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

Started by praveen July 8, 2003
praveenkumar1979@rediffmail.com (praveen) 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. > > > waiting for reply > regards > praveen
As has been said in this thread you cannot sample below 1600kHz without aliasing but if the signal is, as you suggested, a periodic signal, then if your aim is to merely reconstruct the wave shape for the signal you can do it "with aliasing". Do a search for aliasing oscilloscope and see what you find. You should sample at a frequency close to the fundamental of the waveform (ie 200kHz). The resulting output signal will have a fundamental equal to the difference between the two. Aliasing can be exploited when you know the signal you're analysing is periodic. This method is used in very fast oscilloscopes to visualise signals that current technology can not capture us the normal sampling approach. Regards, Paavo Jumppanen, Author of AtSpec : A 2 channel PC based FFT spectrum analyzer http://www.taquis.com
"Jerry Avins" <jya@ieee.org> wrote in message
news:3F0B18E0.182A4919@ieee.org...
> praveen wrote: > > > > 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.
> 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.
I was hoping that Praveen would say more. It depends on the sidebands of the four harmonics. If they aren't too wide, that seems to be a good solution. It may be that it is a homework problem, and that is the solution that they should come up with. It could also be four carriers each modulated by a different signal. If there are no sidebands, nine samples are enough to get the DC, and amplitude and phase of the four harmonics, though that isn't a very interesting problem. -- glen -- glen
"Glen Herrmannsfeldt" <gah@ugcs.caltech.edu> wrote in message news:<PsCOa.8701$Ph3.1159@sccrnsc04>...
> "praveen" <praveenkumar1979@rediffmail.com> wrote in message > news:ff8a3afb.0307080637.324d0faf@posting.google.com... > > Hello, > > I have a signal consisting of 4 harmonics (200k,400k,600k,and 800k Hz) > > and dc component.The signal is very pure and SNR better than 60 dB. I > > have to sample it in sub Nyquisit rate(lesser than 1600k). What > > sampling rate should i choose so that there no alaising. I cannot > > chose higher sampling rate because of my hardware constraints. > > Do you mean it only has those four harmonics, plus DC? > > No modulation or side bands? Then nine samples are enough. > > On the other hand, if you sample at 900kHz, Fn is 450kHz, the 800kHz alias > is at 100kHz and the 600kHz alias is at 300kHz, which can be separated from > the others, as long as the sidebanks (modulation) are less than 50kHz wide. > > I think to really answer we need more details on the system, and what you > are trying to measure. > > -- glen
Hi, Glen is right. But if you have some kind of modulated signal be aware that signals at 600 and 800kHz (100 and 300kHz after sampling) will have their spectra inverted. This is no problem to deal with if you are aware of it. The best way to think of sampling is like multiplication of your signal with sequence of pulses. Multiplication in time domain <=> convolution in frequency domain. Goran
"Glen Herrmannsfeldt" <gah@ugcs.caltech.edu> wrote in message
news:frIOa.11571$N7.1717@sccrnsc03...
> > "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) >
<snip>
> -- glen > >
I know that extreme example sounds wacky, but it is not that far off real systems. I have a digital scope on my workbench that has a bandwidth of 50GHz, with a sample rate of 30kHz. With averaging you can get 14 bit resolution. Regards Ian
Ian wrote:
>> 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.
Gotta be even more careful here ;-) Think of a signal from 5kHz..20kHz (BW 15kHz) - when sampled with 30kHz the range from 15..20kHz is aliased to 15..10kHz, i.e. into the middle of of the source-band... Mattias
Mattias Schick wrote:
> Ian wrote: > >>>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. > > > Gotta be even more careful here ;-) > Think of a signal from 5kHz..20kHz (BW 15kHz) - when sampled > with 30kHz the range from 15..20kHz is aliased to 15..10kHz, > i.e. into the middle of of the source-band... > Mattias
So you don't do that. You mix down, or complex sample, or.... Regards, Steve
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 !
Hmm, on the net are nice articles on generalization of basic WTK theorem, as I remeber in titles are phrases "50 years after Shannon" and "seven decades after Nyquist" One of basic ideas is, if you can give some function (and it inverse) that transforms the original signal X(t) to some Y(tau) and in new domain (Y,tau) you don't violate bandlimiteness of sampling than you can reconstruct original signal X(t) from it samples that for example may have non uniform delta_t. Of course formulas for analysis and reconstruction are not so simple as in original WTK case :)
>> 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.
It depends on deviations (bandwith) from pure sinusoids but simple test with 1024-bins fft with (empirically choosen) fs 105kHz and even with 11.05kHz!!! gave good results: all peaks (with DC) are separated in original order without big leakage. Yes, I know I have idealized sampler (zero time) and real signal isn't sinusoidal but test with simulated 8-bit A/D and SNR only 6 dB is also good. Mirek
Steve Underwood wrote:
> Mattias Schick wrote: >> Gotta be even more careful here ;-) >> Think of a signal from 5kHz..20kHz (BW 15kHz) - when sampled >> with 30kHz the range from 15..20kHz is aliased to 15..10kHz, >> i.e. into the middle of of the source-band... >> Mattias > > So you don't do that. You mix down, or complex sample, or....
Hi Steve, clear. All i wanted to say is that he (praveen) cannot sample his 600kHz-BW-Signal with 1.2MHz. Ok, we all knew that... Mattias