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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.
Discrete Frequency Warped Wavelets: Theory and Applications
 IEEE Trans. Signal Processing
, 1998
"... In this paper, we extend the definition of dyadic wavelets to include frequency warped wavelets. The new wavelets are generated and the transform computed in discretetime by alternating the Laguerre transform with perfect reconstruction filterbanks. This scheme provides the unique implementation of ..."
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Cited by 14 (7 self)
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In this paper, we extend the definition of dyadic wavelets to include frequency warped wavelets. The new wavelets are generated and the transform computed in discretetime by alternating the Laguerre transform with perfect reconstruction filterbanks. This scheme provides the unique implementation of orthogonal or biorthogonal warped wavelets by means of rational transfer functions. We show that the discretetime warped wavelets lead to welldefined continuoustime wavelet bases, satisfying a warped form of the twoscale equation. The shape of the wavelets is not invariant by translation. Rather, the "wavelet translates" are obtained from one another by allpass filtering. We show that the phase of the delay element is asymptotically a fractal. A feature of the warped wavelet transform is that the cutoff frequencies of the wavelets may be arbitrarily assigned while preserving a dyadic structure. The new transform provides an arbitrary tiling of the timefrequency plane, which can be designed by selecting as little as a single parameter. This feature is particularly desirable in cochlear and perceptual models of speech and music, where accurate bandwidth selection is an issue. As our examples show, by defining pitchsynchronous wavelets based on warped wavelets, the analysis of transients and denoising of inharmonic pseudoperiodic signals is greatly enhanced.
Parametric Least Squares Approximation Using Gamma Bases
"... We study the problem of linear approximation of a signal using the parametric Gamma bases in L 2 space. These bases have a time scale parameter which has the effect of modifying the relative angle between the signal and the projection space, thereby yielding an extra degree of freedom in the appro ..."
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Cited by 5 (2 self)
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We study the problem of linear approximation of a signal using the parametric Gamma bases in L 2 space. These bases have a time scale parameter which has the effect of modifying the relative angle between the signal and the projection space, thereby yielding an extra degree of freedom in the approximation. Gamma bases have a simple analog implementation which is a cascade of identical lowpass filters . We derive the normal equation for the optimum value of the time scale parameter and decouple it from that of the basis weights. Using statistical signal processing tools we further develop a numerical method for estimating the optimum time scale. EDICS NO: SP 2.3.1 Correspondence : Jose C. Principe Address : Computational Neuroengineering Laboratory CSE 447 University of Florida Gainesville FL32611 Phone : (904) 3922662 Fax : (904) 3920044 EMail : principe@synapse.ee.ufl.edu Page 2 of 8
FrequencyWarped Filter Banks and Wavelet Transforms: A DiscreteTime Approach via Laguerre Expansion
 IEEE Transactions on Signal Processing
, 1998
"... In this paper, we introduce a new generation of perfectreconstruction filter banks that can be obtained from classical critically sampled filter banks by means of frequency transformations. ..."
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Cited by 3 (1 self)
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In this paper, we introduce a new generation of perfectreconstruction filter banks that can be obtained from classical critically sampled filter banks by means of frequency transformations.
A comparison of performance of three orthogonal polynomials in extraction of wideband response using early time and low frequency data
 IEEE Trans. Antennas Propag
, 2005
"... Abstract—The objective of this paper is to generate a wideband and temporal response of threedimensional composite structures by using a hybrid method that involves generation of early time and lowfrequency information. The data in these two separate time and frequency domains are mutually complem ..."
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Cited by 2 (2 self)
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Abstract—The objective of this paper is to generate a wideband and temporal response of threedimensional composite structures by using a hybrid method that involves generation of early time and lowfrequency information. The data in these two separate time and frequency domains are mutually complementary and contain all the necessary information for a sufficient record length. Utilizing a set of orthogonal polynomials, the time domain signal (be it the electric or the magnetic currents or the near/far scattered electromagnetic field) could be expressed in an efficient way as well as the corresponding frequency domain responses. The available data is simultaneously extrapolated in both domains. Computational load for electromagnetic analysis in either domain, time or frequency, can be thus significantly reduced. Three orthogonal polynomial representations including Hermite polynomial, Laguerre function and Bessel function are used in this approach. However, the performance of this new method is sensitive to two important parameters—the scaling factor I and the expansion order.It is therefore important to find the optimal parameters to achieve the best performance. A comparison is presented to illustrate that for the classes of problems dealt with, the choice of the Laguerre polynomials has the best performance as illustrated by a typical scattering example from a dielectric hemisphere. Index Terms—Extrapolation, marching on in time (MOT), method of moments (MoM), scaling factor, time and frequency domain. I.
An Iterative Solution For The Optimal Poles In A Kautz Series
 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP’01
, 2001
"... Kautz series allow orthogonal series expansion of finiteenergy signals defined on a semiinfinite axis. The Kautz series consists of orthogonalized exponential functions or sequences. This series has as free parameters an ordered set of poles, each pole associated with an exponential function or seq ..."
