On Fri, 22 Nov 2013 12:41:45 -0600, Les Cargill <lcargill99@comcast.com> wrote:>julius wrote: >> On Thursday, November 21, 2013 9:21:31 AM UTC-5, westocl wrote: >>> Is it possible to even simulate a true bandlimited process? That is >>> we would like the spectrum to be zero at some frequency less that >>> nyquist. >>> >>> Surely passing gaussian noise through some FIR filter would shape >>> the noise to be 'small' in the band of non-interest but is not >>> exactly zero. But seeting up a FIR is probably a quick and easy way >>> out. >>> >>> Would a better means of simulating a bandlimited process be setting >>> up a distribution and drawing from it or would i run into the same >>> type deal that no distribution would actually be exactly >>> bandlimited it would be similar to running white noise into an >>> FIR? >>> >>> thanks in advance >>> >> >> You may not be expecting this answer, but it depends on the algebra. >> For signals that are periodic in time, this is possible; for >> non-periodic signals strictly speaking this is not possible (see >> Time-Frequency representation) except under limited circumstances. >> >> For most people a "bandlimited process" under non-periodic algebra >> simply means that you run a white noise onto properly designed FIR >> filter. I would simply take this definition and not worry about >> things too much, unless you are trying to do a PhD thesis on the >> time-frequency analysis. I had the pleasure of listening to Bob >> Gallager and Sanjoy Mitter argue whether "bandlimited white noise" >> made sense many years ago. The argument lasted a good full hour, and >> while it was very interesting, I can't even remember which of them >> said it was theoretically possible, and which said it wasn't >> possible. >> > >Tone wheels* exist, and are bandlimited white noise. You can >simulate them in the same way. > >*as used in Hammond organs.Hammond tone wheels don't work from noise, but from a generated tone, usually synched to the power line frequency with a synchronous motor. The tones aren't always pure sinusoids, but they're closer to a limited Fourier Series than noise. http://www.youtube.com/watch?v=jLbKlyz4Hbo There are a variety of different tone generators used in old electric organs, including mechanical methods using wheels in an analogous way.> >-- >Les CargillEric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Question about a Bandlimited Process
Started by ●November 21, 2013
Reply by ●November 22, 20132013-11-22
Reply by ●November 22, 20132013-11-22
Eric Jacobsen wrote:> On Fri, 22 Nov 2013 12:41:45 -0600, Les Cargill > <lcargill99@comcast.com> wrote: > >> julius wrote: >>> On Thursday, November 21, 2013 9:21:31 AM UTC-5, westocl wrote: >>>> Is it possible to even simulate a true bandlimited process? That is >>>> we would like the spectrum to be zero at some frequency less that >>>> nyquist. >>>> >>>> Surely passing gaussian noise through some FIR filter would shape >>>> the noise to be 'small' in the band of non-interest but is not >>>> exactly zero. But seeting up a FIR is probably a quick and easy way >>>> out. >>>> >>>> Would a better means of simulating a bandlimited process be setting >>>> up a distribution and drawing from it or would i run into the same >>>> type deal that no distribution would actually be exactly >>>> bandlimited it would be similar to running white noise into an >>>> FIR? >>>> >>>> thanks in advance >>>> >>> >>> You may not be expecting this answer, but it depends on the algebra. >>> For signals that are periodic in time, this is possible; for >>> non-periodic signals strictly speaking this is not possible (see >>> Time-Frequency representation) except under limited circumstances. >>> >>> For most people a "bandlimited process" under non-periodic algebra >>> simply means that you run a white noise onto properly designed FIR >>> filter. I would simply take this definition and not worry about >>> things too much, unless you are trying to do a PhD thesis on the >>> time-frequency analysis. I had the pleasure of listening to Bob >>> Gallager and Sanjoy Mitter argue whether "bandlimited white noise" >>> made sense many years ago. The argument lasted a good full hour, and >>> while it was very interesting, I can't even remember which of them >>> said it was theoretically possible, and which said it wasn't >>> possible. >>> >> >> Tone wheels* exist, and are bandlimited white noise. You can >> simulate them in the same way. >> >> *as used in Hammond organs. > > Hammond tone wheels don't work from noise, but from a generated tone, > usually synched to the power line frequency with a synchronous motor. > The tones aren't always pure sinusoids, but they're closer to a > limited Fourier Series than noise. > > http://www.youtube.com/watch?v=jLbKlyz4Hbo > > There are a variety of different tone generators used in old electric > organs, including mechanical methods using wheels in an analogous way. >Know what? You are absolutely right. My bad. Here is what is weird - I managed to make something that sounded a lot *like* a tonewheel by bandlimiting white noise, after I'd read that Hammonds worked that way.