Fourier series | Sensitivity analysis
Fourier amplitude sensitivity testing (FAST) is a variance-based global sensitivity analysis method. The sensitivity value is defined based on conditional variances which indicate the individual or joint effects of the uncertain inputs on the output. FAST first represents conditional variances via coefficients from the multiple Fourier series expansion of the output function. Then the ergodic theorem is applied to transform the multi-dimensional integral to a one-dimensional integral in evaluation of the Fourier coefficients. A set of incommensurate frequencies is required to perform the transform and most frequencies are irrational. To facilitate computation a set of integer frequencies is selected instead of the irrational frequencies. The integer frequencies are not strictly incommensurate, resulting in an error between the multi-dimensional integral and the transformed one-dimensional integral. However, the integer frequencies can be selected to be incommensurate to any order so that the error can be controlled meeting any precision requirement in theory. Using integer frequencies in the integral transform, the resulted function in the one-dimensional integral is periodic and the integral only needs to evaluate in a single period. Next, since the continuous integral function can be recovered from a set of finite sampling points if the Nyquist–Shannon sampling theorem is satisfied, the one-dimensional integral is evaluated from the summation of function values at the generated sampling points. FAST is more efficient to calculate sensitivities than other variance-based global sensitivity analysis methods via Monte Carlo integration. However the calculation by FAST is usually limited to sensitivities referred to as “main effects” or “first-order effects” due to the computational complexity in computing higher-order effects. (Wikipedia).
Electrical Engineering: Ch 19: Fourier Transform (12 of 45) Find Fourier Transformation: Ex. 3
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the Fourier transform of a double pulse input of amplitude=1 to -1 and width=2 (from -1 to 1) into the frequency domain. Example 3. Next video in this series can be seen at: https://youtu.be/Kn0
From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM
Electrical Engineering: Ch 19: Fourier Transform (13 of 45) Find Fourier Transformation: Ex. 4
Visit http://ilectureonline.com for more math and science lectures! In this video I will find find the Fourier transform of a single transient pulse input of amplitude=1 and width=0 to infinity into the frequency domain. Example 4. Next video in this series can be seen at: https://youtu.
From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM
Electrical Engineering: Ch 19: Fourier Transform (2 of 45) What is a Fourier Transform? Math Def
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the mathematical definition and equation of a Fourier transform. Next video in this series can be seen at: https://youtu.be/yl6RtWp7y4k
From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM
Electrical Engineering: Ch 19: Fourier Transform (9 of 45) Conv. from Fourier Series to Transform
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the relationship between the Fourier series and Fourier transform with respect to the number of pulses. Next video in this series can be seen at: https://youtu.be/KRfS_3tnKec
From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM
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Easy explanation of the Fourier transform and the Discrete Fourier transform, which takes any signal measured in time and extracts the frequencies in that signal. This is a work in progress, let me know if anything doesn't make sense, and I will update the video to make that clearer. Tha
From playlist Fourier
To Understand the Fourier Transform, Start From Quantum Mechanics
Develop a deep understanding of the Fourier transform by appreciating the critical role it plays in quantum mechanics! Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up Sign up for my newsletter for additional physics lessons: https://www.physicswithelliot.c
From playlist Physics Mini Lessons
Virtualizing quantum errors: open-loop controls for (...) - M. Biercuk - PRACQSYS 2018 - CEB T2 2018
Michael Biercuk (ARC Centre for Engineered Quantum Systems, School of Physics, The University of Sydney, NSW Australia & National Measurement Institute, West Lindfield, Australia) / 06.07.2018 Virtualizing quantum errors: open-loop controls for noise characterization and modification of e
