Results 1  10
of
44
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 19 (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 15 (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 ES and the ..."
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Cited by 14 (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 11 (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.
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.
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 10 (2 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.
On the systematic measurement errors of correlative mobile radio channel sounders
 IEEE Trans. Commun
, 2002
"... Abstract—We show that measurements of timevarying mobile radio channels obtained with uncalibrated correlative channel sounders are affected by four different types of systematic errors (commutation, pulsecompression, aliasing, and misinterpretation error). We analyze these errors and provide uppe ..."
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Cited by 8 (2 self)
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Abstract—We show that measurements of timevarying mobile radio channels obtained with uncalibrated correlative channel sounders are affected by four different types of systematic errors (commutation, pulsecompression, aliasing, and misinterpretation error). We analyze these errors and provide upper error bounds that are formulated in terms of channel and sounder parameters. Based on these error bounds, we provide guidelines for a judicious choice of important sounder parameters. Computer simulations using a simple twopath channel illustrate our theoretical results. Finally, we show how our results can be used to assess the accuracy of measured channel data. Index Terms—Channel measurements, channel sounder, mobile radio channels, timevarying channels. I.
Nonstationary spectral analysis based on timefrequency operator symbols and underspread approximations
 IEEE TRANS. INF. THEORY
, 2006
"... We present a unified framework for timevarying or time–frequency (TF) spectra of nonstationary random processes in terms of TF operator symbols. We provide axiomatic definitions and TF operator symbol formulations for two broad classes of TF spectra, one of which is new. These classes contain all m ..."
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Cited by 8 (4 self)
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We present a unified framework for timevarying or time–frequency (TF) spectra of nonstationary random processes in terms of TF operator symbols. We provide axiomatic definitions and TF operator symbol formulations for two broad classes of TF spectra, one of which is new. These classes contain all major existing TF spectra such as the Wigner–Ville, evolutionary, instantaneous power, and physical spectrum. Our subsequent analysis focuses on the practically important case of nonstationary processes with negligible highlag TF correlations (socalled underspread processes). We demonstrate that for underspread processes all TF spectra yield effectively identical results and satisfy several desirable properties at least approximately. We also show that Gabor frames provide approximate Karhunen–Loève (KL) functions of underspread processes and TF spectra provide a corresponding approximate KL spectrum. Finally, we formulate simple approximate input–output relations for the TF spectra of underspread processes that are passed through underspread linear timevarying systems. All approximations are substantiated mathematically by upper bounds on the associated approximation errors. Our results establish a TF calculus for the secondorder analysis and timevarying filtering of underspread processes that is as simple as the conventional spectral calculus for stationary processes.
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 8 (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.