Efficient Algorithms for Discrete Gabor Transforms on a Nonseparable Lattice

Wiesmeyr, Christoph; Holighaus, Nicki; Søndergaard, Peter

doi:10.1109/tsp.2013.2275311

Cited by 14 publications

(16 citation statements)

References 38 publications

(72 reference statements)

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“…Here we will outline the theory of discrete Gabor transforms, for a more complete picture of the theory and algorithms we refer to [6]. An in-depth investigation of the computational complexities of the finite discrete Gabor transform can be found in [14,18]. The continuous theory is described in [9,12].…”

Section: Preliminariesmentioning

confidence: 99%

An optimally concentrated Gabor transform for localized time-frequency components

Ricaud

Stempfel²,

Torrésani

et al. 2013

Adv Comput Math

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Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

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Section: Preliminariesmentioning

confidence: 99%

An optimally concentrated Gabor transform for localized time-frequency components

Ricaud

Stempfel²,

Torrésani

et al. 2013

Adv Comput Math

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“…In our numerical experiments, we omitted the pre-multiplication but post-multiplied by Γ, which turned out to be the inverse of a frame operator and for which then fast computational schemes are available, cf. [27]. Other alternatives are special matrix storage management and chopping images into smaller pieces to reduce the matrix size to deal with.…”

Section: Discussionmentioning

confidence: 99%

“…Since each T j is supposed to be a filter, there are then fast algorithms to apply Γ within the filter bank scheme, cf. [27]. Since it may not be clear how the premultiplication of Γ 1/2 changes the signal before the actual filters {T j } n j=1 come into play in Fig.…”

Section: Modifications and Numerical Experimentsmentioning

confidence: 99%

Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames

Ehler

2015

Journal of Applied Mathematics

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We turn a given filter bank into a filtering scheme that provides perfect reconstruction, synthesis is the adjoint of the analysis part (so-called unitary filter banks), all filters have equal norm, and the essential features of the original filter bank are preserved. Unitary filter banks providing perfect reconstruction are induced by tight generalized frames, which enable signal decomposition using a set of linear operators. If, in addition, frame elements have equal norm, then the signal energy is spread through the various filter bank channels in some uniform fashion, which is often more suitable for further signal processing. We start with a given generalized frame whose elements allow for fast matrix vector multiplication, as, for instance, convolution operators, and compute a normalized tight frame, for which signal analysis and synthesis still preserve those fast algorithmic schemes.

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“…Some authors have proposed truncating the Gaussian window when its value falls below a given threshold, such as 0.01% of its maximum value, or using a truncated window with a length equal to six-times the standard deviation of the full-length window,

. Instead of truncating the Gaussian window, some authors propose using an efficient computation of the DGT with the full-length Gaussian window, based on a factorization algorithm [ 82 , 83 , 84 ], but this approach has a low penetration in the fault diagnosis field.…”

Section: Cost-effective Im Fault Diagnosis Using the Truncated Slementioning

confidence: 99%

Fault Diagnosis of Induction Machines in a Transient Regime Using Current Sensors with an Optimized Slepian Window

Burriel-Valencia

Puche-Panadero

Martínez-Román

et al. 2018

Sensors

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The aim of this paper is to introduce a new methodology for the fault diagnosis of induction machines working in the transient regime, when time-frequency analysis tools are used. The proposed method relies on the use of the optimized Slepian window for performing the short time Fourier transform (STFT) of the stator current signal. It is shown that for a given sequence length of finite duration, the Slepian window has the maximum concentration of energy, greater than can be reached with a gated Gaussian window, which is usually used as the analysis window. In this paper, the use and optimization of the Slepian window for fault diagnosis of induction machines is theoretically introduced and experimentally validated through the test of a 3.15-MW induction motor with broken bars during the start-up transient. The theoretical analysis and the experimental results show that the use of the Slepian window can highlight the fault components in the current’s spectrogram with a significant reduction of the required computational resources.

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Efficient Algorithms for Discrete Gabor Transforms on a Nonseparable Lattice

Cited by 14 publications

References 38 publications

An optimally concentrated Gabor transform for localized time-frequency components

An optimally concentrated Gabor transform for localized time-frequency components

Preconditioning Filter Bank Decomposition Using Structured Normalized Tight Frames

Fault Diagnosis of Induction Machines in a Transient Regime Using Current Sensors with an Optimized Slepian Window

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