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.
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.
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!!!
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.
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.
Hey Professor Mark, I’m a surgeon from Taiwan and I’m really into machine learning. Your video was super helpful. It broke down the concepts in a way that was easy to understand. Hope everything’s going great for you this year!
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.
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.
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
😅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.
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.
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...
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"
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.
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.
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.
@@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.
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.
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.
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!!!
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.
I've been looking for this video for 20 years! Acoustics makes so much more sense now. Thanks for explaining the magic!!
My search for intuition behind convolution comes to an end with Mark Newman being the game changer. Thanks a ton Mark. Liked and subbed.
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.
You're welcome. It is a labour of love. Thanks for your kind words.
Your explanation is a work of art. I could cry. :)
Это лучшее объяснение свёртки, что я видел. Спасибо!
Brilliant! Thank you for producing an excellent visual presentation and explanation. I really like the "score" concept!
Thank a lot, not been this clear with other videos.
Amazing. Happy to have helped
What a great explanation! I'm not coming out of college blind after all.
Hey Professor Mark,
I’m a surgeon from Taiwan and I’m really into machine learning. Your video was super helpful. It broke down the concepts in a way that was easy to understand.
Hope everything’s going great for you this year!
mark is the electrical engineering professor we wish all the rest of them could be
Absolutely perfect video. Thank you so much!
This video is totally awesome!
Really glad you found it helpful.
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.
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.
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
ohhh man, best prof everrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
you are really one of the best
Thanks for such a good explanation.
Very perfect explanation 👍👍👍
Such a beautiful explanation 👍
❤❤thanks for your explanation
Amazing content
😅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.
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.
Oh my goodness! Thank you so much!
You are so welcome!
Thank you for this great video!
Wonderful explanation
Glad it was helpful!
thank you Mark!
This is GREAT! Thanx! 😊
fantastic video
Thank you.
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...
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"
Nice Sir my self Dr RP shukla from India
Great video
Keep up the great work!
Will do!
this has to be the clearest explanation of what convolution is..
Bro, plz make more such videos. . .wonderful
Thanks. I'm making one as we speak all about i and the Fourier Transform.
Can you please do a comparison between AM and FM modulations?
Is it possible to get the fourier transform of a sound signal by just using the formulas?
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.
Mate, how do I learn how to do physics animation and make graphs such as yourself?
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.
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.
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.
@@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.
Best！Bset！Best！
Shouldn't the final convolution function (the integral) be plotted against time not tau? Since what we are varying is the time offset?
The last plot at 6:00, right? I think you're right.
Amazing😂🌹
Thanks
Sinusoids are not symmetrical. sin(-tau)=-sin(tau). There are several other problems with this exposition and it intermingles cause and effect.
Test wave he used is cosine wave, so no need to worry
kc
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