From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik) Subject: Re: Band-limited wiggle limit? Date: 6 Sep 2000 12:12:49 -0400 Newsgroups: sci.math Summary: [missing] In article <39B612BF.2042@mindspring.com>, Ron Hardin wrote: :Dennis Yelle wrote: :> :> Ron Hardin wrote: :> > :> > What's the most zero crossings you can have in an interval :> > with a band-limited function? :> > :> > Is there any limit? :> :> It has been a while, but I don't see how to :> get more than 200 zero crossings per second in a signal :> with no component over 100 Hz, for example. : :Well, why can't _any_ function over an interval be extended in a way :that cancels out all the frequencies over the band limit? Unless I am missing something in the previous question, the obstacle to having nonzero time-limited functions which wouls also be band-limited is Paley-Wiener Theorem: a band-limited function has an extension to an entire function of exponential type (the easy part of the theorem). Such a function (if nonzero) has only isolated roots which (if there are infinitely many of them) diverge to infinity. (I forgot: is there any estimate of the rate at which they diverge for the entire functions of exponential type? I would suspect at least linear rate.) Cheers, ZVK(Slavek)