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
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The final thing to know about the Fourier transform is how to convert unit-indices to frequencies in Hz. You will also learn about frequency resolution and how to increase resolution by zero-padding. Patrick McGoohan makes another guest appearance. The video uses files you can download f
From playlist OLD ANTS #2) The discrete-time Fourier transform
Cosmology with LSS (Lecture 3) by John Peacock
Program Cosmology - The Next Decade ORGANIZERS : Rishi Khatri, Subha Majumdar and Aseem Paranjape DATE : 03 January 2019 to 25 January 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The great observational progress in cosmology has revealed some very intriguing puzzles, the most i
From playlist Cosmology - The Next Decade
Stochastic Astrophysical Foreground From Compact Binary Mergers (Lecture 4) by Vuc Mandic
PROGRAM ICTS SUMMER SCHOOL ON GRAVITATIONAL-WAVE ASTRONOMY (ONLINE) ORGANIZERS: Parameswaran Ajith (ICTS-TIFR, India), K. G. Arun (CMI, India), Bala R. Iyer (ICTS-TIFR, India) and Prayush Kumar (ICTS-TIFR, India) DATE : 05 July 2021 to 16 July 2021 VENUE : Online This school is part
From playlist ICTS Summer School on Gravitational-Wave Astronomy (ONLINE)
Observing Cosmic Dawn Through 21-cm Signal by Saurabh singh
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From playlist LESS TRAVELLED PATH TO THE DARK UNIVERSE
Fourier Optics used for Optical Pattern Recognition
Optical Fourier transformations were performed using small lithographic patterns of different characters. A DLP projector can be used as a Fourier filter to do simple pattern recognition. Video contents: 0:00 General introduction 1:44 Fourier explained (simple) 3:45 Digging a bit deeper
From playlist optics
Lessons from Astrophysical Models of Sgr A* and the Event Horizon Telescope - George Nathaniel Wong
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From playlist Astrophysics Seminar
MagLab User Summer School: Measuring Fermi Surfaces in Extreme Magnetic Fields
This video was recorded in 2016 at the National MagLab’s annual User Summer School, where early-career scientists learn from lab experts best practices for conducting experiments at the lab. For more information, please visit https://nationalmaglab.org/user-summer-school
From playlist User Summer School Talks
The Discrete Fourier Transform: Sampling the DTFT
http://AllSignalProcessing.com for free e-book on frequency relationships and more great signal processing content, including concept/screenshot files, quizzes, MATLAB and data files.
From playlist Fourier
Key Radio Unification Steps Before 1980 and Some Related Recent Radio Observations by A. Readhead
Extragalactic Relativistic Jets: Cause and Effect PROGRAM LINK: www.icts.res.in/program/ERG2015 DATES: Monday 12 Oct, 2015 - Tuesday 20 Oct, 2015 VENUE: Ramanujan Lecture Hall, ICTS Bangalore DESCRIPTION : Active Galactic Nuclei (AGN) are the luminous centers of galaxies that are belie
From playlist Extragalactic Relativistic Jets: Cause and Effect
Electrical Engineering: Ch 19: Fourier Transform (11 of 45) Find Fourier Transformation: Ex. 2
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the Fourier transform of a single pulse input of amplitude=1 and width=2 (from -1 to 1) into the frequency domain. Example 2. Next video in this series can be seen at: https://youtu.be/Y2Xma0yoB
From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM
Sylvia Biscoveanu - Source characterization of individual compact binary coalescences - IPAM at UCLA
Recorded 20 September 2021. Sylvia Biscoveanu of the Massachusetts Institute of Technology presents "Source characterization of individual compact binary coalescences using Bayesian inference" at IPAM's Mathematical and Computational Challenges in the Era of Gravitational Wave Astronomy Tu
From playlist Tutorials: Math & Computational Challenges in the Era of Gravitational Wave Astronomy
Gravitational wave data analysis: Detection by Chris Van Den Broeck
Summer School on Gravitational-Wave Astronomy PROGRAM LINK : http://www.icts.res.in/program/gws2015 TALK LINK : https://www.icts.res.in/program/all/talks_tab/360/ ORGANIZERS : Parameswaran Ajith, K. G. Arun and Bala Iyer DATES : Monday 29 Jun, 2015 - Friday 10 Jul, 2015 VENUE : ICTS
From playlist Summer School on Gravitational-Wave Astronomy
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From playlist Fourier