julius wrote:> > On May 26, 3:01 pm, "Vista" <a...@gmai.com> wrote: > > > Thanks Rune. But my signal x(t) doesn't have a physical meaning to allow me > > put a natural bound on the spectrum. So I don't have an aprior knowledge > > about B, and the support [-B, B]. I need to estimate it based on some > > mathematical derivations. Any pointers? > > > > Once B is determined, then the sampling rate is determined, but for how long > > a piece of x(t) shall I sample? x(t) is also infinitely supported and not > > periodic. I have to truncate it first and then sample it. Is there a way to > > figure out how long shall I sample? That's to say, I now know Ts the > > sampling period, but I still need to decide the number of samples N I > > collect. Is there a way to determine that N? > > > > Thanks! > > You know, there's this thing called the lowpass filter, which > makes it so that the output of the filter is bandlimited to > whatever you set the filter to. > > Then you can play around and see if you are happy or not. > Maybe this is what you are missing? Pick a sampling rate, > set the lowpass filter rate to be less than 1/2 of the sampling > rate, and see if you are happy or not. >How will he know if he is happy? If you are talking about a digital filter, any aliasing that will occur will have already happened before he filters. At best, what he might learn something about the spectral content. If the filter doesn't change the signal in any significant way (besides delay) he will then know he could safely sample at a lower rate. -jim> Of course, I omitted some details ;-). > > Julius----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----
bandwidth and spectrum
Started by ●May 26, 2007
Reply by ●May 26, 20072007-05-26
Reply by ●May 26, 20072007-05-26
Vista wrote:> "jim" <".sjedgingN0sp"@m@mwt.net> wrote in message > news:1180217194_23709@sp12lax.superfeed.net... >> >> Vista wrote: >>> "Rune Allnor" <allnor@tele.ntnu.no> wrote in message >>> news:1180211015.196566.157140@k79g2000hse.googlegroups.com... >>>> On 26 May, 22:01, "Vista" <a...@gmai.com> wrote: >>>> >>>>> my signal x(t) doesn't have a physical meaning to allow me >>>>> put a natural bound on the spectrum. >>>>> Once B is determined, then the sampling rate is determined, >>>> So your signal has "no physical meaning" and you still >>>> have to sample it? >>>> >>>> Sorry, can't help with that one. >>>> >>>> Rune >>>> >>> What's wrong with signal with "no physical meaning"? Those examples of >>> signals in typical DSP and S&S books, are they all sound signals, audio >>> signals, video signals, etc? No they are not. They are mathematical >>> objects. >>> Mine the same. So the natural signal bound intuition doesn't work here. >> This seems like a pretty simple problem. Just set it up so that you can >> try different sample rates. You can sample at one rate and then sample at >> twice that rate and compare. Unless you are working with something like >> fractal geometry you should be able to arrive at a rate that meets your >> requirements fairly easily. >> >> -jim > > Thanks Jim, of course I can do that. However, this is a manual and > experimental method...What is it that you actually expect to sample? Whatever it is, it has to be continuous. Either you have a recording (or its equivalent) or maybe equations or a procedure for generating it. You obviously can't sample a list of numbers, so what are you doing? Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●May 26, 20072007-05-26
On May 26, 5:44 pm, jim <"sjedgingN0sp"@m...@mwt.net> wrote:> How will he know if he is happy? If you are talking about a digital > filter, any aliasing that will occur will have already happened before > he filters. > At best, what he might learn something about the spectral content. If > the filter doesn't change the signal in any significant way (besides > delay) he will then know he could safely sample at a lower rate. > > -jim >How do you know that he will necessarily be unhappy? I did not say that it will solve all the problem. And of course I meant an analog anti-aliasing filter. Another approach is to try a parametric approach, which does not necessarily require a signal to be strictly bandlimited in any way, but how can we know without knowing that the parameter of interest is in the first place? Test and play around and learn, I say. Julius
Reply by ●May 27, 20072007-05-27