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Cited by 1 (0 self)
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Kautz series allow orthogonal series expansion of finiteenergy signals defined on a semiinfinite axis. The Kautz series consists of orthogonalized exponential functions or sequences. This series has as free parameters an ordered set of poles, each pole associated with an exponential function or sequence. For reasons of approximation and compact representation (coding), an appropriate set of ordered poles is therefore convenient. An iterative procedure to establish the optimal parameters according to an enforced convergence criterion is introduced.
Electromagnetic Pulse Signal Representation Using Orthonormal Laguerre Sequences
, 1995
"... The notion of representing discretetime electromagnetic pulse (EMP) signals using orthonormal Laguerre sequences is introduced. The motivation for doing so is that EMP signals and Laguerre sequences are both characterized by decaying exponentials. It is shown that very efficient Laguerre representa ..."
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Cited by 1 (1 self)
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The notion of representing discretetime electromagnetic pulse (EMP) signals using orthonormal Laguerre sequences is introduced. The motivation for doing so is that EMP signals and Laguerre sequences are both characterized by decaying exponentials. It is shown that very efficient Laguerre representation of EMP signals is possible using this approach. 1 Laguerre Expansion Fundamentals Given a sequence x(n), its Laguerre expansion is defined as [1],[2] x(n) = 1 X k=0 c k (b)l k (n; b) (1) where n is the time index, 0 ! b ! 1 is a parameter, l k (n; b) is the kth Laguerre sequence, and c k is the kth coefficient of the expansion. Supported by NASA Grant NAGW 3293 obtained through the Microelectronics Research Center, The University of New Mexico The Laguerre sequences in (1) are orthonormal; i.e. 1 X n=0 l k (n; b)l m (n; b) = ( 1; k = m 0; k 6= m (2) where l k (n; b) = Z \Gamma1 f p 1 \Gamma b 2 (z \Gamma1 \Gamma b) k (1 \Gamma bz \Gamma1 ) k+1 g; k = 0; ...
SYSTEM MODELING USING GENERALIZED LINEAR FEEDFORWARD NETWORKS By
, 1999
"... There are many people who made the completion of this work possible. First and foremost I would like to thank my research professor, Dr. Jose C. Principe. He has taught me the valuable skills of rigor and completeness. Also, his patience with my progress while I juggled both research and a busy care ..."
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Cited by 1 (0 self)
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There are many people who made the completion of this work possible. First and foremost I would like to thank my research professor, Dr. Jose C. Principe. He has taught me the valuable skills of rigor and completeness. Also, his patience with my progress while I juggled both research and a busy career was greatly appreciated. I would like to thank my supervisory committee members – Dr. Yunmei Chen, Dr. William W. Edmonson, Dr. John G. Harris, and Dr. Jian Li – for their encouragement and direction. Many thanks go to the management within the 46 Test Wing, Eglin AFB, FL, who made it possible for me to attend the University of Florida through the longterm fulltime training program. This organization fosters an atmosphere that encourages academic achievement, and it has continually provided me with the opportunity to further my education. There are no words to describe the wisdom, guidance, and support I have received from my parents. Their love to this day is endless. Above all I would like to give the highest recognition to my loving wife, Donna,
On The Laguerre Representation Of A Class Of Exponential Signals
"... The notion of using orthonormal Laguerre sequences to represent discretetime signals (sequences) [1.],[2.] was recently used for the representation of electromagnetic pulse (EMP) data [3.]. This formulations resulted in an error function that needed to be minimized with respect to a Laguerre paramet ..."
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The notion of using orthonormal Laguerre sequences to represent discretetime signals (sequences) [1.],[2.] was recently used for the representation of electromagnetic pulse (EMP) data [3.]. This formulations resulted in an error function that needed to be minimized with respect to a Laguerre parameter. The objective of this paper is to introduce some sufficient conditions for this error function to be unimodal. KEYWORDS: Laguerre expansions, exponential signals, Fibonacci search LAGUERRE EXPANSION FUNDAMENTALS Given a sequence x(n), its Laguerre expansion is defined as [1.],[2.] x(n) = 1 X k=0 c k (b)l k (n; b) (1) where n is the time index, 0 ! b ! 1 is a parameter, l k (n; b) is the kth Laguerre sequence, and c k is the kth coefficient of the expansion. The set of Laguerre sequences in (1) are orthonormal; i.e. 1 X n=0 l k (n; b)l m (n; b) = ( 1; k = m 0; k 6= m (2) where l k (n; b) = Z \Gamma1 8 ! : p 1 \Gamma b 2 (z \Gamma1 \Gamma b) k (1 \Gamma bz \Ga...
A STC Design Based on DL Networks for Discrete Unstructured Systems
, 1999
"... This paper proposes a design method of STC for discrete unstructured systems based on DL networks. The proposed scheme determines the control input composed of arbitrary system matrices of constructed DL networks, and thus it makes it possible to design the STC for unstructured systems whose prior ..."
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This paper proposes a design method of STC for discrete unstructured systems based on DL networks. The proposed scheme determines the control input composed of arbitrary system matrices of constructed DL networks, and thus it makes it possible to design the STC for unstructured systems whose priori knowledges are not available. The simulation results show that the proposed scheme provides satisfactory performances both in MPS and NMPS for the STC design of unstructured systems.