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Design of Neural Network Filters
 Electronics Institute, Technical University of Denmark
, 1993
"... Emnet for n rv rende licentiatafhandling er design af neurale netv rks ltre. Filtre baseret pa neurale netv rk kan ses som udvidelser af det klassiske line re adaptive lter rettet mod modellering af uline re sammenh nge. Hovedv gten l gges pa en neural netv rks implementering af den ikkerekursive, ..."
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Cited by 21 (12 self)
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Emnet for n rv rende licentiatafhandling er design af neurale netv rks ltre. Filtre baseret pa neurale netv rk kan ses som udvidelser af det klassiske line re adaptive lter rettet mod modellering af uline re sammenh nge. Hovedv gten l gges pa en neural netv rks implementering af den ikkerekursive, uline re adaptive model med additiv st j. Formalet er at klarl gge en r kke faser forbundet med design af neural netv rks arkitekturer med henblik pa at udf re forskellige \blackbox " modellerings opgaver sa som: System identi kation, invers modellering og pr diktion af tidsserier. De v senligste bidrag omfatter: Formulering af en neural netv rks baseret kanonisk lter repr sentation, der danner baggrund for udvikling af et arkitektur klassi kationssystem. I hovedsagen drejer det sig om en skelnen mellem globale og lokale modeller. Dette leder til at en r kke kendte neurale netv rks arkitekturer kan klassi ceres, og yderligere abnes der mulighed for udvikling af helt nye strukturer. I denne sammenh ng ndes en gennemgang af en r kke velkendte arkitekturer. I s rdeleshed l gges der v gt pa behandlingen af multilags perceptron neural netv rket.
Linear Multichannel Blind Equalizers of Nonlinear FIR Volterra Channels
 IEEE Trans. Signal Processing
, 1997
"... Truncated Volterra expansions model nonlinear systems encountered with satellite communications, magnetic recording channels, and physiological processes. A general approach for blind deconvolution of singleinput multipleoutput Volterra finite impulse response (FIR) systems is presented. It is sho ..."
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Cited by 14 (3 self)
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Truncated Volterra expansions model nonlinear systems encountered with satellite communications, magnetic recording channels, and physiological processes. A general approach for blind deconvolution of singleinput multipleoutput Volterra finite impulse response (FIR) systems is presented. It is shown that such nonlinear systems can be blindly equalized using only linear FIR filters. The approach requires that the Volterra kernels satisfy a certain coprimeness condition and that the input possesses a minimal persistenceofexcitation order. No other special conditions are imposed on the kernel transfer functions or on the input signal, which may be deterministic or random with unknown statistics. The proposed algorithms are corroborated with simulation examples.
Equivalent system model and equalization of a differential impulse radio UWB system
 IEEE J. Sel. Areas Commun
, 2005
"... Abstract—A discretetime equivalent system model is derived for differential and transmitted reference (TR) ultrawideband (UWB) impulse radio (IR) systems, operating under heavy intersymbolinterference (ISI) caused by multipath propagation. In the systems discussed, data is transmitted using diffe ..."
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Cited by 13 (2 self)
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Abstract—A discretetime equivalent system model is derived for differential and transmitted reference (TR) ultrawideband (UWB) impulse radio (IR) systems, operating under heavy intersymbolinterference (ISI) caused by multipath propagation. In the systems discussed, data is transmitted using differential modulation on a framelevel, i.e., among UWB pulses. Multiple pulses (frames) are used to convey a single bit. Time hopping and amplitude codes are applied for multi user communications, employing a receiver frontend that consists of a bank of pulsepair correlators. It is shown that these UWB systems are accurately modeled by secondorder discretetime Volterra systems. This proposed nonlinear equivalent system model is the basis for developing optimal and suboptimal receivers for differential UWB communications systems under ISI. As an example, we describe a maximum likelihood sequence detector with decision feedback, to be applied at the output of the receiver frontend sampled at symbol rate, and an adaptive inverse modeling equalizer. Both methods significantly increase the robustness in presence of multipath interference at tractable complexity. Index Terms—Differential receivers, equalization, impulse radio (IR), transmitted reference, ultrawideband (UWB) communications, Volterra systems. I.
