Convolution — Topic Summaries
AI-powered summaries of 8 videos about Convolution.
8 summaries
Convolutions | Why X+Y in probability is a beautiful mess
Adding two independent random variables isn’t just a matter of “adding their means”—it reshapes their entire probability distribution through a...
A pretty reason why Gaussian + Gaussian = Gaussian
Adding two independent normally distributed variables produces another normal distribution—a “stability” result that explains why the Gaussian is the...
Distributions 13 | Convolution
Convolution, first defined for ordinary integrable functions, can be extended to distributions by shifting the definition onto test functions and...
Fourier Transform 18 | Dirichlet Kernel
Dirichlet kernel DN sits at the heart of Fourier series: it turns a Fourier partial sum into an integral (or convolution/inner product) against DN,...
An Approximation Theorem for Functions (old)
A continuous function on 3n can be uniformly approximated on any compact set by smooth (C3) functions using convolution with a carefully...
An Approximation Theorem for Continuous Functions
Continuous functions on n can be uniformly approximated on any compact set by smooth (-infinity) functions via convolution with a carefully...
Distributions 17 | Convolution with Distributions of Compact Support
Convolution for distributions becomes workable far beyond the “test function + distribution” setting once one input is restricted to have compact...
Distributions 16 | Distributions with Compact Support
Distributions can be applied not only to compactly supported test functions, but also to a larger class of smooth functions—provided the distribution...