Hello Given, S2 = S1 + Noise; Given only S2, Is it possible to estimate its SNR? What additional information can help us? Thanks in advance Parthasarathy
SNR of a Signal?
Started by ●February 2, 2005
Reply by ●February 2, 20052005-02-02
Parthasarathy wrote:> Hello > > Given, > S2 = S1 + Noise; > > Given only S2, Is it possible to estimate its SNR? > What additional information can help us?If S1 is a steady, single-frequency waveform or a flat-topped square wave, it's relatively easy. I guess that if nothing is known about S1, it's not possible. Even knowing that S1 is periodic can be enough. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 2, 20052005-02-02
On Wed, 02 Feb 2005 11:26:34 -0500, Jerry Avins <jya@ieee.org> wrote:>Parthasarathy wrote: > >> Hello >> >> Given, >> S2 = S1 + Noise; >> >> Given only S2, Is it possible to estimate its SNR? >> What additional information can help us? > >If S1 is a steady, single-frequency waveform or a flat-topped square >wave, it's relatively easy. I guess that if nothing is known about S1, >it's not possible. Even knowing that S1 is periodic can be enough.If S1 comes from a limited set of symbols and the SNR is high enough, it may be possible to guess the value of S1 from S2, and therefore determine the SNR exactly. (This is rather like the actions of a decision feedback equaliser.) Regards, Allan
Reply by ●February 2, 20052005-02-02
Parthasarathy wrote:> Hello > > Given, > S2 = S1 + Noise; > > Given only S2, Is it possible to estimate its SNR? > What additional information can help us? > > > Thanks in advance > ParthasarathyIf you know nothing about S1 or Noise, then you cannot estimate SNR. You need some info about either S1 or about the noise.
Reply by ●February 2, 20052005-02-02
Allan Herriman wrote:> On Wed, 02 Feb 2005 11:26:34 -0500, Jerry Avins <jya@ieee.org> wrote: > > >>Parthasarathy wrote: >> >> >>>Hello >>> >>>Given, >>>S2 = S1 + Noise; >>> >>>Given only S2, Is it possible to estimate its SNR? >>>What additional information can help us? >> >>If S1 is a steady, single-frequency waveform or a flat-topped square >>wave, it's relatively easy. I guess that if nothing is known about S1, >>it's not possible. Even knowing that S1 is periodic can be enough. > > > If S1 comes from a limited set of symbols and the SNR is high enough, > it may be possible to guess the value of S1 from S2, and therefore > determine the SNR exactly. > (This is rather like the actions of a decision feedback equaliser.) > > Regards, > AllanTo generalize what we both wrote, if the nature of S1 allows it to be deduced exactly from a sufficiently good approximation of it, then the SNR of S2 can be found. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 2, 20052005-02-02
Jerry Avins wrote:> Allan Herriman wrote: > > > On Wed, 02 Feb 2005 11:26:34 -0500, Jerry Avins <jya@ieee.org>wrote:> > > > > >>Parthasarathy wrote: > >> > >> > >>>Hello > >>> > >>>Given, > >>>S2 =3D S1 + Noise; > >>> > >>>Given only S2, Is it possible to estimate its SNR? > >>>What additional information can help us? > >> > >>If S1 is a steady, single-frequency waveform or a flat-toppedsquare> >>wave, it's relatively easy. I guess that if nothing is known aboutS1,> >>it's not possible. Even knowing that S1 is periodic can be enough. > > > > > > If S1 comes from a limited set of symbols and the SNR is highenough,> > it may be possible to guess the value of S1 from S2, and therefore > > determine the SNR exactly. > > (This is rather like the actions of a decision feedback equaliser.) > > > > Regards, > > Allan > > To generalize what we both wrote, if the nature of S1 allows it to be > deduced exactly from a sufficiently good approximation of it, thenthe> SNR of S2 can be found. > > Jerry > -- > Engineering is the art of making what you want from things you canget.>=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF= =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF You don't say if the noise is white. If so, one technique requiring little knowledge of S1 is to compute the power spectrum of S2 and sort the bins into increasing order. Average the bottom 10% of the bins and use that as a measure of the noise power per bin, P. Then multiply P by the total number of bins and divide into the sum of all the bins. That gives you the ratio (S+N)/N from which you can get SNR. You have to make sure the spectral occupancy of S1 is below 90%, or else change the percentile. Also watch out for any filter rolloff near DC and Fs/2 and exclude those bins if necessary. We use this technique all the time for classifying activity in an unknown RF environment. It is crude, but simple and useful in some situations. John
