Bilinear maps | Functional analysis | Fourier analysis
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions (f and g) that produces a third function that expresses how the shape of one is modified by the other. The term convolution refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see ). The integral is evaluated for all values of shift, producing the convolution function. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution differs from cross-correlation only in that either f(x) or g(x) is reflected about the y-axis in convolution; thus it is a cross-correlation of g(−x) and f(x), or f(−x) and g(x). For complex-valued functions, the cross-correlation operator is the adjoint of the convolution operator. Convolution has applications that include probability, statistics, acoustics, spectroscopy, signal processing and image processing, geophysics, engineering, physics, computer vision and differential equations. The convolution can be defined for functions on Euclidean space and other groups (as algebraic structures). For example, periodic functions, such as the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution. (See row 18 at DTFT § Properties.) A discrete convolution can be defined for functions on the set of integers. Generalizations of convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing. Computing the inverse of the convolution operation is known as deconvolution. (Wikipedia).
How do we multiply polynomials
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Easiest Way to Multiply Two Trinomials by Each Other - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply a Trinomial by a Trinomial
Multiply a Trinomial by a Trinomial Using a Rectangle - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply a Trinomial by a Trinomial
How to Simplify an Expression Using Distributive Property - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Solving Inequalities using Addition and Subtraction
This video is about Solving Inequalities using Addition and Subtraction
From playlist Equations and Inequalities
How to Learn the Basics of The Distributive Property
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Why does the distributive property Where does it come from
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Multiplying Polynomials - Math Tutorial
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials
Lec 10 | MIT RES.6-008 Digital Signal Processing, 1975
Lecture 10: Circular convolution Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES6-008S11 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.6-008 Digital Signal Processing, 1975
Convolution in the time domain
Now that you understand the Fourier transform, it's time to start learning about time-frequency analyses. Convolution is one of the best ways to extract time-frequency dynamics from a time series. Convolution can be conceptualized and implemented in the time domain or in the frequency doma
From playlist OLD ANTS #3) Time-frequency analysis via Morlet wavelet convolution
Depthwise Separable Convolution - A FASTER CONVOLUTION!
In this video, I talk about depthwise Separable Convolution - A faster method of convolution with less computation power & parameters. We mathematically prove how it is faster, and discuss applications where it is used in modern research. If you liked that video, hit that like button. If
From playlist Deep Learning Research Papers
Convolution in the time domain
This video lesson is part of a complete course on neuroscience time series analyses. The full course includes - over 47 hours of video instruction - lots and lots of MATLAB exercises and problem sets - access to a dedicated Q&A forum. You can find out more here: https://www.udemy.
From playlist NEW ANTS #3) Time-frequency analysis
Convolution via frequency domain multiplication
Is time-domain convolution too slow? (Yes it is.) Learn how to do lightning-fast convolution in the frequency domain. This will also help you understand that wavelet convolution is really just filtering. The video uses files you can download from https://github.com/mikexcohen/ANTS_youtube
From playlist OLD ANTS #3) Time-frequency analysis via Morlet wavelet convolution
Convolution Neural Networks - EXPLAINED
In this video, we talk about Convolutional Neural Networks. Give the video a thumbs up and hit that SUBSCRIBE button for more awesome content. Code to demonstrate Equivariance wrt Translation: https://github.com/ajhalthor/cnn-notes/blob/master/trans_conv_combined.py My video on Generati
From playlist Convolution Neural Networks
Convolutional Neural Networks – Architectures Full project: https://github.com/Atcold/torch-Video-Tutorials Network available at the full project repository. A more exhaustive overview of the most relevant architectures for image recognition can be found at https://culurciello.github.io/t
From playlist Deep-Learning-Course
The Evolution of Convolution Neural Networks
From the one that started it all "LeNet" (1998) to the deeper networks we see today like Xception (2017), here are some important CNN architectures you should know. If you like the video, show your support with a like, and SUBSCRIBE for more awesome content on Machine Learning, deep Learni
From playlist Deep Learning Research Papers
Deep Learning Lecture 5.3 - ConvNets
Convolutional Neural Networks: - Overall Architecture of a CNN Classifier - Convolutional Layers - Nonlinear Activation Function - Pooling or Striding - Boundary (Zero Padding) - LeNet-5 - AlexNet - Convolutions on different topologies
From playlist Deep Learning Lecture
Convolution as spectral multiplication
This video lesson is part of a complete course on neuroscience time series analyses. The full course includes - over 47 hours of video instruction - lots and lots of MATLAB exercises and problem sets - access to a dedicated Q&A forum. You can find out more here: https://www.udemy.
From playlist NEW ANTS #3) Time-frequency analysis
Learn How to Use the Distributive Property to Multiply Polynomials
👉 Learn how to multiply polynomials. To multiply polynomials, we use the distributive property. The distributive property is essential for multiplying polynomials. The distributive property is the use of each term of one of the polynomials to multiply all the terms of the other polynomial.
From playlist How to Multiply Polynomials