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choosing a sampling rate lesser than nyquist rate(sub nyquist rate)

Started by praveen July 8, 2003
Hello,
I have a signal consisting of 4 harmonics (200k,400k,600k,and 800k Hz)
and dc component.The signal is very pure and SNR better than 60 dB. I
have to sample it in sub Nyquisit rate(lesser than 1600k). What
sampling rate should i choose so that there no alaising. I cannot
chose higher sampling rate because of my hardware constraints.


waiting for reply
regards
praveen
---- Original Message -----
From: "praveen" <praveenkumar1979@rediffmail.com>
Newsgroups: comp.dsp
Sent: Tuesday, July 08, 2003 4:37 PM
Subject: choosing a sampling rate lesser than nyquist rate(sub nyquist rate)


> Hello, > I have a signal consisting of 4 harmonics (200k,400k,600k,and 800k Hz)
You will never be able to produce an 800 Khz frequency with less than the double samplerate !
> and dc component.The signal is very pure and SNR better than 60 dB. I > have to sample it in sub Nyquisit rate(lesser than 1600k). What > sampling rate should i choose so that there no alaising. I cannot > chose higher sampling rate because of my hardware constraints. >
Nyquist. Since a sine wave has 2 boundaries ( high and low) it takes 2 mesurements to mesure a wave. To be able to mesure at an 800 khz sine you have to mesure 2 * 800 khz = 1600 k times pr second. If you can't mesure at 1600 khz then choose the highest poosible sample frequency and accept that your highest sine frequency will be half that samplerate.
> > waiting for reply > regards > praveen
In article ceBOa.14788$Kb2.706790@news010.worldonline.dk, Jesper Buch at
jesperbuch@hotmail.com wrote on 07/08/2003 11:16:

> ---- Original Message ----- > From: "praveen" <praveenkumar1979@rediffmail.com> > Newsgroups: comp.dsp > Sent: Tuesday, July 08, 2003 4:37 PM > Subject: choosing a sampling rate lesser than nyquist rate(sub nyquist rate) > > >> Hello, >> I have a signal consisting of 4 harmonics (200k,400k,600k,and 800k Hz) > > You will never be able to produce an 800 Khz frequency with less than the > double samplerate !
"double" is not sufficient. it has to be *more* than double.
> >> and dc component.The signal is very pure and SNR better than 60 dB. I >> have to sample it in sub Nyquisit rate(lesser than 1600k). What >> sampling rate should i choose so that there no alaising. I cannot >> chose higher sampling rate because of my hardware constraints. >> > > Nyquist. > Since a sine wave has 2 boundaries ( high and low) it takes 2 mesurements to > mesure a wave. > To be able to mesure at an 800 khz sine you have to mesure 2 * 800 khz = > 1600 k times pr second.
double is not sufficient. those two samples ("measurements") could be from an infinite number of sine waves. it is a mistake to assume that the two samples came from the top and the bottom of the sine wave. r b-j
"robert bristow-johnson" <rbj@surfglobal.net> skrev i en meddelelse
news:BB305F08.2127%rbj@surfglobal.net...
> In article ceBOa.14788$Kb2.706790@news010.worldonline.dk, Jesper Buch at > jesperbuch@hotmail.com wrote on 07/08/2003 11:16: > > > ---- Original Message ----- > > From: "praveen" <praveenkumar1979@rediffmail.com> > > Newsgroups: comp.dsp > > Sent: Tuesday, July 08, 2003 4:37 PM > > Subject: choosing a sampling rate lesser than nyquist rate(sub nyquist
rate)
> > > > > >> Hello, > >> I have a signal consisting of 4 harmonics (200k,400k,600k,and 800k Hz) > > > > You will never be able to produce an 800 Khz frequency with less than
the
> > double samplerate ! > > "double" is not sufficient. it has to be *more* than double.
ok preferably infinite samplerate would be better . . . but then at least double to be able to sample max sine frequency at all ( if the phase is correct). think of 44.100 khz sample rate for CD . . . maximum frequency is 20Khz
> > > >> and dc component.The signal is very pure and SNR better than 60 dB. I > >> have to sample it in sub Nyquisit rate(lesser than 1600k). What > >> sampling rate should i choose so that there no alaising. I cannot > >> chose higher sampling rate because of my hardware constraints. > >> > > > > Nyquist. > > Since a sine wave has 2 boundaries ( high and low) it takes 2
mesurements to
> > mesure a wave. > > To be able to mesure at an 800 khz sine you have to mesure 2 * 800 khz = > > 1600 k times pr second. > > double is not sufficient. those two samples ("measurements") could be
from
> an infinite number of sine waves. it is a mistake to assume that the two > samples came from the top and the bottom of the sine wave.
ok double frequency is for playinig back sample thats has it's high and low ajacent ( the right phase). I see your point in the actual sampling you don't know the phase but my point is that with less than 1600 Khz he can't capture the 800 khz sine at all. But yes 180000 Khz sample rate would be better. The point is that less than 1600 khz will not work at all capturing 800 khz. antialiasing or not
> r b-j >
"praveen" <praveenkumar1979@rediffmail.com> wrote in message
news:ff8a3afb.0307080637.324d0faf@posting.google.com...
> Hello, > I have a signal consisting of 4 harmonics (200k,400k,600k,and 800k Hz) > and dc component.The signal is very pure and SNR better than 60 dB. I > have to sample it in sub Nyquisit rate(lesser than 1600k). What > sampling rate should i choose so that there no alaising. I cannot > chose higher sampling rate because of my hardware constraints.
Do you mean it only has those four harmonics, plus DC? No modulation or side bands? Then nine samples are enough. On the other hand, if you sample at 900kHz, Fn is 450kHz, the 800kHz alias is at 100kHz and the 600kHz alias is at 300kHz, which can be separated from the others, as long as the sidebanks (modulation) are less than 50kHz wide. I think to really answer we need more details on the system, and what you are trying to measure. -- glen
praveen wrote:
> > Hello, > I have a signal consisting of 4 harmonics (200k,400k,600k,and 800k Hz) > and dc component.The signal is very pure and SNR better than 60 dB. I > have to sample it in sub Nyquisit rate(lesser than 1600k). What > sampling rate should i choose so that there no alaising. I cannot > chose higher sampling rate because of my hardware constraints. > > waiting for reply > regards > praveen
You can subtract out the DC and measure it separately, then deal with a 600 KHz bandwidth. If you sample at a frequency that interleaves the aliases with the real signal, say by folding 550 KHz, then your prior knowledge of the signal will allow the components to be separated. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Jesper Buch wrote:
>
...
> > think of 44.100 khz sample rate for CD . . . maximum frequency is 20Khz
44.100 is more than double 20. Simplistically, 40.1 would be enough, but not 40. Since the signal consists of a few pure tones known in advance, aliasing doesn't destroy knowledge of the signal. You were too quick to say "can't". Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
On Tue, 8 Jul 2003 17:16:38 +0200, "Jesper Buch"
<jesperbuch@hotmail.com> wrote:

