Bob, It is more to do with how you define "increased resolution" > While it is usually stated in the time domain the sampling theorem > applies equally to the frequency domain. Exactly. If we zero pad the FFT (by adding zeros from pi/2 to -pi/2 .. ) ..and obtain the time domain signal .., we get the upsampled the time domain signal.. but between two adjacent samples, we are interpolating... if that's what you call increasing the resolution, we agree. -Akshay. ----- Original Message ----- From: Bob Cain <arcane@arca...> To: <audiodsp@audi...> Sent: Saturday, October 27, 2001 1:53 AM Subject: Re: [audiodsp] Re: zeroing the FFT > "Andrew V. Nesterov" wrote: > > > > > > yes, since adding a bunch of zeroes does not add additional > > information to the sampled signal, thus zero padding would > > not increase frequency resolution. > > What do you mean then by resolution? If it covers the same space with > more samples of it is this not increased resolution? The sampling > theorem shows how to determine any value between samples exactly by sinc > interpolation when the sampled function is band limited by the Nyquist > criterion. That the new information which comes from zero padding is > redundant when it comes to reconstructing the function does not negate > the validity of the new information. > > While it is usually stated in the time domain the sampling theorem > applies equally to the frequency domain. > > Bob > -- > > "Things should be described as simply as possible, but no simpler." > > A. Einstein > > > ////////////////////////////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \\\ > > To contribute your unused processor cycles to the fight against cancer: > > http://www.intel.com/cure > > \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\//////////////////////////////////// /// > > > > _____________________________________ > Note: If you do a simple "reply" with your email client, only the author of this message will receive your answer. You need to do a "reply all" if you want your answer to be distributed to the entire group. > > _____________________________________ > About this discussion group: > > To Join: audiodsp-subscribe@audi... > > To Post: audiodsp@audi... > > To Leave: audiodsp-unsubscribe@audi... > > Archives: http://groups.yahoo.com/group/audiodsp > > Other DSP-Related Groups: http://www.dsprelated.com > > > ">http://docs.yahoo.com/info/terms/ > >
zeroing the FFT
Started by ●October 23, 2001
Reply by ●October 29, 20012001-10-29
Reply by ●October 29, 20012001-10-29
Sorry to send this to you twice, Akshay, but once again I expected "Reply" to go to the list like it does with other lists and with usenet. Can that be fixed or is it an unchangable yahooism? Akshay Joshi wrote: > > Bob, > > It is more to do with how you define "increased resolution" > > > While it is usually stated in the time domain the sampling theorem > > applies equally to the frequency domain. > > Exactly. If we zero pad the FFT (by adding zeros from pi/2 to -pi/2 .. ) > ..and obtain the time domain signal .., we get the upsampled the time domain > signal.. but between two adjacent samples, we are interpolating... if that's > what you call increasing the resolution, we agree. Yep. We agree. I think that what we are agreeing on is what people generally want when they ask if they can get increased resolution by zero extension. Bob -- "Things should be described as simply as possible, but no simpler." A. Einstein ////////////////////////////////////////\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ To contribute your unused processor cycles to the fight against cancer: http://www.intel.com/cure \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\///////////////////////////////////////
Reply by ●October 30, 20012001-10-30
> Date: Mon, 29 Oct 2001 10:48:22 -0800 > From: Bob Cain <arcane@arca...> > > Sorry to send this to you twice, Akshay, but once again I expected > "Reply" to go to the list like it does with other lists and with > usenet. Can that be fixed or is it an unchangable yahooism? > > Akshay Joshi wrote: > > > > Bob, > > > > It is more to do with how you define "increased resolution" > > > > > While it is usually stated in the time domain the sampling theorem > > > applies equally to the frequency domain. > > > > Exactly. If we zero pad the FFT (by adding zeros from pi/2 to -pi/2 .. ) > > ..and obtain the time domain signal .., we get the upsampled the time domain > > signal.. but between two adjacent samples, we are interpolating... if that's > > what you call increasing the resolution, we agree. > > Yep. We agree. I think that what we are agreeing on is what people > generally want when they ask if they can get increased resolution by > zero extension. Dear both, Since one of the previous emails (of Bob) referred to my email, I'd like to add that I also meant interpolation (as I stated in one of my previous emails to this list) is the result of zero-padding. So we agree if we would call interpolation as increasing the resolution. I am sorry Bob that I did not resend my replys to your emails on that last Friday (or when it was) -- I was reall in a hurry to do something. Regards, Andrew > > > Bob > -- > > "Things should be described as simply as possible, but no simpler." > > A. Einstein > >
