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Something kinda neat is it seems like if you ever want to convolve two bitsets (i cant think of a reason you would but shrug), that you can just multiply them together as integers.
LTTP, but in general it's not related to the basis being orthonormal or not. The keyword you want to look for is "convolution theorem". It holds for certain transforms, but is proved independently for each one.
i know the convolution theorem, but what's LTTP?
Had to dig deep to remember that it’s “Late To The Party” in some circles, knew I had seen it before.
This is my recollection as well. I find it unhelpful that we call things convolutions when they aren’t or are only under certain conditions I.e. the FFT can only implement convolution with appropriate zero-padding - otherwise it more generally implements “circular convolution”.
From memory this book https://www.bookdepository.com/Signal-Processing-with-Lapped-Transforms-Henrique-S-Malvar/9780890064672 … Goes into detail about implementing various orthogonal transforms (dct, dft, dht, etc) and makes statements on what ones can be used to implement convolutions, what the conditions are, and why you probably should stick with a dft :)
I would think any locally supported basis wouldn’t have this property, it probably ties into shift (rotation) invariance of a basis
Hrm ok, interesting
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