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Hiroshi Kanai, Tohoku University (Japan)
Michie Sato, Tohoku University (Japan)
Noriyoshi Chubachi, Tohoku University (Japan)
We present a new method for estimation of spectrum transition of a nonstationary signals in low signal-to-noise ratio cases. Instead of basic functions which are employed by the previously proposed time-varying AR modeling, we introduce the spectrum transition constraint in the cost function described by the partial correlation coefficients so that the method is applicable to noisy nonstationary signals of which spectrum transition patterns are complex. By applying this method to the analysis of vibration signals on the interventricular septum of the heart, noninvasively measured by the method developed in our laboratory using ultrasonics, spectrum transition pattern is clearly obtained during one beat period for a normal individual and a patient.
ic972013.pdf ic972013.pdf
TOPJakob Ängeby, Chalmers University of Technology (Sweden)
Primarily the structured auto-regressive (AR) model was introduced as a mean to estimate the parameters of non-stationary signals in additive noise. However, it is straightforward to use the structured AR model as a model-based time-frequency distribution (TFD). It is shown that the structured AR TFD can be interpreted as a member of Cohen's class with a non-stationary adaptive kernel. The interpretation of the structured AR TFD as a member of Cohen's class establishes a link between TFD:s and signal parameter estimation.
ic972017.pdf ic972017.pdf TOP
Chenshu Wang, Villanova University (U.S.A.)
Moeness G. Amin, Villanova University (U.S.A.)
The zero-tracking time-frequency distribution (TFD) is introduced. The local autocorrelation function of the TFD, defined by an appropriate kernel, is usedto form a polynomial whose roots correspond to the instantaneous frequencies of the multicomponent signal. Two techniques for zero-tracking based on TFD are presented. The first technique requires updating all of the polynomial signal and extraneous zeros, and is based on the formula relating, to the first order approximation, the changes in the polynomial roots and coefficients.The second technique employs the zero-finding Newton's method to only obtain the zero-trajectories of interest.
ic972021.pdf TOP
Daniel Seidner, Tel-Aviv University (Israel)
Meir Feder, Tel-Aviv University (Israel)
This work extends Papoulis' General Sampling Expansion to the vector case where N band limited signals are passed through a multi-input multi-output (MIMO) LTI system that generates M (Mgreater-or-equal-to N) output signals. We find necessary and sufficient conditions for reconstructing the N input signals from the samples of the M output signals, all sampled at N/M the Nyquist rate. A surprising necessary condition is that M/N must be an integer. This condition is no longer necessary when each of the output signals can be sampled at a different rate.
ic972025.pdf ic972025.pdf TOP
Paolo Prandoni, EPFL (Switzerland)
Martin Vetterli, EECS, UC Berkeley (U.S.A.)
Michael Goodwin, EECS, UC Berkeley (U.S.A.)
The idea of optimal joint time segmentation and resource allocation for signal modeling is explored with respect to arbitrary segmentations and arbitrary representation schemes. When the chosen signal modeling techniques can be quantified in terms of a cost function which is additive over distinct segments, a dynamic programming approach guarantees the global optimality of the scheme while keeping the computational requirements of the algorithm sufficiently low. Two immediate applications of the algorithm to LPC speech coding and to sinusoidal modeling of musical signals are presented.
ic972029.pdf ic972029.pdf TOP
Michael Vrhel, Biomedical Engineering and Instrumentation (U.S.A.)
Akram Aldroubi, Biomedical Engineering and Instrumentation (U.S.A.)
We introduce a new method for initializing the multi-wavelet decomposition algorithm. The approach assumes that the input signal is contained within some well-defined subspace of L2 (e.g. the space of bandlimited functions). The initialization algorithm is the orthogonal projection of the input signal into the space defined by the multi-scaling function. Unlike an interpolation approach, the projection method will always have a solution. We provide examples and implementation details.
ic972033.pdf TOPMichael Goodwin, U.C.Berkeley (U.S.A.)
