alt Hacker NewsA 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 :-)
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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.
It’s literally the Heisenberg uncertainty principle, applied to signal processing.
> 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.
The self loading dishwasher would be the greatest marriage saving invention since car navigation systems.
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.