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Xi Zhang - One of the best experts on this subject based on the ideXlab platform.
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Design of Hilbert transform pairs of Orthonormal Wavelet bases with improved analyticity
2011 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2011Co-Authors: Xi ZhangAbstract:This paper proposes a class of Hilbert transform pairs of Orthonormal Wavelet bases with improved analyticity. To improve the analyticity of complex Wavelet, a different allpass filter is used for the half-sample delay approximation. We present a design method for allpass filters with the specified degree of flatness at ω = 0 and equiripple phase response in the approximation band. Remez exchange algorithm is applied in the approximation band, and then a set of filter coefficients can be obtained easily by solving the eigen-value problem. Therefore, the equiripple phase response is attained through a few iterations. Furthermore, the corresponding filter banks are constructed from the designed allpass filters by using the method proposed in. The resulting Orthonormal Wavelet bases possess the maximum number of vanishing moments. Finally, one example is presented to demonstrate the improvement of the analyticity.
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ICASSP - Design of Hilbert transform pairs of Orthonormal Wavelet bases with improved analyticity
2011 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2011Co-Authors: Xi ZhangAbstract:This paper proposes a class of Hilbert transform pairs of Orthonormal Wavelet bases with improved analyticity. To improve the analyticity of complex Wavelet, a different allpass filter is used for the half-sample delay approximation. We present a design method for allpass filters with the specified degree of flatness at ω = 0 and equiripple phase response in the approximation band. Remez exchange algorithm is applied in the approximation band, and then a set of filter coefficients can be obtained easily by solving the eigenvalue problem. Therefore, the equiripple phase response is attained through a few iterations. Furthermore, the corresponding filter banks are constructed from the designed allpass filters by using the method proposed in [7]. The resulting Orthonormal Wavelet bases possess the maximum number of vanishing moments. Finally, one example is presented to demonstrate the improvement of the analyticity.
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Design of Hilbert transform pairs of Orthonormal Wavelet bases using IIR filters
2010 10th International Symposium on Communications and Information Technologies, 2010Co-Authors: Dai-wei Wang, Xi ZhangAbstract:Conventionally, FIR filters have been often used to design the dual tree complex Wavelet transforms (DTCWTs), where two real Orthonormal Wavelet bases form a Hilbert transform pair, whereas IIR filters are seldom used, although they require a lower computational complexity than FIR filters. In this paper, a new class of Hilbert transform pairs of Orthonormal Wavelet bases is proposed by using general IIR filters. To obtain the maximum number of vanishing moments, the conventional design methods located as many zeros as possible at z = -1. This paper proposes a new design method for DTCWTs by locating a specified number of zeros at z = -1 and minimizing the stopband error. The proposed method uses the well-known Remez exchange algorithm to approximate an equiripple magnitude response in the stopband. Therefore, a set of filter coefficients can be easily obtained by solving the eigenvalue problem. Furthermore, the optimal solution is attained through a few iterations. The advantage of the proposed method is that the number of zeros at z = -1 can be specified arbitrarily and an improved frequency selectivity can be obtained.
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ICIP - Design of Hilbert transform pairs of Orthonormal Wavelet bases using Remez exchange algorithm
2009 16th IEEE International Conference on Image Processing (ICIP), 2009Co-Authors: Xi ZhangAbstract:This paper proposes a new method for designing Hilbert transform pairs of Orthonormal Wavelet bases proposed by Selesnick in [9]. The conventional method located as many zeros as possible at z = − 1 to obtain the maximum number of vanishing moments. In this paper, we specify the number of zeros at z = − 1, and then use the remaining degree of freedom to get the best possible frequency selectivity. The Remez exchange algorithm is applied in the stopband to approximate the equiripple magnitude response. Therefore, a set of filter coefficients can be obtained easily by solving a system of linear equations. Furthermore, the optimal solution is attained through a few iterations. Since the number of zeros at z = −1 can be specified arbitrarily, a new class of Hilbert transform pairs of Orthonormal Wavelet bases with the specified number of vanishing moments can be generated.