julius wrote:> > On May 26, 5:44 pm, jim <"sjedgingN0sp"@m...@mwt.net> wrote: > > > How will he know if he is happy? If you are talking about a digital > > filter, any aliasing that will occur will have already happened before > > he filters. > > At best, what he might learn something about the spectral content. If > > the filter doesn't change the signal in any significant way (besides > > delay) he will then know he could safely sample at a lower rate. > > > > -jim > > > > How do you know that he will necessarily be unhappy? I did not say > that it will solve all the problem. And of course I meant an analog > anti-aliasing filter.I don't know that he will be unhappy. My point was he won't know anything at all. It sounds like he can't use an analog filter since he doesn't have an analog signal. He says he is generating the samples using some sort of mathematics. -jim> > Another approach is to try a parametric approach, which does not > necessarily require a signal to be strictly bandlimited in any way, > but how can we know without knowing that the parameter of interest > is in the first place? > > Test and play around and learn, I say. > > Julius----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----
Reply by ●May 27, 20072007-05-27
jim wrote:> ... He says he is generating the samples using some sort of > mathematics.Then the math should give him the bandwidth directly. It may be more than his intuition tells him, but that's remediable. ... Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●May 27, 20072007-05-27
"jim" <"sjedgingN0sp"@m@mwt.net> wrote in message news:1180234960_24925@sp12lax.superfeed.net...> > > julius wrote: >> >> On May 26, 5:44 pm, jim <"sjedgingN0sp"@m...@mwt.net> wrote: >> >> > How will he know if he is happy? If you are talking about a digital >> > filter, any aliasing that will occur will have already happened before >> > he filters. >> > At best, what he might learn something about the spectral >> > content. If >> > the filter doesn't change the signal in any significant way (besides >> > delay) he will then know he could safely sample at a lower rate. >> > >> > -jim >> > >> >> How do you know that he will necessarily be unhappy? I did not say >> that it will solve all the problem. And of course I meant an analog >> anti-aliasing filter. > > I don't know that he will be unhappy. My point was he won't know > anything at all. > It sounds like he can't use an analog filter since he doesn't have an > analog signal. He says he is generating the samples using some sort of > mathematics. > > -jim >Jim, you are exactly right. I wrote out some mathematical formulation of the signal (ODE), just as an exercise. I don't have any physical meaning for such signal in my mind... And as I said, I am going to change the coefficients of the ODEs and want to see the spectrum of the ODEs solutions...
Reply by ●May 27, 20072007-05-27
On May 27, 7:21 pm, "Vista" <a...@gmai.com> wrote:> "jim" <"sjedgingN0sp"@m...@mwt.net> wrote in message > > news:1180234960_24925@sp12lax.superfeed.net... > > > > > > > julius wrote: > > >> On May 26, 5:44 pm, jim <"sjedgingN0sp"@m...@mwt.net> wrote: > > >> > How will he know if he is happy? If you are talking about a digital > >> > filter, any aliasing that will occur will have already happened before > >> > he filters. > >> > At best, what he might learn something about the spectral > >> > content. If > >> > the filter doesn't change the signal in any significant way (besides > >> > delay) he will then know he could safely sample at a lower rate. > > >> > -jim > > >> How do you know that he will necessarily be unhappy? I did not say > >> that it will solve all the problem. And of course I meant an analog > >> anti-aliasing filter. > > > I don't know that he will be unhappy. My point was he won't know > > anything at all. > > It sounds like he can't use an analog filter since he doesn't have an > > analog signal. He says he is generating the samples using some sort of > > mathematics. > > > -jim > > Jim, you are exactly right. I wrote out some mathematical formulation of the > signal (ODE), just as an exercise. I don't have any physical meaning for > such signal in my mind... And as I said, I am going to change the > coefficients of the ODEs and want to see the spectrum of the ODEs > solutions...Ok - if you solve an ODE numerically you need a step size. The step size is the reciprocal of sampling frequency which is say fs. You then need a low-pass filter at least at fs/2. Of course when you simulate analogue systems you automatically convert them to digital unless...you use an analogue computer. Wang King
Reply by ●May 27, 20072007-05-27
