Home HomeAykut Bultan, EMU, TRNC (Turkey)
A new four-parameter atomic decomposition of chirplets is developed for compact representation of signals with chirp components. The four-parameter atom is obtained by scaling the Gaussian function, and then applying the fractional Fourier transform (FRFT), time-shift and frequency-shift operators to the scaled Gaussian. The decomposition is realized by extending the matching pursuit algorithm to four parameters. For this purpose, the four-parameter space is discretized to obtain a dense subset in the Hilbert space. Also, a related time-frequency distribution is developed for clear visualization of the signal components. The decomposition provides a more compact and precise representation of chirp components as compared to the three-parameter ones.
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Yang Wang, Georgia Institute of Technology (U.S.A.)
Guotong Zhou, Georgia Institute of Technology (U.S.A.)
Nonstationary signals appear often in real-life applications and many of them can be modeled as polynomial phase signals (PPS). High-order ambiguity function (HAF) was first introduced to estimate the parameters of a single component PPS. But due to its high nonlinearity, HAF has not been widely used for multi-component PPS which appear for example, in Doppler radar applications when multiple targets are tracked simultaneously. We present a theory in this paper that HAF is virtually additive for multi-component PPS and illustrate our findings with numerical simulations.
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Shubha Kadambe, AAEC (U.S.A.)
Richard Orr, AAEC (U.S.A.)
A novel cross term deleted Wigner representation can be obtained by expanding the Wigner Distribution (WD) in terms of two complementary Gabor coefficients of the signal and a translated set of Wigner basis functions. Two such complementary Gabor coefficients of a signal can be obtained by reversing the role of Gabor synthesis window $h(t)$ and its biorthogonal function $b(t)$. Such a representation is defined here, as Cross-Biorthogonal representation (XBIO). Details of derivation of this new representation is provided in this paper. The choice of the synthesis functions and their corresponding biorthogonal functions with respect to (i) concentration/resolution capabilities, (ii) redundancy vs. minimum-dimension tradeoffs, (iii) noise reduction and (iv) basis set properties of the XBIO representation are also discussed. Simulation results are provided to substantiate the theoretical findings.
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Eugene J. Zalubas, University of Michigan (U.S.A.)
Jeffrey C. O'Neill, University of Michigan (U.S.A.)
William J. Williams, University of Michigan (U.S.A.)
Alfred Olivier Hero, University of Michigan (U.S.A.)
Different signal realizations generated from a given source may not appear the same. Time shifts, frequency shifts, and scales are among the signal variations commonly encountered. Time-frequency distributions (TFDs) covariant to time and frequency shifts and scale changes reflect these variations in a predictable manner. Based on such TFDs, representations invariant to these signal distortions are possible. Presented here are two approaches for discriminating between signal classes where within class translation and scale variation occur. The first method uses an auto-correlation followed by a scale transform to achieve the invariances. The second method treats the TFD as a two-dimensional probability density function and applies a transformation that removes the mean and variance to provide the shift and scale invariance. Each method employs discrimination mechanisms to yield powerful results.
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Cécile Huet, University of Nice (France)
Joël LeRoux, University of Nice (France)
In this paper, we give two algorithms for linear system blind identification based on the fourth order spectrum (or trispectrum). The first algorithm uses only N data of the fourth order spectrum. The second algorithm uses all the information contained in the fourth order spectra, but gives an optimal solution. This solution needs a previous phase unwrapping step; we give different solutions to unwrap the trispectrum phase. Finally, we establish the link between the well known kurtosis maximization method and the optimal solution presented here; they are equivalent in first approximation. It means that we give an analytic solution to the blind identification problem which is, in first approximation, equivalent to the kurtosis maximization solution. Keywords : HOS - Fourth Order Statistics - Blind Identification.
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Harald Oehlmann, CRAN (France)
David Brie, CRAN (France)
The Local Wigner-Ville Distribution (LWVD) extends the Cohen's class time-frequency distributions (TFD) by the definition of a kernel for each time-frequency point(local kernel). The subject of the paper is the determination of these local kernels for interference reduction. Starting from the simple idea of the local limitation of the Wigner-Ville TFD integral bounds, a method is presented to estimate these limits and to obtain a reduced interference TFD. The effectiveness for interference reduction of this LWVD, specially when compared to global-kernel methods, is shown using example signals.
ic973645.pdf ic973645.pdf TOPJames Pitton, MathSoft, Seattle (U.S.A.)
This paper presents a new foundation for positive time--frequency distributions (TFDs). Based on an integral equation formulation of nonstationary systems, a positive TFD can be constructed from a decomposition of a signal over an orthonormal basis. This basis function definition of a positive TFD is used to obtain a relationship between the Wigner distribution and the positive TFD. The results are then generalized to derive positive joint distributions over arbitrary variables, following the approach of Baraniuk and Jones. This general theory provides a common foundation for the two approaches of computing time-frequency representations: those based on linear decompositions of the signal ( e.g., best basis methods) and those based on a quadratic, or bilinear, functional of the signal ( i.e., Cohen's bilinear class).
