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Heinrich Ruser, Siemens AG, ZT KM1, München (Germany)
Martin Vossiek, Siemens AG, ZT KM1, München (Germany)
Alexander v.Jena, Siemens AG, ZT KM1, München (Germany)
Valentin Mágori, Siemens AG, ZT KM1, München (Germany)
Ultrasonic pulsed wave range Doppler sensors provide application in various fields, e.g. intruder alarm systems or autonomous vehicle steering. The time-frequency methods commonly used in these sensors, however, inhere the problem that, due to the transdu cer's non constant and direction-dependent transfer functions, the Doppler frequency cannot be determined with high accuracy needed for such applications. The easiest way to improve the Doppler resolution is to reduce the signal bandwidth, but only at the expense of worse range resolution. In this paper a direction-dependent inverse filter technique is presented, which compensates erroneous effects of the transfer function in the time-frequency analysis. An ultrasonic intruder alarm system determining loc ation and velocity of persons in rooms serves as an example that the novel approach gives evidently better performance than conventional methods, resulting in both high velocity and range resolution.
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Christoph Delfs, University of Karlsruhe (Germany)
Friedrich Jondral, University of Karlsruhe (Germany)
A topical task is the classification of burst-like signals, e.g. in signal detection. Piano sounds are used here as an example. Different time-frequency methods including wavelet processing are used alternatively for feature extraction. A classifier checks whether the generated features are sufficient to identify the correct piano. Results of the real data signal processing are presented and discussed.
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John G. Apostolopoulos, MIT (U.S.A.)
Jae S. Lim, MIT (U.S.A.)
Transform/subband representations form a basic building block for many signal processing algorithms and applications. Most of the effort has focused on developing representations for infinite-length signals, with simple extensions to finite-length 1-D and rectangular support 2-D signals. However, many signals may have arbitrary length or arbitrarily shaped (AS) regions of support (ROS). We present a novel framework for creating critically sampled perfect reconstruction transform/subband representations for AS signals. Our method selects an appropriate subset of vectors from an (easily obtained) basis for a larger (superset) signal space, in order to form a basis for the AS signal. In particular, we have developed a number of promising wavelet representations for arbitrary-length 1-D signals and AS 2-D/$M$-D signals that provide high performance with low complexity.
ic972097.pdf ic972097.pdf TOPMartin J. Bastiaans, Technical University of Eindhoven (The Netherlands)
The windowed Fourier transform of a time signal is considered, as well as a way to reconstruct the signal from a sufficiently densely sampled version of its windowed Fourier transform using a Gabor representation; following Gabor, sampling occurs on a two-dimensional time-frequency lattice with equidistant time intervals and equidistant frequency intervals. In the limit of infinitely dense sampling, the optimum synthesis window (which appears in Gabor's reconstruction formula) becomes similar to the analysis window (which is used in the windowed Fourier transform). It is shown that this similarity can already be reached for a rather small degree of oversampling, if the sampling distances in the time and frequency directions are properly chosen. A procedure is presented with which the optimum ratio of the sampling intervals can be determined. The theory is elucidated by finding the optimum ratio in the cases of a Gaussian and an exponential analysis window.
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Gianpaolo Evangelista, University of Naples (Italy)
Sergio Cavaliere, University of Naples (Italy)
In this paper we show that the dyadic wavelet transform may be generalized to include non-octave spaced frequency resolution. We introduce orthogonal and complete wavelets whose set of cutoff frequencies may be adapted, in the simplest case, by changing a single parameter. The novel wavelets and the FWWT transform computational structure are obtained via an intermediate Laguerre representation of the signal. The warped wavelets are related to the ordinary wavelets by means of frequency transformations and orthogonalizing filtering. The classical sampled filter bank theory is extended to include frequency dependent upsampling and downsampling operators and dispersive delay lines. The FWWT frequency band flexibility may be exploited in order to adapt the wavelet transform to signals.
ic972105.pdf ic972105.pdf TOPArvid C.D. Breitenbach, EMT, Technical University of Munich (Germany)
Analog Sensors are sometimes described in data sheets as having "infinite" resolution. Although there are no quantization effects in their analog output, their resolution is, of course, limited by the amount of noise present. To test their dynamical performance they have to be excited with a known function, e.g. a sinusoid. Some discussion of possible methods for sensor data evaluation after sinusoidal excitation is given in this paper. A reliable method for sensor data evaluation and Signal-to-Noise Ratio (SNR) determination is proposed. An experimental set-up for this purpose is also described.
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Michael Unser, National Institutes of Health (U.S.A.)
Josiane Zerubia, INRIA Sophia Antipolis (France)
We investigate the problem of the reconstruction of a continuous-time function f(x) in H from the responses of m linear shift-invariant systems sampled at 1/m the reconstruction rate, extending Papoulis' generalized sampling theory in two important respects. First, we allow for arbitrary (non-bandlimited) input signals (typ. H=L_2). Second, we use a more general specification of the reconstruction subspace V((varphi)), so that the output of the system can take the form of a bandlimited function, a spline, or a wavelet expansion. The system that we describe yields an approximation ~f in V((varphi)) that is consistent with the input f(x) in the sense that it produces exactly the same measurements. We show that this solution can be computed by multivariate filtering. We also characterize the stability of the system (condition number). Finally, we illustrate the theory by presenting a new example of interlaced sampling using splines.