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Design of Hilbert transform pairs of Orthonormal Wavelet bases using Remez exchange algorithm
2009 16th IEEE International Conference on Image Processing (ICIP), 2009Co-Authors: Xi ZhangAbstract:This paper proposes a new method for designing Hilbert transform pairs of Orthonormal Wavelet bases proposed by Selesnick. The conventional method located as many zeros as possible at z = - 1 to obtain the maximum number of vanishing moments. In this paper, we specify the number of zeros at z = - 1, and then use the remaining degree of freedom to get the best possible frequency selectivity. The Remez exchange algorithm is applied in the stopband to approximate the equiripple magnitude response. Therefore, a set of filter coefficients can be obtained easily by solving a system of linear equations. Furthermore, the optimal solution is attained through a few iterations. Since the number of zeros at z = -1 can be specified arbitrarily, a new class of Hilbert transform pairs of Orthonormal Wavelet bases with the specified number of vanishing moments can be generated.
H. Carfantan - One of the best experts on this subject based on the ideXlab platform.
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Time-invariant Orthonormal Wavelet representations
IEEE Transactions on Signal Processing, 1996Co-Authors: J.-c. Pesquet, H. Krim, H. CarfantanAbstract:A simple construction of an Orthonormal basis starting with a so-called mother Wavelet, together with an efficient implementation gained the Wavelet decomposition easy acceptance and generated a great research interest in its applications. An Orthonormal basis may not, however, always be a suitable representation of a signal, particularly when time (or space) invariance is a required property. The conventional way around this problem is to use a redundant decomposition. We address the time-invariance problem for Orthonormal Wavelet transforms and propose an extension to Wavelet packet decompositions. We show that it,is possible to achieve time invariance and preserve the Orthonormality. We subsequently propose an efficient approach to obtain such a decomposition. We demonstrate the importance of our method by considering some application examples in signal reconstruction and time delay estimation.
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Estimation of noisy signals using time-invariant Wavelet packets
Proceedings of 27th Asilomar Conference on Signals Systems and Computers, 1993Co-Authors: J.-c. Pesquet, H. Krim, H. Carfantan, J.g. ProakisAbstract:Time-invariance plays a key role in many applications (e.g. signal reconstruction, identification, classification). Orthonormal Wavelet and Wavelet packet representations are known to be time-variant. We propose an extended Wavelet packet decomposition, establish its time-invariance and give an efficient implementation. Some illustrating examples are also provided.
Aime Fournier - One of the best experts on this subject based on the ideXlab platform.
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introduction to Orthonormal Wavelet analysis with shift invariance application to observed atmospheric blocking spatial structure
Journal of the Atmospheric Sciences, 2000Co-Authors: Aime FournierAbstract:Abstract Orthonormal Wavelet analysis (OWA) is a special form of Wavelet analysis, especially suitable for analyzing spatial structures, such as atmospheric fields. For this purpose, OWA is much more efficient and accurate than the nonorthogonal Wavelet transform (WT), which was introduced to the meteorological community recently and which is more suitable for time series analysis. Whereas the continuous WT is strictly correct only for infinite domains, OWA is derived from periodizing and discretizing the infinite-domain case and so is correct for periodic boundary conditions. Unlike Fourier spectra, OWA is not shift invariant. Nor is it equivariant like the WT; that is, the OWA output does not shift as its input shifts. Two remedies are to combine all possible shifts, known as the overcomplete, nonorthogonal shift equivariant WT, or else to use a “best shift,” known as best shift Wavelet analysis. Although shift invariant and Orthonormal w.r.t. arbitrary inputs, the latter’s optimization generally depend...
Roger H Shaw - One of the best experts on this subject based on the ideXlab platform.