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Abdelaziz Ouldali, LSS-CNRS (France)
Messaoud Benidir, LSS-CNRS (France)
In this paper we propose to distinguish between constant amplitude polynomial phase signals and the ones having random amplitude. We study four possibilities for the modulating process. We show that the distinction of this kind of signals is not always possible when using the Polynomial Phase Transform. In fact, in some applications, we show that we cannot estimate the phase of the signal with this transform. In order to solve this problem, we introduce a new transform which allows us to estimate this phase in these particular situations. The obtained transform is referred to as the Modified Polynomial Phase Transform.
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James LeBlanc, NMSU (U.S.A.)
Mysore R. Raghuveer, RIT (U.S.A.)
This paper presents methods for detection and localization of photon-limited objects in noise. As opposed to the correlation based or Fourier transform based techniques which exhibit sensitivity to object scaling, we propose a method based on the continuous wavelet transform with its ability to reject noise and to localize objects in space and time as well as in scale. An advantageous twist presented here is the use of the wavelet transform on the complex envelope of the signal of interest. This has the advantage of reducing ``rippling'' effects seen in the transform of the original waveform. An example of further post-processing on the wavelet-transformed data is provided.
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King Choi Ho, University of Saskatchewan (Canada)
Yiu Tong Chan, Royal Military College (Canada)
Continuous Wavelet Transform (CWT) is a useful technique to analyse time- varying signals. Direct computation of CWT via FFT requires O(NlogN) operations per scale, where N is the data length. This paper compares two fast algorithms that compute CWT at a cost of $O(N)$ per scale. One is a trous algorithm and the other is Shensa algorithm. Although both are based on the multiresolution analysis structure, their accuracy in computing CWT is quite different. Theoretical error expression is derived and simulation results are presented for comparison.
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Ajit S. Bopardikar, RIT. (U.S.A.)
Mysore R. Raghuveer, RIT. (U.S.A.)
B.S. Adiga, MIEL. (India)
This paper, introduces a new filter bank structure called the perfect reconstruction circular convolution (PRCC) filter bank. These filter banks satisfy the perfect reconstruction properties, namely, the paraunitary properties in the discrete frequency domain. We further show how the PRCC analysis and synthesis filter banks are completely implemented in this domain and give a simple and a flexible method for the design of these filters. Finally, we use this filter bank structure for a frequency sampled implementation of the discrete wavelet transform based on orthogonal bandlimited scaling functions and wavelets.
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Birsen Yazici, General Electric (U.S.A.)
Rangsami L. Kashyap, Purdue University (U.S.A.)
In our previous work, we introduced a new class of nonstationary stochastic processes whose spectral representation is associated with the wavelet transforms and established a mathematical framework for the analysis of such processes. We refer to these processes as affine stationary processes. These processes are indexed by the affine group, or ax+b group, which can be thought of as a group of shifts and scalings. Affine stationary processes are nonstationary in the classical sense. However, their second order statistical properties are invariant under the affine group composition law. In this paper, we show that any physically realizable affine stationary process is a wavelet transform of the white noise process. As a result, we derive a spectral decomposition of the affine stationary processes using wavelet transform. Additionally, we apply our results to the fractional Brownian motion (fBm). We show that fBm is an affine stationary process and the filter associated with the fBm is a continuous time analyzing wavelet. Finally, we apply our results to choose an optimal wavelet filter in the development of a spectral representation of fBm via wavelet transforms.
ic973669.pdf TOPHamid Krim, MIT, Cambridge, (U.S.A.)
Adapted wavelet analysis of signals is achieved by optimizing a selected criterion. We recently introduced a majorization framework for constructing selection functionals, which can be as well suited to compression as entropy or others. We show how these functionals operate on the basis selection and their effect on the statistics of the resulting representation.
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Hamayun A. Khan, University of Pittsburgh (U.S.A.)
Luis F. Chaparro, University of Pittsburgh (U.S.A.)
In this paper we consider solutions to the non-stationary Wiener filtering problem using the evolutionary spectral theory. Two cases of interest result from the uncorrelation between the desired signal and the noise. One constrains the support of the generating kernels of the signals and the other imposes orthogonality on their innovation processes. The latter condition is more general and our solution coincides with the one presented previously by Abdrabbo and Priestley. For the first case, we develop a new solution that depends directly on the Wold-Cramer models of the desired and the noisy processes. Implementation is achieved in both cases by estimating the kernels for the Wold-Cramer representations from the spectra using the evolutionary maximum entropy spectral estimation. An example illustrating the filtering is given.
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