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Question about a Bandlimited Process

Started by westocl November 21, 2013
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	 

_____________________________		
Posted through www.DSPRelated.com
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. VLV
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.
"westocl" <31050@dsprelated> writes:

> 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 > > _____________________________ > Posted through www.DSPRelated.com
You are (almost) never going to be able to generate ideal signals like this in the real world. For example, even if you could generate such a signal, how would you test it? Using Matlab? Matlab uses 64-bit double floating point numbers and arithmetic. While that allows huge dynamic range and precision, it isn't infinitely precise, so taking an FFT isn't going to be perfectly precise, i.e., you will probably have some residual energy outside the bandwidth. -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
On Thu, 21 Nov 2013 08:21:31 -0600, 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?
Are you enjoying the range of ambiguous and contradictory answers? Would you like another one for your collection? Strictly speaking, any signal that is finite in time must be infinite in frequency. You can easily cook up some finite-length sequence whose FFT is zero above some frequency -- but as soon as you extend that signal by zero-padding it, it'll no longer be "band limited". What are you trying to do, that having a signal that has significantly less content than the unavoidable noise above some frequency isn't good enough? -- Tim Wescott Control system and signal processing consulting www.wescottdesign.com
>On Thu, 21 Nov 2013 08:21:31 -0600, 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? > >Are you enjoying the range of ambiguous and contradictory answers? Would
>you like another one for your collection? > >Strictly speaking, any signal that is finite in time must be infinite in >frequency. You can easily cook up some finite-length sequence whose FFT >is zero above some frequency -- but as soon as you extend that signal by >zero-padding it, it'll no longer be "band limited". > >What are you trying to do, that having a signal that has significantly >less content than the unavoidable noise above some frequency isn't good >enough? > >-- >Tim Wescott >Control system and signal processing consulting >www.wescottdesign.com
I was trying to validate some results of some linear prediction paper that i had read. It was an IEEE article 'Linear Prediction of Bandlimited Processes with Flat Spectral Densities' . Anway the guy does alot of alegrebra and says here are the theoretical limits of linear prediction with a banlimited process with omega less than some number and here is how you solve for the coefficients. I tried to do the excercise and get the coefficents in MATLAB. My simulation data looked horrible, so i started to squint. Next i threw the question out to you guys. _____________________________ Posted through www.DSPRelated.com
On Thu, 21 Nov 2013 13:52:13 -0600, "westocl" <31050@dsprelated>
wrote:

>>On Thu, 21 Nov 2013 08:21:31 -0600, 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? >> >>Are you enjoying the range of ambiguous and contradictory answers? Would > >>you like another one for your collection? >> >>Strictly speaking, any signal that is finite in time must be infinite in >>frequency. You can easily cook up some finite-length sequence whose FFT >>is zero above some frequency -- but as soon as you extend that signal by >>zero-padding it, it'll no longer be "band limited". >> >>What are you trying to do, that having a signal that has significantly >>less content than the unavoidable noise above some frequency isn't good >>enough? >> >>-- >>Tim Wescott >>Control system and signal processing consulting >>www.wescottdesign.com > > >I was trying to validate some results of some linear prediction paper that >i had read. It was an IEEE article 'Linear Prediction of Bandlimited >Processes with Flat Spectral Densities' . Anway the guy does alot of >alegrebra and says here are the theoretical limits of linear prediction >with a banlimited process with omega less than some number and here is how >you solve for the coefficients.
I'm sure there's a stiff joke in there somewhere when it comes to alegra and bras.
>I tried to do the excercise and get the coefficents in MATLAB. My >simulation data looked horrible, so i started to squint. > >Next i threw the question out to you guys.
You're up against several problems, not the least of which is that it is, sadly, sometimes a fool's errand to try to duplicate results or get an algorithm working strictly from a single published paper. Good papers make that possible, but not all papers fall in that category. So you have my sympathy if you're trying to get something to work from scratch based on a single paper if that paper is of typical quality. That being said, most of the answers you've gotten I think fall into the relevant category for this case which is "how good does it need to be?" Most real-world problems don't need infinite precision or accuracy or reliability. Even the case that you mentioned using a filter to bandlimit a process is only as good as the stop-band attenuation of the filter, which will be limited for any practical filter. Even if a filter was achievable with infinite stop-band attenuation, a practical process will not need infinitely fine performance at the output. So practice usually includes measuring or calibrating the system to make certain it's good enough for the application. How to do that and what threshold determined "good enough" is sometimes the harder part of the task. Sounds like you're not yet at the step of getting things good enough to even recognize whether it's working. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
>On Thu, 21 Nov 2013 13:52:13 -0600, "westocl" <31050@dsprelated> >wrote: > >>>On Thu, 21 Nov 2013 08:21:31 -0600, 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? >>> >>>Are you enjoying the range of ambiguous and contradictory answers?
Would
>> >>>you like another one for your collection? >>> >>>Strictly speaking, any signal that is finite in time must be infinite in
>>>frequency. You can easily cook up some finite-length sequence whose FFT
>>>is zero above some frequency -- but as soon as you extend that signal by
>>>zero-padding it, it'll no longer be "band limited". >>> >>>What are you trying to do, that having a signal that has significantly >>>less content than the unavoidable noise above some frequency isn't good
>>>enough? >>> >>>-- >>>Tim Wescott >>>Control system and signal processing consulting >>>www.wescottdesign.com >> >> >>I was trying to validate some results of some linear prediction paper
that
>>i had read. It was an IEEE article 'Linear Prediction of Bandlimited >>Processes with Flat Spectral Densities' . Anway the guy does alot of >>alegrebra and says here are the theoretical limits of linear prediction >>with a banlimited process with omega less than some number and here is
how
>>you solve for the coefficients. > >I'm sure there's a stiff joke in there somewhere when it comes to >alegra and bras. > >>I tried to do the excercise and get the coefficents in MATLAB. My >>simulation data looked horrible, so i started to squint. >> >>Next i threw the question out to you guys. > >You're up against several problems, not the least of which is that it >is, sadly, sometimes a fool's errand to try to duplicate results or >get an algorithm working strictly from a single published paper. >Good papers make that possible, but not all papers fall in that >category. So you have my sympathy if you're trying to get something >to work from scratch based on a single paper if that paper is of >typical quality. > >That being said, most of the answers you've gotten I think fall into >the relevant category for this case which is "how good does it need to >be?" Most real-world problems don't need infinite precision or >accuracy or reliability. Even the case that you mentioned using a >filter to bandlimit a process is only as good as the stop-band >attenuation of the filter, which will be limited for any practical >filter. Even if a filter was achievable with infinite stop-band >attenuation, a practical process will not need infinitely fine >performance at the output. > >So practice usually includes measuring or calibrating the system to >make certain it's good enough for the application. How to do that >and what threshold determined "good enough" is sometimes the harder >part of the task. > >Sounds like you're not yet at the step of getting things good enough >to even recognize whether it's working. > > >Eric Jacobsen >Anchor Hill Communications >http://www.anchorhill.com
Thanks for you guys responses. The internet is a good tool as it allow me to bounce some quick questions off of bright minds from all over the world.
> sometimes a fool's errand to try to duplicate results or >get an algorithm working strictly from a single published paper.
I dont find it foolish to try and validate some results if time permits should find the paper interesting. _____________________________ Posted through www.DSPRelated.com
On Thu, 21 Nov 2013 15:02:40 -0600, "westocl" <31050@dsprelated>
wrote:

