Iterative Algorithms to Approximate Canonical Gabor Windows: Computational Aspects

Janssen, Ajem Guido; Søndergaard, Peter

doi:10.1007/s00041-006-6069-y

Cited by 19 publications

(21 citation statements)

References 34 publications

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“…The function gabdualnorm will return the maximal reconstruction error of any signal when using the pair g, γ as windows for analysis and synthesis. 8,32 In particular for two windows that generate dual Gabor systems, the numerical precision is returned.…”

Section: Dual/tight Windowsmentioning

confidence: 99%

The Linear Time Frequency Analysis Toolbox

Søndergaard

Torrésani

Balázs

2012

Int. J. Wavelets Multiresolut Inf. Process.

Self Cite

100

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The Linear Time Frequency Analysis Toolbox is a MATLAB/Octave toolbox for computational time-frequency analysis. It is intended both as an educational and computational tool. The toolbox provides the basic Gabor, Wilson and MDCT transform along with routines for constructing windows (filter prototypes) and routines for manipulating coefficients. It also provides a bunch of demo scripts devoted either to demonstrating the main functions of the toolbox, or to exemplify their use in specific signal processing applications. In this paper we describe the used algorithms, their mathematical background as well as some signal processing applications.

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Section: Dual/tight Windowsmentioning

confidence: 99%

The Linear Time Frequency Analysis Toolbox

Søndergaard

Torrésani

Balázs

2012

Int. J. Wavelets Multiresolut Inf. Process.

Self Cite

100

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“…For simplicity we only construct the minimal factor, that L min has to be multiplied with, as stated in (23).…”

Section: Further Optimizationmentioning

confidence: 99%

Efficient Algorithms for Discrete Gabor Transforms on a Nonseparable Lattice

Wiesmeyr¹,

Holighaus²,

Søndergaard³

2013

IEEE Trans. Signal Process.

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The Discrete Gabor Transform (DGT) is the most commonly used transform for signal analysis and synthesis using a linear frequency scale. It turns out that the involved operators are rich in structure if one samples the discrete phase space on a subgroup. Most of the literature focuses on separable subgroups, in this paper we will survey existing methods for a generalization to arbitrary groups, as well as present an improvement on existing methods. Comparisons are made with respect to the computational complexity, and the running time of optimized implementations in the C programming language. The new algorithms have the lowest known computational complexity for nonseparable lattices and the implementations are freely available for download. By summarizing general background information on the state of the art, this article can also be seen as a research survey, sharing with the readers experience in the numerical work in Gabor analysis.

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“…Instead, they must be computed using a translated and modulated window function w(t), the analysis window, such that cm,n = <ir , wm,n> [75]- [80]. This window must satisfy the biorthonormality condition: …”

Section: Choice Of the Lattice Parameters T ωmentioning

confidence: 99%

Diagnosis of Induction Motor Faults via Gabor Analysis of the Current in Transient Regime

Riera-Guasp

Pineda-Sánchez

Pérez-Cruz

et al. 2012

IEEE Trans. Instrum. Meas.

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IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS. But a fine tuning of their parameters is needed in order to obtain a high resolution image of the fault in the time-frequency domain, and they also require a much higher processing effort than traditional diagnosis techniques, such as the Fourier Transform (FT). The new method proposed in this paper addresses both problems using the Gabor analysis of the current via the chirp z-transform (CZT), which can be easily adapted to generate high resolution time-frequency stamps of different types of faults. In this paper, it is used to diagnose broken bars of an IM using the current during a startup transient. This new approach is theoretically introduced and experimentally validated with a 1.1 kW commercial motor in faulty and healthy conditions.

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Iterative Algorithms to Approximate Canonical Gabor Windows: Computational Aspects

Cited by 19 publications

References 34 publications

The Linear Time Frequency Analysis Toolbox

The Linear Time Frequency Analysis Toolbox

Efficient Algorithms for Discrete Gabor Transforms on a Nonseparable Lattice

Diagnosis of Induction Motor Faults via Gabor Analysis of the Current in Transient Regime

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