The Convolution Theorem in Modern Analysis

Blackwell, C. A.; Simpson, R.

doi:10.1109/te.1966.4321930

Cited by 5 publications

(3 citation statements)

References 1 publication

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“…To numerically obtain the distribution of turnover times and avoid analytically solving the convolutions, we evaluate it computationally using the convolution theorem based on Fourier transforms. 28 Therefore, the two-and three-step distributions (i.e. 𝑝 2 and 𝑝 3 , respectively) are…”

Section: Rate Of a Catalytic Turnover Cycle (F1-atpase Model)mentioning

confidence: 99%

A Simple Algorithm for Converting Random Number Generator Outputs to Universal Distributions to Aid Teaching and Research in Modern Physical Chemistry

Li,

Duong,

Neuhauser

et al. 2024

Preprint

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Molecules and materials often display distributed heterogeneous properties. Modeling the behavior of a single molecule with these properties (e.g. via Monte-Carlo simulations) requires a rapid way to sample distributions of interest and describe how they evolve. Here, we pedagogically introduce a simple algorithm that converts evenly distributed random number generator outputs to any defined probability density function (PDF) called the Random Number Converter (RNC). We demonstrate a numerical approach to obtain cumulative distribution functions (CDFs) and utilize a binary search algorithm to circumvent the need for analytical inverse CDFs. This simple method is demonstrated for various distributions, including single-exponential and Gaussian distributions and non-standard PDFs, for which neither the CDF nor its inverse are analytically solvable. We then apply this algorithm to the rate analysis of catalytic turnover cycles and Fourier spectroscopy, enabling the study of complex reaction kinetics and retrospective interferometry analysis. Our algorithm and examples can be used to train undergraduates on the tools that underlay Monte Carlo methods and connect physical chemistry to standard computer science and statistics. We provide a MATLAB and Python module in the Supporting Information with customizable parameters.

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Section: Rate Of a Catalytic Turnover Cycle (F1-atpase Model)mentioning

confidence: 99%

A Simple Algorithm for Converting Random Number Generator Outputs to Universal Distributions to Aid Teaching and Research in Modern Physical Chemistry

Li,

Duong,

Neuhauser

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Based on Fourier optics, the Fourier lens of optical element can realize the Fourier transform and complete the conversion of time-space domain and frequency domain. According to the convolution theorem [29], the convolution of two two-dimensional continuous functions in the space domain can be obtained by the inverse transformation of the product of their corresponding two Fourier transforms. On the contrary, convolution in the frequency domain can be obtained by Fourier transform of product in the space domain.…”

Section: The Implementation Based On the Fourier Transformmentioning

confidence: 99%

Research progress in optical neural networks: theory, applications and developments

et al. 2021

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With the advent of the era of big data, artificial intelligence has attracted continuous attention from all walks of life, and has been widely used in medical image analysis, molecular and material science, language recognition and other fields. As the basis of artificial intelligence, the research results of neural network are remarkable. However, due to the inherent defect that electrical signal is easily interfered and the processing speed is proportional to the energy loss, researchers have turned their attention to light, trying to build neural networks in the field of optics, making full use of the parallel processing ability of light to solve the problems of electronic neural networks. After continuous research and development, optical neural network has become the forefront of the world. Here, we mainly introduce the development of this field, summarize and compare some classical researches and algorithm theories, and look forward to the future of optical neural network.

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“…Since the complementary optical sensors permit precise measurements of CO 2 both in the sidestream cavity and at-mouth, the instrument transfer function can be obtained that enables the sidestream NO signal to be accurately transformed into the at-mouth F E NO. Formally, to achieve this, we employ the convolution theorem [47] and calculate the instrument response function for the DAS-CEAS system at each exhalation.…”

Section: Measurement Of F E No Expirogramsmentioning

confidence: 99%

Accurate real-time F_ENO expirograms using complementary optical sensors

et al. 2020

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The fraction of exhaled nitric oxide (FENO) is an important biomarker for the diagnosis and management of asthma and other pulmonary diseases associated with airway inflammation. In this study we report on a novel method for accurate, highly time-resolved, real time detection of FENO at the mouth. The experimental arrangement is based on a combination of optical sensors for the determination of the temporal profile of exhaled NO and CO2 concentrations. Breath CO2 and exhalation flow are measured at the mouth using diode laser absorption spectroscopy (at 2 μm) and differential pressure sensing, respectively. NO is determined in a sidestream configuration using a quantum cascade laser based, cavity-enhanced absorption cell (at 5.2 μm) which simultaneously measures sidestream CO2. The at-mouth and sidestream CO2 measurements are used to enable the deconvolution of the sidestream NO measurement back to the at-mouth location. All measurements have a time resolution of 0.1 s, limited by the requirement of a reasonable limit of detection for the NO measurement, which on this timescale is 4.7 ppb (2 σ). Using this methodology, NO expirograms (FENOgrams) were measured and compared for eight healthy volunteers. The FENOgrams appear to differ qualitatively between individuals and the hope is that the dynamic information encoded in these FENOgrams will provide valuable additional insight into the location of the inflammation in the airways and potentially predict a response to therapy. A validation of the measurements at low-time resolution is provided by checking that results from previous studies that used a two-compartment model of NO production can be reproduced using our technology.

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The Convolution Theorem in Modern Analysis

Cited by 5 publications

References 1 publication

A Simple Algorithm for Converting Random Number Generator Outputs to Universal Distributions to Aid Teaching and Research in Modern Physical Chemistry

A Simple Algorithm for Converting Random Number Generator Outputs to Universal Distributions to Aid Teaching and Research in Modern Physical Chemistry

Research progress in optical neural networks: theory, applications and developments

Accurate real-time F_ENO expirograms using complementary optical sensors

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The Convolution Theorem in Modern Analysis

Cited by 5 publications

References 1 publication

A Simple Algorithm for Converting Random Number Generator Outputs to Universal Distributions to Aid Teaching and Research in Modern Physical Chemistry

A Simple Algorithm for Converting Random Number Generator Outputs to Universal Distributions to Aid Teaching and Research in Modern Physical Chemistry

Research progress in optical neural networks: theory, applications and developments

Accurate real-time FENO expirograms using complementary optical sensors

Contact Info

Product

Resources

About

Accurate real-time F_ENO expirograms using complementary optical sensors