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CamperBob2 parent
Your question is an excellent example of why skipping all that math wasn't a good idea. (The answer literally goes all the way back to the Heisenberg uncertainty principle.)

You don't need to be able to regurgitate it all on a test, but you must be comfortable with the general ideas behind the DFT and what motivates them.

Llamamoe
The answer is also completely unnecessary to actually using said filters. There are countless data structures and algorithms built on decades of research, and yet no programmer writes tutorials where they demand you understand the entire history of computation before you're worthy of learning them the way mathematicians do with even the most basic of concepts.
CamperBob2 OP
Largely true, although eventually you'd wonder why it sounded so awful when you tried to create infinitely-narrow filter passbands.

In this case, if you'd known there was such a thing as time-frequency uncertainty, you'd never have needed to ask the question in the first place.

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