>---- Original Message ----- >From: "praveen" <praveenkumar1979@rediffmail.com> >Newsgroups: comp.dsp >Sent: Tuesday, July 08, 2003 4:37 PM >Subject: choosing a sampling rate lesser than nyquist rate(sub nyquist rate) > > >> Hello, >> I have a signal consisting of 4 harmonics (200k,400k,600k,and 800k Hz) > >You will never be able to produce an 800 Khz frequency with less than the >double samplerate !
Gotta be careful here - Nyquist rate is related to the bandwidth of the signal not the highest frequency and it assumes impulse sampling. So if I have a 100GHz signal with a 1 Hz maximum bandwidth I only need a slow ADC (2 or 3 Hz) but a very good sample and hold :-) If I have a narrow band signal it can't deviate from the ideal sinusiod by much in a short time interval can it? So I only need to sample occasionally to sample the (low frequency) deviations from the assumed "carrier". Hand-waving justification for sub-sampling. Sub-sampling works when you have good apriori knowledge of a narrow band signal. The case in point here though is a signal with a bandwidth from DC to 800 kHz so that is the bandwidth. the ide though of dealing with DC separately and then allowing folding (aliasing), as suggested by others, is also what I was thinking. You still need a sample window much much shorter than 1/1600kHz but the sample rate requirement is relaxed. Ian
"Ian" <i.wilson.no@s.p.am.considered.com.au.delete.no.spam> wrote in message
news:n1imgvcqe5dumi3m5apdnm6crhrdjgn6nh@4ax.com...
> On Tue, 8 Jul 2003 17:16:38 +0200, "Jesper Buch" > <jesperbuch@hotmail.com> wrote:
(snip)
> Gotta be careful here - Nyquist rate is related to the bandwidth of > the signal not the highest frequency and it assumes impulse sampling. > > So if I have a 100GHz signal with a 1 Hz maximum bandwidth I only need > a slow ADC (2 or 3 Hz) but a very good sample and hold :-)
That is an amazing sample and hold! I suppose you can count the 100GHz signal (very carefully) to find the sampling points. (snip)
> The case in point here though is a signal with a bandwidth from DC to > 800 kHz so that is the bandwidth. the ide though of dealing with DC > separately and then allowing folding (aliasing), as suggested by > others, is also what I was thinking. You still need a sample window > much much shorter than 1/1600kHz but the sample rate requirement is > relaxed.
It indicates 200kHz, 400kHz, 600kHz, and 800kHz, but nothing about the bandwidth at those frequencies. -- glen
Sample at 1100. Your signal will show up at 200, 300, 400, and 500.

-jim

praveen wrote:
> > Hello, > I have a signal consisting of 4 harmonics (200k,400k,600k,and 800k Hz) > and dc component.The signal is very pure and SNR better than 60 dB. I > have to sample it in sub Nyquisit rate(lesser than 1600k). What > sampling rate should i choose so that there no alaising. I cannot > chose higher sampling rate because of my hardware constraints. > > waiting for reply > regards > praveen
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