Convolution

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This is my video series about Real Analysis. We talk about sequences, series, continuous functions, differentiable functions, and integral. I hope that it will help everyone who wants to learn about it.

This is #Day21 in the series.

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I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[mueezadam]

Mathematicians 🤝 using star to denote every new operation

[pinklady]

I have let the ads play out to their ends so that you get paid and make more videos. Thanks for continuing to make more videos on notations

[surendrabarsode]

Well explained but I wish you could have given an example to illustrate the concept. Also, you could have defined this for a discrete function. Please add another video when possible. Thanks and regards.

[Rene_Christensen]

It can be quite informative to think of the special situation of either f or g being an impulse; hence the convolution will sum a lot of impulse responses, which is what the output of a (linear time-invariant) system would be, as it is defined via its impulse reponses. This becomes very clear when looking at discrete signals.

[UdarRusskihPudgei]

Ordinary polynomial multiplication is a good example of a convolution defined over powers of *x*.

[xinpingdonohoe]

The only issue is that some integrate it on (-∞, ∞) and others integrate it on [0, x], and I can't figure out why the divide is there. Does one type work better for Laplace/Fourier transforms, for instance?

[whatitmeans]

There exist an inverse operation alike a "deconvolution"?

[opokufrederick]

This is unlike you no intuition in the formula...