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&t=4s
- 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&ab_channel=EEVblog
Conv. NN Animation: https://www.youtube.com/watch?v=f0t-OCG79-U&ab_channel=IsraelVicars
Fourier Series Animation: https://www.youtube.com/watch?v=k8FXF1KjzY0&ab_channel=BrekMartin
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&ab_channel=TonyC
Music:
Winter Lane (Remix) - Nujabes
Investigation Core 2001 - Ace Attorney
Sweet Mystery Galaxy - Super Mario Galaxy 2