Reply by ●February 3, 20052005-02-03
"john" <johns@xetron.com> wrote in message news:1107388294.994488.134550@z14g2000cwz.googlegroups.com... Jerry Avins wrote:> Allan Herriman wrote: > > > On Wed, 02 Feb 2005 11:26:34 -0500, Jerry Avins <jya@ieee.org>wrote:> > > > > >>Parthasarathy wrote: > >> > >> > >>>Hello > >>> > >>>Given, > >>>S2 = S1 + Noise; > >>> > >>>Given only S2, Is it possible to estimate its SNR? > >>>What additional information can help us? > >> > >>If S1 is a steady, single-frequency waveform or a flat-toppedsquare> >>wave, it's relatively easy. I guess that if nothing is known aboutS1,> >>it's not possible. Even knowing that S1 is periodic can be enough. > > > > > > If S1 comes from a limited set of symbols and the SNR is highenough,> > it may be possible to guess the value of S1 from S2, and therefore > > determine the SNR exactly. > > (This is rather like the actions of a decision feedback equaliser.) > > > > Regards, > > Allan > > To generalize what we both wrote, if the nature of S1 allows it to be > deduced exactly from a sufficiently good approximation of it, thenthe> SNR of S2 can be found. > > Jerry > -- > Engineering is the art of making what you want from things you canget.>���������������������������������������������������������������������� You don't say if the noise is white. If so, one technique requiring little knowledge of S1 is to compute the power spectrum of S2 and sort the bins into increasing order. Average the bottom 10% of the bins and use that as a measure of the noise power per bin, P. Then multiply P by the total number of bins and divide into the sum of all the bins. That gives you the ratio (S+N)/N from which you can get SNR. You have to make sure the spectral occupancy of S1 is below 90%, or else change the percentile. Also watch out for any filter rolloff near DC and Fs/2 and exclude those bins if necessary. We use this technique all the time for classifying activity in an unknown RF environment. It is crude, but simple and useful in some situations. John ------------------ You may also need to average a number of spectral estimates because there will be a variance in the spectral samples. If you don't average them then the bottom 10% may be a low estimate of the actual noise simply because you only have one sample at each frequency. Fred
Reply by ●February 4, 20052005-02-04
> > You don't say if the noise is white.Thanks you all, for the responses. We also know that the signal can be a multicomponent signal in the range 100 KHz to 200 KHz. No information about the noise. One more quetion to the group. How reliable will be the estimate of SNR, if we assume the noise to be white, but it is not in reality? With regards, Parthasarathy
Reply by ●February 4, 20052005-02-04
"Parthasarathy" <parth175@yahoo.co.in> wrote in message news:7f126353.0502032245.36820e1c@posting.google.com...>> >> You don't say if the noise is white. > > > Thanks you all, for the responses. > > We also know that the signal can be a multicomponent signal in the > range > 100 KHz to 200 KHz. > > No information about the noise. > > One more quetion to the group. > How reliable will be the estimate of SNR, if we assume the noise to be > white, but it is not in reality?As reliable as the whiteness assumption.... ? Fred
Reply by ●February 26, 20052005-02-26
another related problem (i'm relatively new to signal theory) i want to decode a SITOR-B signal (FSK) containing two unknown frequencies. in fact, they are known, but we do not know if the rf receiver is tuned precisely, nor if the baseband suffers a time-drift 1) is it a good idea to estimate the SNR calculating SNR = somelogfunc(PEAK/MEAN) of the baseband power spectrum in order to have some measurement of reception? 2) one algorithm to find the fsk center-frequency would be to calculate the mean amplitude of the power-spectrum, only taking into account amplitudes above a certain treshold, that could be some value tr = MEAN+(PEAK-MEAN)*MEAN/PEAK. (this would have to be done continuously to adjust the bandpass filter coefficients accordingly) in simulation this works well, but i am not entirely sure about the implications and i do not want to re-invent the wheel. therefore, i will appreciate your comments! This message was sent using the Comp.DSP web interface on www.DSPRelated.com
