Rocking Out With Convolutions | Two Minute Papers #73

dear fellow Scholars this is 2minute papers with Caro and today we are here to answer one question what is a convolution I have heard many University students crying in despair over their perilous journeys of understanding what convolutions are and why they are useful let me give a helping hand there a convolution is a mathematical technique to mix together two signals a lot of really useful tasks can be accomplished through this operation for instance convolutions can be used to add reverberation to a recorded instrument so I play my guitar here in my room and it can sound like as if it were recorded in a large concert hall now dear fellow Scholars put on a pair of headphones and let me rock out on my guitar to show it to you first you'll hear the dry guitar signal and this is the same signal with the added reverberation it sounds much more convincing right in simple words a convolution is a bit like saying guitar plus Concert Hall equals a guitar sound that was played in a concert hall the only difference is that we don't say guitar plus Concert Hall we say guitar convolved with the concert hall if we want to be a bit more accurate we could say that the impulse response of the hall which records how this place reacts to a person who starts to play the guitar in there people use the living hell out of convolution reverberation plugins in the music industry convolutions can also be used to blur or sharpen an image we also had many examples of convolutional neural networks that provide efficient means to for instance get machines to recognize traffic signs we can also use them to add sophisticated light transport effects such as subsurface scattering to images this way we can conjure up digital characters with stunningly high quality skin and other translucent materials in our animations and computer games we have had a previous episode on this and it is available in the video description box make sure to have a look as we said before Computing a convolution is not at all like addition not even close for instance the convolution of two boxes is a triangle wow what kind of Witchcraft is this it doesn't sound intuitive at all the computation of the convolution means that we start to push this box over the other one and at every point in time we take a look at the intersection between the two signals as you can see at first they don't touch at all then as they start to overlap we have highlighted the intersected area with green and as they get closer to each other this area increases when they are completely overlapped we get the maximum intersection area which then starts to dwindle as they separate it is a miracle of mathematics that by Computing things like this we can rock out in a virtual church or a stadium which sounds very close to the real deal and before we go a quick shout out to immersive math really intuitive resource for learning linear algebra if you're into math you simply have to check this one out it's really cool thanks for watching and for your generous support and I'll see you next time