conjunction with the autoc orrelation function to solve the problem.
Abstract: In many problems of digital signal processing, it is required to determine a model matching the statistics of a given observation of a generally non-Gaussian random process. Because of the wide range of systems that can be represented by Volterra series and Wiener expansions, the discrete nonlinear second-order Wiener filter (NSWF) driven by white Gaussian noise has been used in this study to match the statistics of a discrete zero-mean stationary non-Gaussian random process. First, we derive the autocorrelation function and show that it does not provide sufficient information necessary for estimating the parameters of the proposed model. Next, we derive the third-order moment sequence and show that it provides additional information that can be used in conjunction with the autocorrelation function to solve the problem. The power spectrum and bispectrum of the discrete NSWF have been also derived.
11 citations
TL;DR: This paper uses an algorithm of kernel identification of the Volterra series which greatly reduces the computational burden and eliminates the restriction of using white Gaussian input as a test signal.
11 citations
TL;DR: An algorithm to numerically obtain Volterra kernels from the output x(t) through sampling the input space by linear combinations of delta functions is presented, a nonlinear analogue of the classical method of impulse response.
Abstract: We consider vector-valued autonomous differential equations of the form x' = f(x) + phi with analytic f and investigate the nonanticipative solution operator phi bar right arrow A(phi) in terms of its Volterra series. We show that Volterra kernels of order > 1 occurring in the series expansion of the solution operator A are continuous functions, and establish recurrence relations between the kernels allowing their explicit calculation. A practical tensor calculus is provided for the finite-dimensional case. In addition to analytically calculating the kernels, we present an algorithm to numerically obtain them from the output x(t) through sampling the input space by linear combinations of delta functions. We call this "differential sampling". It is a nonlinear analogue of the classical method of impulse response. We prove a continuity theorem stating that, in the finite-dimensional case, approximate delta functions give rise to approximate Volterra kernels and that continuity holds in the sense of weak convergence. Finally, we discuss a practical implementation of differential sampling and relate it to the Wiener method.
11 citations
TL;DR: A Volterra expansion is investigated from which a set of linear-quadratic filters is derived using higher order statistics, applicable for single frame and multiple frames of a single scene imaged under low-light levels.
Abstract: We consider the use of nonlinear estimators for the noise smoothing of images obtained under quantum-limited imaging conditions. A Volterra expansion is investigated from which a set of linear-quadratic filters is derived using higher order statistics. The filters are applicable for single frame and multiple frames of a single scene imaged under low-light levels. >
11 citations