EXTRA NOTES: -The convolution matrix is a Toeplitz matrix. -If the bakery's impulse response was to give cookies periodically (e.g. giving cookies every week), you would get circular convolution. -Another intuition of flipping the impulse response is that if you DIDN'T flip, the system would be using signals from the future input to calculate the present output, which is impossible in a time-dependent system. - Fourier Transform video mentioned in footnote at 8:08: https://www.youtube.com/watch?v=7Vma1G2p6A8 - Origin and History of Convolutions: https://www.slideshare.net/Alexdfar/origin-adn-history-of-convolution Timestamps 0:00 Introduction 0:47 Bakery 1:38 Fancy Word #1: Impulse Response 2:13 Fancy Word #2: Time-Invariant 3:21 Fancy Word #3: Linear 4:12 pausing/replaying highly encouraged here 4:39 Linear Algebra 8:56 Fancy Word #4: Convolution 9:17 Practical Applications Clips: Oscilliscope Footage: https://www.youtube.com/watch?v=uMH2hGvqhlE Conv. NN Animation: https://www.youtube.com/watch?v=f0t-OCG79-U Fourier Series Animation: https://www.youtube.com/watch?v=k8FXF1KjzY0 Pascal's Triangle GIF: https://daugerresearch.com/vault/parallelpascalstriangle.shtml Circuit Animation Website: https://www.falstad.com/circuit/ Tacoma Narrows Bridge Collapse: https://www.youtube.com/watch?v=j-zczJXSxnw Music: Winter Lane (Remix) - Nujabes Investigation Core 2001 - Ace Attorney Sweet Mystery Galaxy - Super Mario Galaxy 2