Robust Full Bayesian Learning for Neural Networks
, 1999
"... In this paper, we propose a hierarchical full Bayesian model for neural networks. This model treats the model dimension (number of neurons), model parameters, regularisation parameters and noise parameters as random variables that need to be estimated. We develop a reversible jump Markov chain Monte ..."
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Cited by 12 (9 self)
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In this paper, we propose a hierarchical full Bayesian model for neural networks. This model treats the model dimension (number of neurons), model parameters, regularisation parameters and noise parameters as random variables that need to be estimated. We develop a reversible jump Markov chain Monte Carlo (MCMC) method to perform the necessary computations. We find that the results obtained using this method are not only better than the ones reported previously, but also appear to be robust with respect to the prior specification. In addition, we propose a novel and computationally efficient reversible jump MCMC simulated annealing algorithm to optimise neural networks. This algorithm enables us to maximise the joint posterior distribution of the network parameters and the number of basis function. It performs a global search in the joint space of the parameters and number of parameters, thereby surmounting the problem of local minima. We show that by calibrating the full hierarchical ...
Nonlinear Acoustic Echo Cancellation With 2nd Order Adaptive Volterra Filter
 Proc. ICASSP'99
"... Acoustic echo cancellers in today's speakerphones or video conferencing systems rely on the assumption of a linear echo path. Lowcost audio equipment or constraints of portable communication systems cause nonlinear distortions, which limit the echo return loss enhancement achievable by linear adapt ..."
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Cited by 12 (3 self)
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Acoustic echo cancellers in today's speakerphones or video conferencing systems rely on the assumption of a linear echo path. Lowcost audio equipment or constraints of portable communication systems cause nonlinear distortions, which limit the echo return loss enhancement achievable by linear adaptation schemes. These distortions are a superposition of different effects, which can be modelled either as memoryless nonlinearities or as nonlinear systems with memory. Proper adaptation schemes for both cases of nonlinearities are discussed. An echo canceller for nonlinear systems with memory based on an adaptive second order Volterra filter is presented. Its performance is demonstrated by measurements with small loudspeakers. The results show an improvement in the echo return loss enhancement of 7 dB over a conventional linear adaptive filter. The additional computational requirement for the presented Volterra filter is comparable to that of existing acoustic echo cancellers. 1.
An efficient approximation to the quadratic Volterra filter and its application in realtime loudspeaker linearization
, 1995
"... Nonlinear filtering based on the Volterra series expansion a powerful and popular approach in signal processing. However, a serious problem is the increased filter complexity as compared to linear filtering. This paper presents an efficient approximation to the 2nd order Volterra filter. The propose ..."
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Cited by 11 (3 self)
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Nonlinear filtering based on the Volterra series expansion a powerful and popular approach in signal processing. However, a serious problem is the increased filter complexity as compared to linear filtering. This paper presents an efficient approximation to the 2nd order Volterra filter. The proposed filter structure, called Multi Memory Decomposition (MMD), is composed of 3 linear FIR filters and one multiplier. Hence, the number of required filter operations is linear in the filter memory length. MMD coefficient determination with respect to a 2nd order reference kernel is presented. Additionally, block oriented and adaptive algorithms are proposed which calculate the filter weights from input and output measurements of an unknown system. The good performance of the MMD model is demonstrated by simulations and in a realtime application. Therefore, the linearization scheme for the compensation of nonlinear distortions with a preprocessor is introduced. The preprocessor was implemented...
Color image interpolation using vector rational filters
 in Proc. of SPIE/EI Conf., Nonlinear Image Processing IX
, 1998
"... Rational lters are extended to multichannel signal processing and applied to the image interpolation problem. The proposed nonlinear interpolator exhibits desirable properties, such as, edge and details preservation. In this approach the pixels of the color image are considered as 3component vector ..."
