Comment by Jun8
1 day ago
A signal cannot be both time and frequency band limited. Many years ago I was amazed when I read that this fact I learned in my undergraduate is equivalent to the Uncertainty Principle!
On a more mundane note: my wife and I always argue whose method of loading the dishwasher is better: she goes slow and meticulously while I do it fast. It occurred to me we were optimizing for frequency and time domains, respectively, ie I was minimizing time so spent while she was minimizing number of washes :-)
Signals can be approximately frequency and time bandlimited, though, meaning the set of values such that the absolute value exceeds any epsilon is compact in both domains. A Gaussian function is one example.
Another example: ears are excellent at breaking down the frequency of sounds, but are imprecise about where the sound is coming from; whereas eyes are excellent at telling you where light is coming from, but imprecise about how its frequencies break down.
that's mostly due to light waves being FAR shorter and many orders of magnitude more "sensors"
Ears are essentially 2 "pixels" of sound sensing; and for that limitation they are ABSOLUTELY AMAZING at pointing out the sound source.
It’s literally the Heisenberg uncertainty principle, applied to signal processing.
For those who don't get this comment, the Heisenberg uncertainty principle applies to any two quantities that are connected in QM via a Fourier transform. Such as position and momentum, or time and energy. It is really a mathematical theorem that there is a lower bound on the variance of a function times the variance of its Fourier transform.
That lower bound is the uncertainty principle, and that lower bound is hit by normal distributions.
thank you for that reminder/clarification. I forget sometimes how much we think we have clear pictures of how things like that work when really we're just listening to someone trying to explain what the math is doing and we're adding in detail.
Thats. I always assumed it was more a quirk of the universe than something driven by pure mathematics. Amazing.
1 reply →
> I was minimizing time so spent while she was minimizing number of washes
I'm probably just slow, but I'm not following. Do you mean because you went fast, you had to run another cycle to clean everything properly?
If you haven't already, you should watch the Technology Connections series on dishwashers.
https://www.youtube.com/watch?v=jHP942Livy0
Since I’m rushing to load it as fast as possible the packing is not as good as hers so some dishes are left out. Overall this leads to more loads.
Ahhh that makes sense!
Do you two ever play friendly games of Tetris against one another?
The self loading dishwasher would be the greatest marriage saving invention since car navigation systems.
you just need to go "if you want it loaded your way, you do it" and all is solved
And if loading dishwasher is on top of your marital issues you're probably in very happy marriage.
The constant small degree of conflict and strife is key to happiness, people can't be permanently happy, they just find ways to sabotage when they do