Convolution and the Fourier Transform explained visually

Convolution and the Fourier Transform go hand in hand. The Fourier Transform uses convolution to convert a signal from the time domain into the frequency domain. In this video I demonstrate an intuitive way of understanding what convolution is, explain the convolution equation and demonstrate how it is used in the Fourier Transform.
0:00 - Introduction
0:17 - A visual example of convolution
0:52 - Ident
0:57 - Welcome
1:19 - The formal definition of convolution
2:24 - The signal being analyzed
2:36 - The test wave
3:00 - The independent variable
3:31 - Stage 1: Sliding the test wave over the signal
4:34 - Stage 2: Multiplying the signals by the test wave
4:51 - Stage 3: Integration (finding the area under the graph)
5:31 - Why convolution is used in the Fourier Transform
7:28 - Challenge
Other works used in this video:
2 Crowd Green Screen and Crowd Talking Sounds
by Creative Film
• 2 Crowd Green Screen a...

[@MarkNewmanEducation]

At 3:58, for anyone who would like to know why, in general convolution, g(τ) has to be reversed so that it becomes g(-τ), it is because, if it isn't, then the response comes out backwards. For the Fourier Transform, however, as I mention in the video reversing g(τ) when it is a sinusoid has no effect as sinusoids are symmetrical.

[@teddyspaw]

I was never aware of the special case of the sinusoid, as an even function, not "caring" if it was reversed or not. That factoid greatly increased my understanding of relationship between convolution and the Fourier transform.

[@dddderek]

Blew my mind! I left a huge reply on your next video that isn't even out yet!!! This is the teaching I've been waiting my entire life for!!! Thank you so much!!! Love the graphics, too. Boy, convolving the image of yourself with yourself, what a great visual example!!!

[@MarkNewmanEducation]

Thank you so much for your comments. That might be a first for me, getting a comment on a video that is just a "coming soon" place holder for a video that is currently in production 😁. The visual approach was really missing for me at Uni. My lecturers seemed to think that the formulae explained everything. This is something I really want to address in these videos. It appears that I'm not the only one who has a problem with this approach and I want to help people like me who need a diagram or two to explain things. In the next video, we're going to dissect the for Fourier Transform equation, see how imaginary numbers can be thought of as a rotation in geometric terms and see how by looking at the spiral shape of the complex exponential in 3 dimensions, it does the whole convolution operation in one go without having to slide g(τ) over the signal.

[@littleKingSolomon]

My search for intuition behind convolution comes to an end with Mark Newman being the game changer. Thanks a ton Mark. Liked and subbed.

[@dancxjo]

I've been looking for this video for 20 years! Acoustics makes so much more sense now. Thanks for explaining the magic!!

[@sylvesterjonas9141]

Discovering your channel is like discovering a diamond mine. You deserve every single good thing for your contributions to the development of the human race. Thanks goodness for your existence.

[@MarkNewmanEducation]

You're welcome. It is a labour of love. Thanks for your kind words.

[@seahawkers101]

Your explanation is a work of art. I could cry. :)

[@teddyspaw]

Brilliant! Thank you for producing an excellent visual presentation and explanation. I really like the "score" concept!

[@arjungoud3450]

Thank a lot, not been this clear with other videos.

[@MarkNewmanEducation]

Amazing. Happy to have helped

[@dhrubjun]

Such a beautiful explanation 👍

[@ercoco1az]

What a great explanation! I'm not coming out of college blind after all.

[@MOHNAKHAN]

Very perfect explanation 👍👍👍

[@ANJA-mj1to]

Showing presentation quite different - diverse illustrated than others in the a Fourier transform in case of useful properties as signal is brilliant idea to this important concept that in practical phyhisics can be given by an example like imaging a perfect spectometar and so on represent the Spectral Power Density. Thanks for fluorescent presentation 👍 and brilliant input to the Convolution Theorem

[@theoaks1941]

Thank you for this great video!

[@fardinfahim3832]

this has to be the clearest explanation of what convolution is..

[@Murphyalex]

Nice to see you back with more videos, Mark. You're the only person who's made the Fourier Transform clear to me. It's all a bit dusty again, so I hope to review your older content and also look forward to any new stuff you put out.

[@MarkNewmanEducation]

Thank you. The next video is currently in production and I hope to release it in a few weeks time. In it, we consider what the imaginary number "i" is doing in the Fourier Transform equation and how it makes the convolution operation quicker.