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Jaakko Astola, Tampere University of Technology (Finland)
Karen Egiazarian, Tampere University of Technology (Finland)
Heikki Huttunen, Tampere University of Technology (Finland)
This paper is devoted to the theoretical analysis of the fitness function in genetic algorithms using wavelet packet (WP) transforms. More specifically, WP transforms are used to calculate the average fitness value of a schema. Based on this one can decide whether a certain function is easy or hard for a genetic algorithm. The result is an extension of Bethke's work who discovered an efficient method for calculating schema average fitness values using the Walsh transform.
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Xiang-Gen Xia, University of Delaware (U.S.A.)
Shie Qian, National Instruments (U.S.A.)
An iterative time-frequency (TF) synthesis/time-varying filtering algorithm in the discrete Gabor transform domain is proposed. A sufficient condition is obtained for the Gabor synthesis and analysis window functions so that the iterative algorithm converges. It is proved that under the condition the algorithm converges to a signal that has its Gabor transform located exactly in a desired domain specified by the user in the TF plane. Under the condition the solution from the first iteration is exactly the least square solution. Our numerical examples show: about 3.5 dB or more SNR gain over the least square solution; about 13dB SNR increase over the SNR without filtering; lower computational complexity.
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Patrick Loughlin, University of Pittsburgh (U.S.A.)
Dale Groutage, NSWC (U.S.A.)
Robert Rohrbaugh, NSWC (U.S.A.)
We apply time-frequency analysis to various acoustic transients. Estimates of the conditional mean frequency and the conditional bandwidth exhibit characteristic trends for different transients. This information may be helpful in distinguishing between different classes of transients, and in understanding the underlying mechanisms generating the transient.
ic972125.pdf ic972125.pdf TOPMark A. Coffey, University of Colorado, Boulder (U.S.A.)
We investigate the formulation of boundary compensated wavelet transforms supported on a finite interval. A unified approach to boundary compensated wavelet transforms is presented which fosters new insights into previous constructions, including both continuous and discrete approaches to the problem. The framework enables the design of boundary-compensated transforms with specific properties, including among others arbitrary frequency response, matching moments, and staggered supports.
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Israel Cohen, Technion - IIT, Haifa (Israel)
Shalom Raz, Technion - IIT, Haifa (Israel)
David Malah, Technion - IIT, Haifa (Israel)
The Wigner distribution (WD) possesses a number of desirable mathematical properties relevant time-frequency analysis. However, the presence of interference terms renders the WD of multicomponent signals extremely difficult to interpret. In this work, we propose an adaptive decomposition of the WD using extended libraries of orthonormal bases. A prescribed signal is expanded on a basis of adapted waveforms, that best match the signal components, and subsequently transformed into the Wigner domain. The interference terms are controlled by thresholding the cross WD of interactive basis functions according to their degree of adjacency in an idealized time-frequency plane. This measure is implicitly adapted to the local distribution of the signal, thus compensating for a global nonadaptive threshold. In particular we focus on a shift-invariant decomposition in an extended library of wavelet packets. The resulting modified distribution achieves high time-frequency resolution, and is superior in eliminating interference terms associated with bilinear distributions.
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Antonio S. Pena, Universidad de Vigo (Spain)
Nuria González-Prelcic, Universidad de Vigo (Spain)
Carlos A. Serantes, Universidad de Vigo (Spain)
A segmentation procedure of time sequences based on a time-frequency analysis is presented in this paper. The use of both a wavelet packet transform and the original time signal provides a set of spectral and time parameters that allows the algorithm to locate some proper break points to split the input frame into a discrete number of smaller segments. Some examples showing the performance of the method are also presented. An application to wavelet-based audio coding is briefly discussed.
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Mehran Jahed, Sharif University of Technology (Iran)
Bizhan Najafi, Sharif University of Technology (Iran)
Ali Khamene, Sharif University of Technology (Iran)
Stephen J. Lai-Fook, University of Kentucky (U.S.A.)
The velocities of stress waves transmitted through the inflated lung parenchyma depend on the lung stiffness, as defined by bulk and shear moduli, and lung density. We examined the relationship between stress wave velocities and lung density. Wavelet analysis was used to calculate the time delay and frequency character of the wave that is propagated on the surface of three canine lungs. The discrete wavelet analysis that was used in this study , was a cubic spline wavelet. Following the analysis, a new energy localization algorithm was utilized to detect dominant signal power regions. The analysis verified previous results ascertaining the linear elastic model. Time delays between the source and the receiver transducers were calculated and compared to a theoretical estimate. As the lung density was increased, wave velocities were decreased. For the first time, the analysis presented the exact time-frequency relationship for the dominant stress wave velocities.
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