The matching pursuit algorithm derives an expansion of a signal in terms of the elements of a large dictionary of time-frequency atoms. This paper considers the use of matching pursuit for computing signal expansions in terms of damped sinusoids. First, expansion based on complex damped sinusoids is explored; it is shown that the expansion can be efficiently derived using the FFT and simple recursive filterbanks. Then, the approach is extended to provide decompositions in terms of real damped sinusoids. This extension relies on generalizing the matching pursuit algorithm to derive expansions with respect to dictionary subspaces; of specific interest is the subspace spanned by a complex atom and its conjugate. Developing this particular case leads to a framework for deriving real-valued expansions of real signals using complex atoms. Applications of the damped sinusoidal decomposition include system identification, spectral estimation, and signal modeling for coding and analysis--modification--synthesis.
ic972037.pdf ic972037.pdf TOP
Antonia Papandreou-Suppappola, University of Rhode Island (U.S.A.)
Robin L. Murray, University of Rhode Island (U.S.A.)
Faye G. Boudreaux-Bartels, University of Rhode Island (U.S.A.)
We discuss the existence of classes of quadratic time-frequency representations (QTFRs), e.g. Cohen, power, and generalized time-shift covariant, that satisfy a time-frequency (TF) concentration property. This important property yields perfect QTFR concentration along group delay curves. It also (1) simplifies the QTFR formulation and property kernel constraints as the kernel reduces from 2-D to 1-D, (2) reduces the QTFR computational complexity, and (3) yields simplified design algorithms. We derive the intersection of Cohen's class with the new power exponential class, and show that it belongs to Cohen's localized-kernel subclass. In addition to the TF shift covariance and concentration properties, these intersection QTFRs preserve power exponential time shifts, important for analyzing signals passing through exponentially dispersive systems.
ic972041.pdf ic972041.pdf TOP
Jack McLaughlin, University of Washington (U.S.A.)
James Droppo, University of Washington (U.S.A.)
Les E. Atlas, University of Washington (U.S.A.)
We propose a property for kernel design which results in distributions for each of two classes of signals which maximally separates their energies in the time-frequency plane. Such maximally separated distributions may result in improved classification because the signal representation is optimized to accentuate the differences in signal classes. This is not the case with other time-frequency kernels which are optimized based upon some criteria unrelated to the classification task. Using our operator theory formulation for time-frequency representations, our "maximal separation" criteria takes on a very easily solved form. Analysis of the solution in both the time-frequency and ambiguity planes is given along with an example on discrete signals.
ic972045.pdf ic972045.pdf TOP
Franz Hlawatsch, Vienna University of Technology (Austria)
Teresa Twaroch, Vienna University of Technology (Austria)
We extend the characteristic function method (CFM) to more general groups, operators, and signal spaces. We show that the extended CFM can be applied to projected unitary operators as well as discrete-time/periodic signals.
ic972049.pdf ic972049.pdf TOP
Ljubisa Stankovic, University of Montenegro (Yugoslavia)
Srdjan Stankovic, University of Montenegro (Yugoslavia)
Igor Djurovic, University of Montenegro (Yugoslavia)
A method for the Polynomial Wigner-Ville distributions realization, in the case of multicomponent signals, is presented. It is based on the author's recently proposed S-method. Using this method one may, theoretically, get the sum of the Polynomial Wigner-Ville distributions of each component separately. Architecture for the Polynomial Wigner-Ville distributions realization, starting from the short time Fourier transform, is given. Method is illustrated on a numerical example.
ic972053.pdf TOP
Michael S. Richman, Cornell University (U.S.A.)
Thomas W. Parks, Cornell University (U.S.A.)
The concept of rotations in continuous-time, continuous-frequency is extended to discrete-time, discrete-frequency as it applies to the Wigner distribution. As in the continuous domain, discrete rotations are defined to be elements of the special orthogonal group over the appropriate (discrete) field. Use of this definition ensures that discrete rotations will share many of the same mathematical properties as continuous ones. A formula is given for the number of possible rotations of a prime-length signal, and an example is provided to illustrate what such rotations look like. In addition, by studying a 90 degree rotation, we formulate an algorithm to compute a prime-length discrete Fourier transform (DFT) based on convolutions and multiplications of discrete, periodic chirps. This algorithm provides a further connection between the DFT and the discrete Wigner distribution based on group theory.
ic972057.pdf ic972057.pdf TOP