>>On Thu, 21 Nov 2013 13:52:13 -0600, "westocl" <31050@dsprelated> >>wrote: >> >>>>On Thu, 21 Nov 2013 08:21:31 -0600, 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? >>>> >>>>Are you enjoying the range of ambiguous and contradictory answers? >Would >>> >>>>you like another one for your collection? >>>> >>>>Strictly speaking, any signal that is finite in time must be infinite in > >>>>frequency. You can easily cook up some finite-length sequence whose FFT > >>>>is zero above some frequency -- but as soon as you extend that signal by > >>>>zero-padding it, it'll no longer be "band limited". >>>> >>>>What are you trying to do, that having a signal that has significantly >>>>less content than the unavoidable noise above some frequency isn't good > >>>>enough? >>>> >>>>-- >>>>Tim Wescott >>>>Control system and signal processing consulting >>>>www.wescottdesign.com >>> >>> >>>I was trying to validate some results of some linear prediction paper >that >>>i had read. It was an IEEE article 'Linear Prediction of Bandlimited >>>Processes with Flat Spectral Densities' . Anway the guy does alot of >>>alegrebra and says here are the theoretical limits of linear prediction >>>with a banlimited process with omega less than some number and here is >how >>>you solve for the coefficients. >> >>I'm sure there's a stiff joke in there somewhere when it comes to >>alegra and bras. >> >>>I tried to do the excercise and get the coefficents in MATLAB. My >>>simulation data looked horrible, so i started to squint. >>> >>>Next i threw the question out to you guys. >> >>You're up against several problems, not the least of which is that it >>is, sadly, sometimes a fool's errand to try to duplicate results or >>get an algorithm working strictly from a single published paper. >>Good papers make that possible, but not all papers fall in that >>category. So you have my sympathy if you're trying to get something >>to work from scratch based on a single paper if that paper is of >>typical quality. >> >>That being said, most of the answers you've gotten I think fall into >>the relevant category for this case which is "how good does it need to >>be?" Most real-world problems don't need infinite precision or >>accuracy or reliability. Even the case that you mentioned using a >>filter to bandlimit a process is only as good as the stop-band >>attenuation of the filter, which will be limited for any practical >>filter. Even if a filter was achievable with infinite stop-band >>attenuation, a practical process will not need infinitely fine >>performance at the output. >> >>So practice usually includes measuring or calibrating the system to >>make certain it's good enough for the application. How to do that >>and what threshold determined "good enough" is sometimes the harder >>part of the task. >> >>Sounds like you're not yet at the step of getting things good enough >>to even recognize whether it's working. >> >> >>Eric Jacobsen >>Anchor Hill Communications >>http://www.anchorhill.com > >Thanks for you guys responses. The internet is a good tool as it allow me >to bounce some quick questions off of bright minds from all over the >world. > >> sometimes a fool's errand to try to duplicate results or >>get an algorithm working strictly from a single published paper. > >I dont find it foolish to try and validate some results if time permits >should find the paper interesting.
I didn't mean that it was foolish, so I should have used different words. I meant that sometimes it's hopeless if the paper doesn't fully describe the algorithm (which happens) or describes it so poorly that it is nearly impossible to implement correctly. From that perspective it may be a bit foolish to take on a hopeless task, but one doesn't know that without giving it a shot. If you learn something, then you have at least that much from it. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
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. -- Les Cargill