Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Trigonometric Fourier series

Trigonometric Fourier series

Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...

Fast Fourier Transform

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...

Convergence of Fourier Series

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...

Parseval's Theorem for Fourier transform

Parseval's Theorem for Fourier transform

Parseval's theorem is a fundamental principle in signal processing that enables the calculation of a signal's energy in either the time domain or the frequency domain. This theorem is pivotal in demonstrating energy conservation between these two domains, ensuring that the computed energy value remains consistent regardless of the domain of analysis.
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a signal's...

Properties of Fourier Transform II

Properties of Fourier Transform II

The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

GSH-Responsive GalNAc-Conjugated Glycopolymer for Targeted Survivin siRNA Delivery in Hepatocellular Carcinoma Therapy.

ACS macro letters·2025

Same author

Promotion framing effects on the purchase of hedonic-utilitarian bundles: ERPs evidence of the moderating role of income source.

Neuroscience letters·2023

Same author

The effect of reviewer's review volumes on online consumer reviews' perceived usefulness: An event-related potential study.

Neuroscience letters·2021

Same author

Prediction of Bead Geometry with Changing Welding Speed Using Artificial Neural Network.

Materials (Basel, Switzerland)·2021

Same author

Magnolol Alleviates Inflammatory Responses and Lipid Accumulation by AMP-Activated Protein Kinase-Dependent Peroxisome Proliferator-Activated Receptor α Activation.

Frontiers in immunology·2018

Same author

The T790M resistance mutation in EGFR is only found in cfDNA from erlotinib-treated NSCLC patients that harbored an activating EGFR mutation before treatment.

BMC cancer·2018

Search research articles

Related Experiment Video

Updated: Jul 2, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Modified Fourier-Hankel method based on analysis of errors in Abel inversion using Fourier transform techniques.

Shuiliang Ma¹, Hongming Gao, Lin Wu

¹State Key Laboratory of Advanced Welding Production Technology, Harbin Institute of Technology, Harbin 150001, China. shlgma@126.com

|August 19, 2008

Summary

Errors in Fourier transform Abel inversion methods were analyzed. A modified Fourier-Hankel method is proposed, offering accuracy, efficiency, and noise filtering for experimental data analysis.

More Related Videos

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

Related Experiment Videos

Last Updated: Jul 2, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

Area of Science:

Applied Mathematics
Data Analysis
Signal Processing

Background:

Discrete Abel inversion is crucial for analyzing experimental data.
Fourier transform techniques are commonly used but have limitations.
Existing methods like Fourier expansion and Fourier-Hankel have specific error profiles and sensitivities.

Purpose of the Study:

To analyze errors in discrete Abel inversion methods using Fourier transforms.
To identify limitations of the Fourier expansion and Fourier-Hankel methods.
To develop an improved method for accurate and noise-robust Abel inversion.

Main Methods:

Analysis of errors in discrete Abel inversion using Fourier transform techniques.
Evaluation of the Fourier expansion method's accuracy and noise sensitivity.
Investigation of the Fourier-Hankel method's systematic deviation and noise filtering properties.
Development of a modified Fourier-Hankel method.

Main Results:

The Fourier expansion method is accurate but highly sensitive to noise.
The Fourier-Hankel method exhibits a radius-dependent systematic negative deviation.
Adjusting a specific factor in the Fourier-Hankel method can reduce inversion error.
Decreasing the factor in both methods demonstrates noise filtering capabilities.

Conclusions:

A modified Fourier-Hankel method is proposed, balancing accuracy, computational efficiency, and noise filtering.
This enhanced method is suitable for application to experimental data requiring robust Abel inversion.
The study provides insights into optimizing Fourier-based Abel inversion techniques.