Time–frequency analysis | Integral transforms | Fourier analysis
In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate domain between time and frequency. Its applications range from filter design and signal analysis to phase retrieval and pattern recognition. The FRFT can be used to define fractional convolution, correlation, and other operations, and can also be further generalized into the linear canonical transformation (LCT). An early definition of the FRFT was introduced by Condon, by solving for the Green's function for phase-space rotations, and also by Namias, generalizing work of Wiener on Hermite polynomials. However, it was not widely recognized in signal processing until it was independently reintroduced around 1993 by several groups. Since then, there has been a surge of interest in extending Shannon's sampling theorem for signals which are band-limited in the Fractional Fourier domain. A completely different meaning for "fractional Fourier transform" was introduced by Bailey and Swartztrauber as essentially another name for a z-transform, and in particular for the case that corresponds to a discrete Fourier transform shifted by a fractional amount in frequency space (multiplying the input by a linear chirp) and evaluating at a fractional set of frequency points (e.g. considering only a small portion of the spectrum). (Such transforms can be evaluated efficiently by Bluestein's FFT algorithm.) This terminology has fallen out of use in most of the technical literature, however, in preference to the FRFT. The remainder of this article describes the FRFT. (Wikipedia).
How to integrate by partial fractions
Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook How to integrate by the method of partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is a fraction such that the numerator
From playlist A second course in university calculus.
Integration & partial fractions
Free ebook http://tinyurl.com/EngMathYT An example of how to integrate using partial fractions (with repeated factors).
From playlist A second course in university calculus.
Integration by partial fractions
Free ebook http://tinyurl.com/EngMathYT Example of how to integrate using partial fractions.
From playlist A second course in university calculus.
Partial fractions + integration
Free ebook http://tinyurl.com/EngMathYT An example on how to integrate using partial fractions.
From playlist A second course in university calculus.
(New Version Available) Partial Fraction Decomposition - Part 1 of 2
New Version Available: https://youtu.be/c2oLHtPA03U This video explain how to perform partial fraction decomposition with linear factors. http://mathispower4u.yolasite.com/
From playlist Integration Using Partial Fraction Decomposition
Integration + partial fractions
Free ebook http://tinyurl.com/EngMathYT An example on how to integrate using partial fractions.
From playlist A second course in university calculus.
Free ebook http://tinyurl.com/EngMathYT An example on how to integrate quickly using partial fractions.
From playlist A second course in university calculus.
Rewriting a rational exponent into radical form
👉 Learn how to convert a rational power to a radical. When the exponent of an expression is a fraction, we can evaluate/simplify the expression by converting the rational power into a radical where the denominator of the fractional exponent of the rational power becomes the index (nth root
From playlist Convert Fractional Exponents to Radicals
Half derivative and Fourier transform
Fourier transform definition of the half derivative For more fun, check out my fractional derivative playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmB_ma3YrfuOXTPOQawokYV_ In this video, I define fractional derivatives by using Fourier transforms. This definition is probably
From playlist Fractional Derivatives
Compositional Structure of Classical Integral Transforms
The recently implemented fractional order integro-differentiation operator, FractionalD, is a particular case of more general integral transforms. The majority of classical integral transforms are representable as compositions of only two transforms: the modified direct and inverse Laplace
From playlist Wolfram Technology Conference 2022
Fourier Transforms: Image Compression, Part 1
Data Science for Biologists Fourier Transforms: Image Compression Part 1 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton
From playlist Fourier
Quantum computation (Lecture 04) by Peter Young
ORGANIZERS : Abhishek Dhar and Sanjib Sabhapandit DATE : 27 June 2018 to 13 July 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore This advanced level school is the ninth in the series. This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics
From playlist Bangalore School on Statistical Physics - IX (2018)
Lecture 9, Fourier Transform Properties | MIT RES.6.007 Signals and Systems, Spring 2011
Lecture 9, Fourier Transform Properties Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES-6.007S11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT RES.6.007 Signals and Systems, 1987
Modulation Spaces and Applications to Hartree-Fock Equations by Divyang Bhimani
We discuss some ongoing interest (since last decade) in use of modulation spaces in harmonic analysis and its connection to nonlinear dispersive equations. In particular, we shall discuss results on Hermite multiplier and composition operators on modulation spaces. As an application to the
From playlist ICTS Colloquia
Lecture: FFT and Image Compression
The applications of the FFT are immense. Here it is shown to be useful in compressing images in the frequency domain.
From playlist Beginning Scientific Computing
ME565 Lecture 18: FFT and Image Compression
ME565 Lecture 18 Engineering Mathematics at the University of Washington FFT and Image Compression Notes: http://faculty.washington.edu/sbrunton/me565/pdf/L18.pdf Matlab code: http://faculty.washington.edu/sbrunton/me565/matlab/compress.m Course Website: http://faculty.washington.edu/sb
From playlist Engineering Mathematics (UW ME564 and ME565)
Converting a rational exponent to radical form
👉 Learn how to convert a rational power to a radical. When the exponent of an expression is a fraction, we can evaluate/simplify the expression by converting the rational power into a radical where the denominator of the fractional exponent of the rational power becomes the index (nth root
From playlist Convert Fractional Exponents to Radicals
Distinguished Visitor Lecture Series Finding better randomness Theodore A. Slaman University of California, Berkeley, USA
From playlist Distinguished Visitors Lecture Series
How to write a rational exponent into radical form
👉 Learn how to convert a rational power to a radical. When the exponent of an expression is a fraction, we can evaluate/simplify the expression by converting the rational power into a radical where the denominator of the fractional exponent of the rational power becomes the index (nth root
From playlist Convert Fractional Exponents to Radicals
Fractional Calderon problem Lecture 1 by Tuhin Ghosh
DISCUSSION MEETING WORKSHOP ON INVERSE PROBLEMS AND RELATED TOPICS (ONLINE) ORGANIZERS: Rakesh (University of Delaware, USA) and Venkateswaran P Krishnan (TIFR-CAM, India) DATE: 25 October 2021 to 29 October 2021 VENUE: Online This week-long program will consist of several lectures by
From playlist Workshop on Inverse Problems and Related Topics (Online)