Convolutions are not Convoluted

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:    • The Linear Algebra of Fourier Transforms  

- Origin and History of Convolutions: https://www.slideshare.net/Alexdfar/o...

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:    • EEVblog #396 - Bode Plotting on Your ...  
Conv. NN Animation:    • Convolutional Neural Network Visualiz...  
Fourier Series Animation:    • Fourier Series Animation (Square Wave)  
Pascal's Triangle GIF: https://daugerresearch.com/vault/para...
Circuit Animation Website: https://www.falstad.com/circuit/
Tacoma Narrows Bridge Collapse:    • Tacoma Narrows Bridge Collapse "Gallo...  

Music:
Winter Lane (Remix) - Nujabes
Investigation Core 2001 - Ace Attorney
Sweet Mystery Galaxy - Super Mario Galaxy 2