The pole behavior of the phase derivative of the short-time Fourier transform

Balázs, Péter; Bayer, Dominik; Jaillet, Florent; Søndergaard, Peter

doi:10.1016/j.acha.2015.10.001

Cited by 41 publications

(14 citation statements)

References 20 publications

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“…After noting that the assumptions imply that W ψ s ∈ C 2 (R× R + , C) (or C 3 (R × R + , C)), the proof of the above result is identical to the proofs of [35,], which only rely on continuous differentiability locally.…”

Section: Derivatives and Analyticity Of The Continuous Wavelet Transfmentioning

confidence: 81%

“…Despite a relevant research activity regarding the phase behavior of time-frequency and time-scale representations, with particular incidence in the short-time Fourier transform (STFT) [33]- [35], applications that consider and/or modify the phase are relatively scarce. Prime examples of analysis tools that successfully use phase information are the so-called reassignment and synchrosqueezing methods [36]- [40] that deform the signal representation using a vector field obtained from the phase gradient of the representation.…”

Section: Introductionmentioning

confidence: 99%

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Characterization of Analytic Wavelet Transforms and a New Phaseless Reconstruction Algorithm

Holighaus

Koliander

Průša

et al. 2019

IEEE Trans. Signal Process.

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We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a by-product of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only coefficients. The cornerstone of our analysis is an expression of the partial derivatives of the continuous WT, which results in phase-magnitude relationships similar to the short-time Fourier transform (STFT) setting and valid for the generalized family of Cauchy wavelets. We show that the existence of such relations is equivalent to analyticity of the WT up to a multiplicative weight and a scaling of the mother wavelet. The implementation of the new phaseless reconstruction method is considered in detail and compared to previous methods. It is shown that the proposed method provides significant performance gains and a great flexibility regarding accuracy versus complexity. Additionally, we discuss the relation between scalogram reassignment operators and the wavelet transform phase gradient and present an observation on the phase around zeros of the WT.

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Section: Derivatives and Analyticity Of The Continuous Wavelet Transfmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Characterization of Analytic Wavelet Transforms and a New Phaseless Reconstruction Algorithm

Holighaus

Koliander

Průša

et al. 2019

IEEE Trans. Signal Process.

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show abstract

“…For all experiments, we used the Meyer-type signature wavelet (2). In order to get a sufficient amount of samples we use five octaves and five scales per octave, which corresponds to a scale sampling of the form a j = 2 − j 5 , with j = 0, .…”

Section: Yieldsmentioning

confidence: 99%

“…Reconstruction algorithms from sign/phase information have been presented in [33] for wavelet coefficients and [45] for the short time Fourier transform. The phase of the short time Fourier transform has been recently analyzed in [23,2]. In [36,46], phase congruency was introduced for signal analysis based on the sign information of Fourier coefficients.…”

Section: Introductionmentioning

confidence: 99%

Signal analysis based on complex wavelet signs

Storath

Demaret

Massopust

2017

Applied and Computational Harmonic Analysis

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We propose a signal analysis tool based on the sign (or the phase) of complex wavelet coefficients, which we call a signature. The signature is defined as the fine-scale limit of the signs of a signal's complex wavelet coefficients. We show that the signature equals zero at sufficiently regular points of a signal whereas at salient features, such as jumps or cusps, it is non-zero. At such feature points, the orientation of the signature in the complex plane can be interpreted as an indicator of local symmetry and antisymmetry. We establish that the signature rotates in the complex plane under fractional Hilbert transforms. We show that certain random signals, such as white Gaussian noise and Brownian motions, have a vanishing signature. We derive an appropriate discretization and show the applicability to signal analysis.

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“…The windows adjacent to each other allow to observe the frequency signal spectrum within time domain. That transformation called Short Time Fourier Transformation (STFT), shows the measured signal frequency spectrum for 3D coordinates: frequency and time [2]. The serious disadvantage of STFT method is the compromise with respect to window size selection, to find nonstationary signal features (then the window should be as narrow as possible), on the other hand, the narrow window size caused the loss of information about the low signal frequencies.…”

Section: Science and Technologymentioning

confidence: 99%