> >> >> -- >> Les Cargill > > Eric Jacobsen > Anchor Hill Communications > http://www.anchorhill.com >-- Les Cargill
Reply by ●November 23, 20132013-11-23
On Friday, November 22, 2013 3:37:08 AM UTC+13, Vladimir Vassilevsky wrote:> On 11/21/2013 8:21 AM, westocl wrote: > > > Is it possible to even simulate a true bandlimited process? That is we > > > would like the spectrum to be zero at some frequency less that nyquist. > > > > > > Surely passing gaussian noise through some FIR filter would shape the noise > > > to be 'small' in the band of non-interest but is not exactly zero. But > > > seeting up a FIR is probably a quick and easy way out. > > > > > > Would a better means of simulating a bandlimited process be yosetting up a > > > distribution and drawing from it or would i run into the same type deal > > > that no distribution would actually be exactly bandlimited it would be > > > similar to running white noise into an FIR? > > > > You can get exactly bandlimited signal by combining bunch of sinusoids > > directly or using inverse Fourier. > > > > VLVInverse Fourier won't be exact since there is a resolution with the FFT. If this were the case you could make an ideal filter with an FFT and since each bin is fs/N in frequency you would need an infinite no of samples.
Reply by ●November 23, 20132013-11-23
On 2013-11-21 15:21, westocl wrote:> Is it possible to even simulate a true bandlimited process? That is we > would like the spectrum to be zero at some frequency less that nyquist.The _dry_ answer is yes. If the process is multiplying the signal by zero, then you'll get in any case a bandlimited result. bye, -- piergiorgio
Reply by ●November 23, 20132013-11-23
On Sunday, November 24, 2013 7:07:22 AM UTC+13, Piergiorgio Sartor wrote:> On 2013-11-21 15:21, westocl wrote: > > > Is it possible to even simulate a true bandlimited process? That is we > > > would like the spectrum to be zero at some frequency less that nyquist. > > > > The _dry_ answer is yes. > > If the process is multiplying the signal by zero, > > then you'll get in any case a bandlimited result. > > > > bye, > > > > -- > > > > piergiorgioIt will be bandlimited but not ideal as in brick-walled.
Reply by ●November 23, 20132013-11-23
On 2013-11-23 20:46, gyansorova@gmail.com wrote: [...]> It will be bandlimited but not ideal as in brick-walled.It is of course a "trivial" case, but the mathematician answer is yes (dry, as I wrote). It is like the old joke about black sheeps in Scotland. bye, -- piergiorgio
Reply by ●November 23, 20132013-11-23
On 11/23/2013 12:07 PM, Piergiorgio Sartor wrote:> On 2013-11-21 15:21, westocl wrote: >> Is it possible to even simulate a true bandlimited process? That is we >> would like the spectrum to be zero at some frequency less that nyquist. > > The _dry_ answer is yes. > If the process is multiplying the signal by zero, > then you'll get in any case a bandlimited result.In Paley-Wiener sense, a realizable signal having non-zero spectral density at any frequency interval of finite size can't have zero spectral density at any other frequency interval of finite size. VLV
Reply by ●November 23, 20132013-11-23
On 2013-11-23 22:25, Vladimir Vassilevsky wrote:> On 11/23/2013 12:07 PM, Piergiorgio Sartor wrote: >> On 2013-11-21 15:21, westocl wrote: >>> Is it possible to even simulate a true bandlimited process? That is we >>> would like the spectrum to be zero at some frequency less that nyquist. >> >> The _dry_ answer is yes. >> If the process is multiplying the signal by zero, >> then you'll get in any case a bandlimited result. > > In Paley-Wiener sense, a realizable signal having non-zero spectral > density at any frequency interval of finite size can't have zero > spectral density at any other frequency interval of finite size.The OP did not seem to ask for non-zero whatever... :-) bye, bye, -- piergiorgio