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the leakage problem of Orthonormal Wavelet transforms when applied to atmospheric turbulence
Journal of Geophysical Research, 1995Co-Authors: Kyaw Tha Paw U, Roger H ShawAbstract:Orthonormal Wavelet transforms are becoming common in the study of turbulence phenomena. Although they are powerful tools in representing a signal, their use as tools to study the characteristics of turbulent structures can create appreciable errors in interpretation. It is shown here that although the Orthonormal Wavelet transform is computationally economical by taking advantage of multiresolution analysis, it has insufficient resolution in both scale and location to resolve detailed information of turbulence structures. Lacking in resolution, the energy at a particular frequency (or wavelength) may leak into neighboring frequencies and may pass down to smaller scales to produce an artificial “cascade” of energy (with a slope close to −2/3). The choice of Wavelet basis function is important to the Wavelet spectrum, especially in the study of turbulence flows dominated by coherent structures, since the method most accurately senses energy contained in pulses that have a similar pattern to the Wavelet function. To use the method as a filter can be problematic owing to the low resolution of the Orthonormal Wavelet transform; nonOrthonormal Wavelet analysis should be employed when high resolution is important. When Orthonormal Wavelet transforms have to be used for signal analysis, segmented averaging should be employed.
Marc B. Parlange - One of the best experts on this subject based on the ideXlab platform.
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the local effect of intermittency on the inertial subrange energy spectrum of the atmospheric surface layer
Boundary-Layer Meteorology, 1996Co-Authors: Jozsef Szilagyi, Marc B. Parlange, John D Albertson, Gabriel G. Katul, Anthony T CahillAbstract:Orthonormal Wavelet expansions are applied to atmospheric surface layer velocity measurements. The effect of intermittent events on the energy spectrum of the inertial subrange is investigated through analysis of Wavelet coefficients. The local nature of the Orthonormal Wavelet transform in physical space makes it possible to identify a relationship between the inertial subrange slope of the local Wavelet spectrum and a simple indicator (i.e. the local variance of the signal) of local intermittency buildup. The slope of the local Wavelet energy spectrum in the inertial subrange is shown to be sensitive to the presence of intermittent events. During well developed intermittent events (coherent structures), the slope of the energy spectrum is somewhat steeper than -5/3, while in less active regions the slope is found to be flatter than -5/3. When the slopes of local Wavelet spectra are ensemble averaged, a slope of -5/3 is recovered for the inertial subrange.
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Intermittency, local isotropy, and non-Gaussian statistics in atmospheric surface layer turbulence
Physics of Fluids, 1994Co-Authors: Gabriel G. Katul, Marc B. ParlangeAbstract:Orthonormal Wavelet expansions are applied to atmospheric surface layer velocity and temperature measurements above a uniform bare soil surface that exhibit a long inertial subrange energy spectrum. In order to investigate intermittency effects on Kolmogorov’s theory, a direct relation between the nth‐order structure function and the Wavelet coefficients is derived. This relation is used to examine deviations from the classical Kolmogorov theory for velocity and temperature in the inertial subrange. The local nature of the Orthonormal Wavelet transform in physical space aided the identification of events directly contributing to intermittency buildup at inertial subrange scales. These events occur at edges of large eddies and contaminate the Kolmogorov inertial subrange scaling. By suppressing these events, the statistical structure of the inertial subrange for the velocity and temperature, as described by Kolmogorov’s theory, is recovered. The suppression of intermittency on the nth‐order structure funct...
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Intermittency in Atmospheric Surface Layer Turbulence: The Orthonormal Wavelet Representation
Wavelets in Geophysics, 1994Co-Authors: Gabriel G. Katul, John D Albertson, Marc B. ParlangeAbstract:Orthonormal Wavelet expansions are applied to atmospheric surface layer velocity measurements that exhibited about three decades of inertial subrange energy spectrum. A direct relation between the nth order structure function and the Wavelet coefficients is derived for intermittency investigations. This relation is used to analyze power-law deviations from the classical Kolmogrov theory in the inertial subrange. The local nature of the Orthonormal Wavelet transform in physical space aided the identification of events contributing to inertial subrange intermittency buildup. By suppressing these events, intermittency effects on the statistical stucture of the inertial subrange is eliminated. The suppression of intermittency on the nth order structure function is carried out via a conditional Wavelet sampling scheme. The conditional sampling scheme relies on an indicator function that identifies the contribution of large dissipation events in the Wavelet space-scale domain. The conditioned Wavelet statistics reproduce the Kolmogrov scaling in the inertial subrange and resulted in a zero intermittency factor. A relation between Kolmogrov's theory and Gaussian statistics is also investigated. Intermittency resulted in non-Gaussian statistics for the inertial subrange scales.
