An optimum complete orthonormal basis for signal analysis and design

Jin, Qu; Luo, Zhi-Quan; Wong, K.M.

doi:10.1109/18.335885

Cited by 7 publications

(18 citation statements)

References 12 publications

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“…For signals on the sphere, the energy concentration problems, explored in the literature, either maximize the measure of energy concentration in spatial or spectral domain, or maximize the weighted sum of measures of energy concentration in spatial and spectral domain. However, the problem of maximizing the product of energy concentrations measures, investigated for signals defined on one dimensional Euclidean domain (time) in [15], has not been considered for signals on the sphere.…”

Section: Relation To Prior Workmentioning

confidence: 99%

“…Proof. We apply the variational principle, also adopted in [15], to find the unit energy function w, that maximizes the product of the energy concentration levels in the spatial and spectral region. Let…”

Section: Remark 1 Since We Obtain Two Pairs Of αP and βP We Define mentioning

confidence: 99%

“…Together with the definition of kernels for the operators SL and SR, given in (4) and (5), respectively, the above equation implies that SRLw( x) = η w( x), where the kernel of the operator SRL is given in (14) and η given in (15).…”

Section: Remark 1 Since We Obtain Two Pairs Of αP and βP We Define mentioning

confidence: 99%

“…as given in (15) serves as a measure of concentration of energy in the spatial and spectral regions of interest.…”

Section: Remark 1 Since We Obtain Two Pairs Of αP and βP We Define mentioning

confidence: 99%

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Maximal multiplicative spatial-spectral concentration on the sphere: Optimal basis

Khalid

Kennedy

2015

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this work, we design complete orthonormal basis functions, which are referred to as optimal basis functions, that span the vector sum of subspaces formed by band-limited spatially concentrated and space-limited spectrally concentrated functions. The optimal basis are shown to be a linear combination of band-limited functions with maximized energy concentration in some spatial region of interest and space-limited functions which maximize the energy concentration in some spectral region. The linear combination is designed with an optimality condition of maximizing the product of measures of energy concentration in the spatial and spectral domain. We also show that each optimal basis is an eigenfunction of a linear operator which maximizes the product of energy concentration measures in spatial and spectral domain. Finally, we discuss the properties of the proposed optimal basis functions and highlight their usefulness for the signal representation and data analysis due to the simultaneous concentration of the proposed basis functions in spatial and spectral domains.

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Section: Relation To Prior Workmentioning

confidence: 99%

Section: Remark 1 Since We Obtain Two Pairs Of αP and βP We Define mentioning

confidence: 99%

Section: Remark 1 Since We Obtain Two Pairs Of αP and βP We Define mentioning

confidence: 99%

“…as given in (15) serves as a measure of concentration of energy in the spatial and spectral regions of interest.…”

Section: Remark 1 Since We Obtain Two Pairs Of αP and βP We Define mentioning

confidence: 99%

See 2 more Smart Citations

Maximal multiplicative spatial-spectral concentration on the sphere: Optimal basis

Khalid

Kennedy

2015

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…To support these applications, we consider the problem of maximizing the product of concentration of energy of signals defined on the ball. The problem of finding optimal basis with maximum energy concentration in spatial and harmonic domains, has been considered for Euclidean [14] and spherical (unit sphere) [15] domains.…”

Section: Introductionmentioning

confidence: 99%

Signal analysis on the ball: Design of optimal basis functions with maximal multiplicative concentration in spatial and spectral domains

Nafees

Khalid

Kennedy

2017

2017 International Conference on Systems, Signals and Image Processing (IWSSIP)

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In this work, we design a set of complete orthonormal optimal basis functions for signals defined on the ball. We design the basis functions by maximizing the product of their energy concentration in some spatial region and that in some spectral region. The optimal basis functions are designed as a linear combination of space-limited functions with maximal concentration in the spectral region and band-limited functions with maximal concentration in the spatial region. The proposed optimal basis functions are shown to form a complete set for signal representation in a subspace formed by the vector sum of the subspaces spanned by space-limited and band-limited functions. We also formulate an integral operator which projects the signal to the joint subspace and maximizes the product of energy concentrations in harmonic as well as spatial domains. Furthermore, with the help of some properties of proposed optimal basis functions we show that these functions are the only eigenfunction of the integral operator.

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Wavelet Technology in Vehicle Power Management

Zhang

2011

Vehicle Power Management

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An optimum complete orthonormal basis for signal analysis and design

Cited by 7 publications

References 12 publications

Maximal multiplicative spatial-spectral concentration on the sphere: Optimal basis

Maximal multiplicative spatial-spectral concentration on the sphere: Optimal basis

Signal analysis on the ball: Design of optimal basis functions with maximal multiplicative concentration in spatial and spectral domains

Wavelet Technology in Vehicle Power Management

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