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 it and then take DFT on computer. F(w) is infitely supported. In order to decide the spacing of sampling, I need to figure out a bandwidth 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 bandwidth of the signal x(t) is [-B, B], and then I can proceed about doing the sampling 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 use DFT to compute it. How do I estimate an approximate B first? Thanks!
bandwidth and spectrum
Started by ●May 26, 2007
Reply by ●May 26, 20072007-05-26
On 26 May, 20:02, "Vista" <a...@gmai.com> wrote:> 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 it and > then take DFT on computer. > > F(w) is infitely supported. > > In order to decide the spacing of sampling, I need to figure out a bandwidth > 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 bandwidth of > the signal x(t) is [-B, B], and then I can proceed about doing the sampling > 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 use DFT > to compute it. > > How do I estimate an approximate B first?You have to use whatever knowledge is available to you about the nature of the signal. Human voice signals, for instance, are usually band-limited well below 20 kHz. Once you decide on an upper limit for what is reasonable to expect from the data (as human voice is concerned, phone systems use 4 kHz, Audio systems 20+ kHz for this upper limit), you use an analog anti-aliasing filter to supress any energy above that upper limit. This determines the "design bandwidth" B in your system. Now that you have decided on a design bandwidth B, you can go on and use Nyquist's criterion to find a sample frequency Fn > B. Once you have sampled some data, you sample for as long you find practical (say, N samples). The output of the DFT will then gine N coeffcients dirstributed evenly in the frequency range [0 Fs]. Rune
Reply by ●May 26, 20072007-05-26
"Rune Allnor" <allnor@tele.ntnu.no> wrote in message news:1180204458.136936.311700@k79g2000hse.googlegroups.com...> On 26 May, 20:02, "Vista" <a...@gmai.com> wrote: >> 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 it >> and >> then take DFT on computer. >> >> F(w) is infitely supported. >> >> In order to decide the spacing of sampling, I need to figure out a >> bandwidth >> 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 bandwidth >> of >> the signal x(t) is [-B, B], and then I can proceed about doing the >> sampling >> 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 use >> DFT >> to compute it. >> >> How do I estimate an approximate B first? > > You have to use whatever knowledge is available to you > about the nature of the signal. Human voice signals, for > instance, are usually band-limited well below 20 kHz. > Once you decide on an upper limit for what is reasonable > to expect from the data (as human voice is concerned, > phone systems use 4 kHz, Audio systems 20+ kHz for this > upper limit), you use an analog anti-aliasing filter to > supress any energy above that upper limit. > > This determines the "design bandwidth" B in your system. > Now that you have decided on a design bandwidth B, you > can go on and use Nyquist's criterion to find a sample > frequency Fn > B. > > Once you have sampled some data, you sample for as long > you find practical (say, N samples). The output of the > DFT will then gine N coeffcients dirstributed evenly > in the frequency range [0 Fs]. > > Rune >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!
Reply by ●May 26, 20072007-05-26
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
Reply by ●May 26, 20072007-05-26
"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.
Reply by ●May 26, 20072007-05-26
On 26 May, 22:28, "Vista" <a...@gmai.com> wrote:> "Rune Allnor" <all...@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.True.> Mine the same. So the natural signal bound intuition doesn't work here.Well, I have yet to come across a problem description in one of that sort of textbook where the statement does NOT include some specification of bandwidth: "Given a base-band signal of bandwidth B..." And then the (academic) problem is developed based on that knowledge of B is available. In real life, one has no choise but to try and investigate whatever physical process generates the signal, and either emprically or (in rare cases) analytically come up with an estimate for the bandwidth. Or use the tabulated results of previous investigations of that type. What is unique about your stated problem is that the signal BOTH makes no physical meaning AND the bandwidth is unknown. Rune
Reply by ●May 26, 20072007-05-26
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.Those made-ip signals have bandwidths and statistics made up along with them. You can pick whatever ones you like. Only th real world can be wrong about details like those. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●May 26, 20072007-05-26
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 ----== 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 26, 20072007-05-26
"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. > > -jimThanks Jim, of course I can do that. However, this is a manual and experimental method...
Reply by ●May 26, 20072007-05-26
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. Of course, I omitted some details ;-). Julius
