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54
Projectionbased approaches for model reduction of weakly nonlinear, timevarying systems
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems
"... Abstract—The problem of automated macromodel generation is interesting from the viewpoint of systemlevel design because if small, accurate reducedorder models of system component blocks can be extracted, then much larger portions of a design, or more complicated systems, can be simulated or verifi ..."
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Cited by 41 (1 self)
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Abstract—The problem of automated macromodel generation is interesting from the viewpoint of systemlevel design because if small, accurate reducedorder models of system component blocks can be extracted, then much larger portions of a design, or more complicated systems, can be simulated or verified than if the analysis were to have to proceed at a detailed level. The prospect of generating the reduced model from a detailed analysis of component blocks is attractive because then the influence of secondorder device effects or parasitic components on the overall system performance can be assessed. In this way overly conservative design specifications can be avoided. This paper reports on experiences with extending model reduction techniques to nonlinear systems of differential–algebraic equations, specifically, systems representative of RF circuit components. The discussion proceeds from linear timevarying, to weakly nonlinear, to nonlinear timevarying analysis, relying generally on perturbational techniques to handle deviations from the linear timeinvariant case. The main intent is to explore which perturbational techniques work, which do not, and outline some problems that remain to be solved in developing robust, general nonlinear reduction methods. Index Terms—Circuit noise, circuit simulation, nonlinear systems, reducedorder systems, timevarying circuits. I.
Pseudodifferential operators and Banach algebras in mobile communications
 Applied and Computational Harmonic Analysis
"... We study linear timevarying operators arising in mobile communication using methods from timefrequency analysis. We show that a wireless transmission channel can be modeled as pseudodifferential operator Hσ with symbol σ in FL1w or in the modulation space M∞,1w (also known as weighted Sjöstrand ..."
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Cited by 22 (5 self)
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We study linear timevarying operators arising in mobile communication using methods from timefrequency analysis. We show that a wireless transmission channel can be modeled as pseudodifferential operator Hσ with symbol σ in FL1w or in the modulation space M∞,1w (also known as weighted Sjöstrand class). It is then demonstrated that Gabor Riesz bases {ϕm,n} for subspaces of L2(R) approximately diagonalize such pseudodifferential operators in the sense that the associated matrix [〈Hσϕm′,n ′ , ϕm,n〉]m,n,m′,n ′ belongs to a Wienertype Banach algebra with exponentially fast offdiagonal decay. We indicate how our results can be utilized to construct numerically efficient equalizers for multicarrier communication systems in a mobile environment. 1
Optimal filtering in fractional Fourier domains
 IN PROC. IEEE INT. CONF. ACOUST., SPEECH, SIGNAL PROCESSING
, 1997
"... For timeinvariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(N log N) time, gives the minimum meansquareerror estimate of the original undistorted signal. For timevarying degradations and nonstationary processes, ..."
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Cited by 21 (9 self)
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For timeinvariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(N log N) time, gives the minimum meansquareerror estimate of the original undistorted signal. For timevarying degradations and nonstationary processes, however, the optimal linear estimate requires O(N 2) time for implementation. We consider filtering in fractional Fourier domains, which enables significant reduction of the error compared with ordinary Fourier domain filtering for certain types of degradation and noise (especially of chirped nature), while requiring only O(N log N) implementation time. Thus, improved performance is achieved at no additional cost. Expressions for the optimal filter functions in fractional domains are derived, and several illustrative examples are given in which significant reduction of the error (by a factor of 50) is obtained.
A timefrequency calculus for timevarying systems and nonstationary processes with applications
, 2000
"... ausgeführt zum Zwecke der Erlangung des akademischen Grades eines ..."
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Cited by 16 (5 self)
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ausgeführt zum Zwecke der Erlangung des akademischen Grades eines
Generalized Evolutionary Spectral Analysis and the Weyl Spectrum of Nonstationary Random Processes
, 1997
"... The evolutionary spectrum (ES) is a "timevarying power spectrum" of nonstationary random processes. Starting from an innovations system interpretation of the ES, we introduce the generalized evolutionary spectrum (GES) as a novel family of timevarying power spectra. The GES contains the ..."
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Cited by 15 (5 self)
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The evolutionary spectrum (ES) is a "timevarying power spectrum" of nonstationary random processes. Starting from an innovations system interpretation of the ES, we introduce the generalized evolutionary spectrum (GES) as a novel family of timevarying power spectra. The GES contains the ES and the recently introduced transitory evolutionary spectrum as special cases. We consider the problem of finding an innovations system for a process characterized by its correlation function, and we discuss the connection between GES analysis and the class of underspread processes. We furthermore show that another special case of the GES, a novel timevarying power spectrum that we call Weyl spectrum, has substantial advantages over all other members of the GES family. The properties of the Weyl spectrum are discussed, and its superior performance is verified experimentally for synthetic and realdata processes. This work was supported by FWF Grants P10012 OPH and S7001MAT. 1 Introduction S...
