Signal Analysis

Allen, Ronald L.; Mills, Duncan W.

doi:10.1002/047166037x

Cited by 56 publications

(12 citation statements)

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“…The wavelet transform examines a time series at various scales to uncover its structure by using both time and frequency components. 42 Given a time series y(t), its wavelet transform defined as…”

Section: Wavelet Transformmentioning

confidence: 99%

“…The wavelet transform examines a time series at various scales to uncover its structure by using both time and frequency components 42 . Given a time series

y(t)

, its wavelet transform defined as

WT\left(y,a,b\right):= \frac{1}{\sqrt{a}}{\int}_{-\infty}^{\infty }y(t)\cdotp \psi \left(\frac{t-b}{a}\right)\kern0.3em dt,

where

a

is a scale parameter called dilation,

b

is a translation parameter called the time shift, and

\psi (t)

is called the mother wavelet function.…”

Section: Introductionmentioning

confidence: 99%

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Classification of stochastic processes with topological data analysis

Güzel

Kaygun

2023

Concurrency and Computation

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SummaryIn this study, we demonstrate that engineered topological features can distinguish time series sampled from different stochastic processes with different noise characteristics, in both balanced and unbalanced sampling schemes. We compare our classification results against the results of the same classification on features coming from descriptive statistics and the wavelet transform. We conclude that machine learning models built on engineered topological features alone perform consistently better than those built on the standard statistical and wavelet features for time series classification tasks. We also apply dimension reduction techniques to our engineered features and compare the result of our classification models before and after dimensionality reduction. Finally, we also show that in our calculations of the engineered topological features, employing parallel computing methods does yield significant improvements in run time and memory footprint.

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Section: Wavelet Transformmentioning

confidence: 99%

“…The wavelet transform examines a time series at various scales to uncover its structure by using both time and frequency components 42 . Given a time series

y(t)

, its wavelet transform defined as

WT\left(y,a,b\right):= \frac{1}{\sqrt{a}}{\int}_{-\infty}^{\infty }y(t)\cdotp \psi \left(\frac{t-b}{a}\right)\kern0.3em dt,

where

a

is a scale parameter called dilation,

b

is a translation parameter called the time shift, and

\psi (t)

is called the mother wavelet function.…”

Section: Introductionmentioning

confidence: 99%

Classification of stochastic processes with topological data analysis

Güzel

Kaygun

2023

Concurrency and Computation

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“…В связи с этим в приложениях оптической метрологии традиционная оценка распределений интенсивности и фазы лучей, распространяющихся через систему, на основе явления интерференции и геометрической оптики перестала удовлетворять практическим нуждам оптимизации оптических систем. Поэтому актуальна проблема анализа систем с высоким разрешением в режиме реального времени на основе свойств оптических сигналов [1][2][3][4].…”

Section: Introductionunclassified

Measurement of the radius of curvature of a spherical surface based on the transport-of-intensity equation

Stsepuro¹,

Kovalev²,

Krasin³

et al. 2022

Computer Optics

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The transport-of-intensity equation provides a new non-interferometric and non-iterative access to quantitative information about the phase of a light wave by measuring intensity distributions. This equation can be used to implement a simple and accurate spatial phase measurement for optical testing of spherical surfaces. The method requires only a CMOS camera, which records transverse field intensity distributions in several planes. Processing of experimental measurements with specialized software allows one to reconstruct the value of the radius of curvature of the spherical surface under test with high accuracy. The method is compared with measurements made by an interferometer, showing the difference between the values of the surface radius of curvature to be 0.01 % or less and indicating good agreement of the results.

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“…In summary, our results will enable practitioners and experimentalistbut also theorists-to visualise and study complex quantum states in considerably larger dimensions. This is accomplished by applying an efficiently computable Fourier series expansion and a fast Fourier transform (FFT) [55]. In particular, Fig.…”

Section: Introductionmentioning

confidence: 99%

Fast computation of spherical phase-space functions of quantum many-body states

Koczor,

Zeier,

Glaser

2020

Preprint

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Quantum devices are preparing increasingly more complex entangled quantum states. How can one effectively study these states in light of their increasing dimensions? Phase spaces such as Wigner functions provide a suitable framework. We focus on phase spaces for finite-dimensional quantum states of single qudits or permutationally symmetric states of multiple qubits. We present methods to efficiently compute the corresponding phase-space functions which are at least an order of magnitude faster than traditional methods. Quantum many-body states in much larger dimensions can now be effectively studied by experimentalist and theorists using these phase-space techniques.

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Signal Analysis

Cited by 56 publications

References 0 publications

Classification of stochastic processes with topological data analysis

Classification of stochastic processes with topological data analysis

Measurement of the radius of curvature of a spherical surface based on the transport-of-intensity equation

Fast computation of spherical phase-space functions of quantum many-body states

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