On 5/16/2011 10:35 AM, Tony Estep wrote: > True of electrons, and other subatomic particles as well. For those who wish > to delve into quantum mechanics and find out what the uncertainty principle > actually deals with:
If you read a bit further down in Wikipedia with respect to the uncertainty principle you will find the following: = = = = = = In the context of signal processing <http://en.wikipedia.org/wiki/Signal_processing>, particularly time--frequency analysis <http://en.wikipedia.org/wiki/Time%E2%80%93frequency_analysis>, uncertainty principles are referred to as the *Gabor limit*, after Dennis Gabor <http://en.wikipedia.org/wiki/Dennis_Gabor>, or sometimes the /Heisenberg--Gabor limit./ The basic result, which follows from Benedicks's theorem, below, is that a function cannot be both time limited <http://en.wikipedia.org/wiki/Time_limited> and band limited <http://en.wikipedia.org/wiki/Band_limited> (a function and its Fourier transform cannot both have bounded domain) -- see bandlimited versus timelimited <http://en.wikipedia.org/wiki/Time_limited#Bandlimited_versus_timelimited>. Stated alternatively, "one cannot simultaneously localize a signal (function) in both the time domain <http://en.wikipedia.org/wiki/Time_domain> (/f/) and frequency domain <http://en.wikipedia.org/wiki/Frequency_domain> (Fourier transform)". When applied to filters, the result is that one cannot achieve high temporal resolution and frequency resolution at the same time; a concrete example are the resolution issues of the short-time Fourier transform <http://en.wikipedia.org/wiki/Short-time_Fourier_transform#Resolution_issues> -- if one uses a wide window, one achieves good frequency resolution at the cost of temporal resolution, while a narrow window has the opposite trade-off. = = = = = = 73, Jim K9YC ______________________________________________________________ Elecraft mailing list Home: http://mailman.qth.net/mailman/listinfo/elecraft Help: http://mailman.qth.net/mmfaq.htm Post: mailto:[email protected] This list hosted by: http://www.qsl.net Please help support this email list: http://www.qsl.net/donate.html