Time–frequency formulation, design, and implementation of timevarying optimal filters for signal estimation
 IEEE TRANS. SIGNAL PROCESS
, 2000
"... This paper presents a time–frequency framework for optimal linear filters (signal estimators) in nonstationary environments. We develop time–frequency formulations for the optimal linear filter (timevarying Wiener filter) and the optimal linear timevarying filter under a projection side constraint ..."
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Cited by 14 (5 self)
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This paper presents a time–frequency framework for optimal linear filters (signal estimators) in nonstationary environments. We develop time–frequency formulations for the optimal linear filter (timevarying Wiener filter) and the optimal linear timevarying filter under a projection side constraint. These time–frequency formulations extend the simple and intuitive spectral representations that are valid in the stationary case to the practically important case of underspread nonstationary processes. Furthermore, we propose an approximate time–frequency design of both optimal filters, and we present bounds that show that for underspread processes, the timefrequency designed filters are nearly optimal. We also introduce extended filter design schemes using a weighted error criterion, and we discuss an efficient time–frequency implementation of optimal filters using multiwindow shorttime Fourier transforms. Our theoretical results are illustrated by numerical simulations.
Homomorphic Modulation Spectra
 in Proceedings of the IEEE ICASSP
, 2004
"... Physical evidence points to the importance of a concept called “modulation frequency. ” This dimension exists jointly with standard Fourier or acoustic frequency. Thus, akin to other timevarying analysis, we seek a twodimensional representation, the “modulation spectrum, ” where the first dimension ..."
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Cited by 13 (4 self)
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Physical evidence points to the importance of a concept called “modulation frequency. ” This dimension exists jointly with standard Fourier or acoustic frequency. Thus, akin to other timevarying analysis, we seek a twodimensional representation, the “modulation spectrum, ” where the first dimension is the wellknown acoustic frequency and the second dimension is modulation frequency. We describe some deficiencies in previous discussions of this concept, and then address those deficiencies via a homomorphic approach. We also reduce previous difficulties in homomorphic demultiplication by integrating this processing into modulation spectra and, in particular, show how assumption of analytic and relatively narrowband subbands allows more accurate and practical use of homomorphic demultiplication. Lastly, we show how an unambiguous demultiplication concept is only consistent with complex modulator envelopes. The assumption of complex envelopes is necessary for accurate modulation spectral analysis and filtering.
Linear TimeFrequency Filters: Online Algorithms and Applications
, 2002
"... This chapter discusses practical discretetime methods for the timefrequency (TF) design of linear timevariant (LTV) filters. The filters are specified via a prescribed TF weight function (timevarying transfer function). We consider both explicit TF filter designs where a TF representation of the ..."
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Cited by 11 (3 self)
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This chapter discusses practical discretetime methods for the timefrequency (TF) design of linear timevariant (LTV) filters. The filters are specified via a prescribed TF weight function (timevarying transfer function). We consider both explicit TF filter designs where a TF representation of the LTV filter is matched to the specified TF weight function, and implicit TF filter designs that use an analysisweightingsynthesis procedure involving a linear TF signal representation. All filter designs allow for efficient online implementations and are thus suited to realtime applications. Our theoretical development is complemented by detailed descriptions of online algorithms, discussions of the choice of design parameters, and estimates of computational complexity and memory requirements. The performance and selected applications of the various TF filters are illustrated via numerical simulations.
A FrequencyDomain, Volterra SeriesBased Behavioral Simulation Tool for RF Systems
 Proc. IEEE Custom Integrated Circuits Conference
, 1999
"... In this paper a new behavioral modeling approach for RF systems based is presented, based on a Volterra series inputoutput map representation. The modeling is done purely in the frequency domain, capturing the typical system level specifications for RF building blocks, independent of the implementa ..."
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Cited by 10 (0 self)
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In this paper a new behavioral modeling approach for RF systems based is presented, based on a Volterra series inputoutput map representation. The modeling is done purely in the frequency domain, capturing the typical system level specifications for RF building blocks, independent of the implementation details. A harmonic balance simulation tool has been developed based on those models. The implementation focuses on deterministic effects such as distortion and frequency conversion. The behavioral simulator has been tested for various systems and results are presented.