On 27 May, 09:21, "Vista" <a...@gmai.com> wrote:> Jim, you are exactly right. I wrote out some mathematical formulation of the > signal (ODE), just as an exercise.If you have an *linear* ODE to describe your system, then all you need to do is to find an excpression for the solution, Foorier tranform it, and there you have the spectrum of the signal. Once you know the characteristics of the spectrum, you can set up the sampling parameters.> I don't have any physical meaning for > such signal in my mind...I don't know what ODE you are setting up, but the term "sampling" usually means that one makes some sort of sensor to measure a real-world contionuous process. The corresponding terms in numerical simulations are "discretization" or "step size," depending a bit on what type of solver one uses. Rune
Reply by ●May 28, 20072007-05-28
On May 27, 5:51 am, gyansor...@gmail.com wrote:> On May 27, 7:21 pm, "Vista" <a...@gmai.com> wrote: > > > > > "jim" <"sjedgingN0sp"@m...@mwt.net> wrote in message > > >news:1180234960_24925@sp12lax.superfeed.net... > > > > julius wrote: > > > >> On May 26, 5:44 pm, jim <"sjedgingN0sp"@m...@mwt.net> wrote: > > > >> > How will he know if he is happy? If you are talking about a digital > > >> > filter, any aliasing that will occur will have already happened before > > >> > he filters. > > >> > At best, what he might learn something about the spectral > > >> > content. If > > >> > the filter doesn't change the signal in any significant way (besides > > >> > delay) he will then know he could safely sample at a lower rate. > > > >> > -jim > > > >> How do you know that he will necessarily be unhappy? I did not say > > >> that it will solve all the problem. And of course I meant an analog > > >> anti-aliasing filter. > > > > I don't know that he will be unhappy. My point was he won't know > > > anything at all. > > > It sounds like he can't use an analog filter since he doesn't have an > > > analog signal. He says he is generating the samples using some sort of > > > mathematics. > > > > -jim > > > Jim, you are exactly right. I wrote out some mathematical formulation of the > > signal (ODE), just as an exercise. I don't have any physical meaning for > > such signal in my mind... And as I said, I am going to change the > > coefficients of the ODEs and want to see the spectrum of the ODEs > > solutions... > > Ok - if you solve an ODE numerically you need a step size. The step > size is the reciprocal of sampling frequency which is say fs. You then > need a low-pass filter at least at fs/2. Of course when you simulate > analogue systems you automatically convert them to digital > unless...you use an analogue computer.Wang here got this exactly correct. if you have an ODE, then you either can somehow hope to solve it analytically (then why would you need to sample it? unless you can get a time-domain solution analytically but the continuous Fourier Integral still can't be evaluated) or, if you can solve the ODE analytically, it is, as Wang put it, something that needs a numerical method, usually with a uniform step size (like Euler method or predictor-corrector or Runge- Kutta or something like that). that's the same as a sampling period. so Vista, in any case, you need to make some assumptions on bandwidth of negligible error and a non-zero step size and finite sample rate. there's no way around that, particularly if you want to use the DFT to look at the spectrum. successively increasing (doubling, maybe) the sample rate and comparing your current spectrum with the properly- scaled previous spectrum and stopping when there is no discernable difference in the spectrums is a valid way to deal with this. r b-j
Reply by ●May 28, 20072007-05-28
>Hi all, > >I am facing the following difficulty. > >In order to view the spectrum F(w) of a signal x(t), I have to sample itand>then take DFT on computer. > >F(w) is infitely supported. > >In order to decide the spacing of sampling, I need to figure out abandwidth>that contains 99% of total energy of F(w), which is denoted as 2B. Thus >within 1% of truncation error, I will be able to say that the bandwidthof>the signal x(t) is [-B, B], and then I can proceed about doing thesampling>on x(t) and taking DFT to compute the spectrum on computer. > >I don't have the closed-form solution of F(w), that's why I have to useDFT>to compute it. > >How do I estimate an approximate B first? > >Thanks! > > >It looks so easy. You should set sample rate at a highest speed.And if there has value(not zero) at highest freq,you should increase your sample rate. _____________________________________ Do you know a company who employs DSP engineers? Is it already listed at http://dsprelated.com/employers.php ?