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Cited by 10 (8 self)
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Rational lters are extended to multichannel signal processing and applied to the image interpolation problem. The proposed nonlinear interpolator exhibits desirable properties, such as, edge and details preservation. In this approach the pixels of the color image are considered as 3component vectors in the color space. Therefore, the inherent correlation which exists between the di erent color components is not ignored� thus, leading to better image quality than those obtained by componentwise processing. Simulations show that the resulting edges obtained using vector rational lters (VRF) are free from blockiness and jaggedness, which are usually present in images interpolated using especially linear, but also some nonlinear techniques, e.g. vector median hybrid lters (VMHF [2]). 1.
Optimizing polynomial expressions by algebraic factorization and common subexpression elimination
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems
, 2006
"... Abstract—Polynomial expressions are frequently encountered in many application domains, particularly in signal processing and computer graphics. Conventional compiler techniques for redundancy elimination such as common subexpression elimination (CSE) are not suited for manipulating polynomial expre ..."
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Cited by 8 (0 self)
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Abstract—Polynomial expressions are frequently encountered in many application domains, particularly in signal processing and computer graphics. Conventional compiler techniques for redundancy elimination such as common subexpression elimination (CSE) are not suited for manipulating polynomial expressions, and designers often resort to hand optimizing these expressions. This paper leverages the algebraic techniques originally developed for multilevel logic synthesis to optimize polynomial expressions by factoring and eliminating common subexpressions. The proposed algorithm was tested on a set of benchmark polynomial expressions where savings of 26.7 % in latency and 26.4 % in energy consumption were observed for computing these expressions on the StrongARM SA1100 processor core. When these expressions were synthesized in custom hardware, average energy savings of 63.4 % for minimum hardware constraints and 24.6 % for medium hardware constraints over CSE were observed. Index Terms—Circuit complexity, common subexpression elimination (CSE), highlevel synthesis, polynomials. I.
Piecewise Linear System Modeling Based On A Continuous Threshold Decomposition
 IEEE TRANS. ON SIGNAL PROCESSING
, 1995
"... The continuous threshold decomposition is a segmentation operator used to split a signal into a set of multilevel components. This decomposition method can be used to represent continuous multivariate piecewise linear (PWL) functions, and therefore can be employed to describe PWL systems defined ove ..."
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Cited by 8 (4 self)
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The continuous threshold decomposition is a segmentation operator used to split a signal into a set of multilevel components. This decomposition method can be used to represent continuous multivariate piecewise linear (PWL) functions, and therefore can be employed to describe PWL systems defined over a rectangular lattice. The resulting filters are canonical and have a multichannel structure that can be exploited for the development of rapidly convergent algorithms. The optimum design of the class of PWL filters introduced in the paper can be postulated as a least squares problem whose variables separate into a linear and a nonlinear part. Based on this feature, parameter estimation algorithms are developed. First, a block data processing algorithm that combines linear leastsquares with grid localization through recursive partitioning is introduced. Second, a timeadaptive method based on the combination of an RLS algorithm for coefficient updating and a signed gradient descent module...
Tensor Product Basis Approximations for Volterra Filters
 IEEE Transactions on Signal Processing
, 1996
"... This paper studies approximations for a class of nonlinear filters known as Volterra filters. Although the Volterra filter provides a relatively simple and general representation for nonlinear filtering, often it is highly overparameterized. Due to the large number of parameters, the utility of the ..."
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Cited by 7 (5 self)
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This paper studies approximations for a class of nonlinear filters known as Volterra filters. Although the Volterra filter provides a relatively simple and general representation for nonlinear filtering, often it is highly overparameterized. Due to the large number of parameters, the utility of the Volterra filter is limited. The overparameterization problem is addressed in this paper using a tensor product basis approximation (TPBA). In many cases a Volterra filter may be well approximated using the TPBA with far fewer parameters. Hence, the TPBA offers considerable advantages over the original Volterra filter in terms of both implementation and estimation complexity. Furthermore, the TPBA provides useful insight into the filter response. This paper studies the crucial issue of choosing the approximation basis. Several methods for designing an appropriate approximation basis and error bounds on the resulting meansquare output approximation error are derived. Certain methods are sho...