[@user-or1iu2ym6m]

you are really one of the best

[@muddassirghoorun4322]

Amazing content

[@punditgi]

This video is totally awesome!

[@MarkNewmanEducation]

Really glad you found it helpful.

[@Ishanya_]

ohhh man, best prof everrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

[@curtpiazza1688]

This is GREAT! Thanx! 😊

[@mutalasuragemohammed6954]

😅my God! you made me laugh with the bang with which the formula dropped... It's been our nightmare in undergraduate study. Thank you for the succinct explanation.

[@MarkNewmanEducation]

The way I wince as it falls in the video, was basically how I felt when I first learned it all those years ago at university. My lecturer never explained it properly to me. This is why I am making these videos. There is a visual way of explaining math that is not taught at university. At least, it wasn't when I was there.

[@michaelliu6323]

thank you Mark!

[@manofmen701]

Great video

[@SalmonSushi47]

Keep up the great work!

[@MarkNewmanEducation]

Will do!

[@TheFreeSpiritKID]

Wonderful explanation

[@MarkNewmanEducation]

Glad it was helpful!

[@OurgasmComrade]

Could you also do a video about the Laplace transform and complex frequency domains? (Including 3D representation of frequency response and how it's affected by poles/zeroes of filters)

[@MarkNewmanEducation]

Yes. Totally want to do this! It's been on my to-do list forever. I need to do a bit more research though to understand it properly myself. Once I have totally cracked Fourier, Laplace is next on the list.

[@booky6149]

Oh my goodness! Thank you so much!

[@MarkNewmanEducation]

You are so welcome!

[@rpshukla001]

Nice Sir my self Dr RP shukla from India

[@MrMichaelYD]

fantastic video

[@MarkNewmanEducation]

Thank you.

[@tashi2009]

Bro, plz make more such videos. . .wonderful

[@MarkNewmanEducation]

Thanks. I'm making one as we speak all about i and the Fourier Transform.

[@calvinluiramo5514]

I always love your explanation they so simple with simple conceptualization and are easy to understand, if could run one for "Green's function" I would be grateful...

[@MarkNewmanEducation]

Thank you for your kind words and your suggestion. I'll look into it. New video out later later today called "The Imaginary Number i and the Fourier Transform"

[@keylanoslokj1806]

Can you please do a comparison between AM and FM modulations?

[@johana3097]

Is it possible to get the fourier transform of a sound signal by just using the formulas?

[@MarkNewmanEducation]

You'd need to know the formula of the sound signal. Most sounds are random so they don't have defined formulae. That is why you need the DFT and FFT.

[@SAJAN_ECE]

Actually we are checking the similarity between two signals here. That is called Correlation right? I am confused. Which one are we doing in Fourier Transform? Correlation or Convolution? Please clarify my doubt.

[@MarkNewmanEducation]

In the Fourier transform it is convolution. In convolution, the g(τ) signal is reversed. In correlation, it isn't. But you're right, the two methods are very similar. en.wikipedia.org/wiki/Convolution This Wikipedia page has a good diagram explaining the difference.

[@SAJAN_ECE]

@@MarkNewmanEducation In Fourier Transform we are changing the frequency of the sine waves and checking the similarity between the original signal and sine wave right? In that case that must be Correlation right? In the case of Filtering I agree, that is a convolution between the original signal and the impulse response of the filter. But in the Analysis Equation of Fourier Transform, the actual operation is just correlation right? Please correct me if I am wrong.

[@_tasneem7378]

Amazing😂🌹

[@MarkNewmanEducation]

Thanks

[@XZJAK]

Best！Bset！Best！

[@pradyumnanimbkar8011]

Mate, how do I learn how to do physics animation and make graphs such as yourself?

[@MarkNewmanEducation]

I do a lot of my animations in JavaScript. If helps that I have been a programmer for many years. I love JavaScript. There are tons of really good sites to help you learn it and all you need to run the code is a text editor and a web browser. The video editing I do in a package called Hitfilm.

[@harryhirsch2024]

Sinusoids are not symmetrical. sin(-tau)=-sin(tau). There are several other problems with this exposition and it intermingles cause and effect.

[@findLuxuryHub]

Test wave he used is cosine wave, so no need to worry

[@mujomuric446]

Mehr licht

[@oguzcan815]

sup

[@jameshopkins3541]

??????????