Convolution and the Fourier Transform explained visually

Рет қаралды 31,747

Күн бұрын

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...

Пікірлер: 64

@MarkNewmanEducation 2 жыл бұрын

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 9 ай бұрын

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 2 жыл бұрын

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 2 жыл бұрын

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 Жыл бұрын

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

@seahawkers101 Жыл бұрын

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

@dancxjo 9 ай бұрын

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

@teddyspaw 9 ай бұрын

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

@sylvesterjonas9141 5 ай бұрын

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 5 ай бұрын

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

@dhrubjun Жыл бұрын

Such a beautiful explanation 👍

@theoaks1941 Жыл бұрын

Thank you for this great video!

@arjungoud3450 2 жыл бұрын

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

@MarkNewmanEducation 2 жыл бұрын

Amazing. Happy to have helped

@user-yx5mr8cs8n Ай бұрын

Thanks for such a good explanation.

@ANJA-mj1to 7 ай бұрын

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

@punditgi Жыл бұрын

This video is totally awesome!

@MarkNewmanEducation Жыл бұрын

Really glad you found it helpful.

@MOHNAKHAN Жыл бұрын

Very perfect explanation 👍👍👍

@muddassirghoorun4322 Жыл бұрын

Amazing content

@user-or1iu2ym6m 4 ай бұрын

you are really one of the best

@curtpiazza1688 Жыл бұрын

This is GREAT! Thanx! 😊

@michaelliu6323 9 ай бұрын

thank you Mark!

@Murphyalex 2 жыл бұрын

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 2 жыл бұрын

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.

@ercoco1az Жыл бұрын

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

@manofmen701 Жыл бұрын

Great video

@booky6149 Жыл бұрын

Oh my goodness! Thank you so much!

@MarkNewmanEducation Жыл бұрын

You are so welcome!

@salmonsushi47 2 жыл бұрын

Keep up the great work!

@MarkNewmanEducation 2 жыл бұрын

Will do!

@Ishanya_ 5 ай бұрын

ohhh man, best prof everrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

@MrMichaelYD 2 жыл бұрын

fantastic video

@MarkNewmanEducation 2 жыл бұрын

Thank you.

@TheFreeSpiritKID 2 жыл бұрын

Wonderful explanation

@MarkNewmanEducation 2 жыл бұрын

Glad it was helpful!

@mutalasuragemohammed6954 Жыл бұрын

😅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 Жыл бұрын

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.

@tashi2009 2 жыл бұрын

Bro, plz make more such videos. . .wonderful

@MarkNewmanEducation 2 жыл бұрын

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

@calvinluiramo5514 2 жыл бұрын

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 2 жыл бұрын

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"

@OurgasmComrade 11 ай бұрын

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 11 ай бұрын

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.

@rpshukla001 9 ай бұрын

Nice Sir my self Dr RP shukla from India

@_tasneem7378 10 ай бұрын

Amazing😂🌹

@MarkNewmanEducation 10 ай бұрын

Thanks

@keylanoslokj1806 7 ай бұрын

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

@fardinfahim3832 2 ай бұрын

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

@johana3097 Жыл бұрын

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

@MarkNewmanEducation Жыл бұрын

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.

@hanshen5584 Ай бұрын

Shouldn't the final convolution function (the integral) be plotted against time not tau? Since what we are varying is the time offset?

@andreestevam131 6 күн бұрын

The last plot at 6:00, right? I think you're right.

@pradyumnanimbkar8011 5 ай бұрын

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

@MarkNewmanEducation 5 ай бұрын

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.

@SAJAN_ECE 2 жыл бұрын

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 2 жыл бұрын

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 2 жыл бұрын

@@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.