robert bristow-johnson wrote:> On Apr 20, 5:47 am, Andor <andor.bari...@gmail.com> wrote: >> zqchen wrote: >>> A bandlimited signal may be reconstructed from its samples with an >>> ideal low-pass filter. But is this ideal low-pass filter still the >>> optimal filter if there is noise. If not how to find out the optimal >>> filter? thanks! >> You are mixing up two independent concepts. Sampling and >> reconstruction is concerned with the conditions under which a signal >> may be sampled and perfectly reproduced from the samples. >> >> Noise reduction is concerned with seperating noise and signal. For >> most real-world noise reduction applications, an LTI filter isn't >> sufficient. LTI filters only make sense for noise reduction if >> a) the noise is additive and >> b) noise and signal are in non-overlapping frequency bands. > > dunno if i completely agree, Andor. but i must admit that this takes > me back to grad school and is not stuff that i think about or work on > currently. > > as Dale said, "'optimal' with respect to what criteria? " > > if reconstructing the signal where scaling was important (and you > measure error with a Euclidian norm) then a Weiner filter is optimal > (if scaling isn't important, then it's a Matched filter), and assuming > it's been turned on a long time and the statastics of the noise do not > change, it's LTI. and although you get better performance if the > noise and signal are disjoint in either time or frequency, that is not > the requirement in general.I keep trying to inject the idea that the origin of the noise -- before sampling or during conversion to analog -- matters. Am I being politely ignored because nobody wants to embarrass a genial old geezer, or isn't anyone listening? Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
reconstruct a signal from its samples in the presence of noise
Started by ●April 19, 2007
Reply by ●April 21, 20072007-04-21
Reply by ●April 21, 20072007-04-21
On 21 Apr., 20:47, robert bristow-johnson <r...@audioimagination.com> wrote:> On Apr 20, 5:47 am, Andor <andor.bari...@gmail.com> wrote: > > > zqchen wrote: > > > A bandlimited signal may be reconstructed from its samples with an > > > ideal low-pass filter. But is this ideal low-pass filter still the > > > optimal filter if there is noise. If not how to find out the optimal > > > filter? thanks! > > > You are mixing up two independent concepts. Sampling and > > reconstruction is concerned with the conditions under which a signal > > may be sampled and perfectly reproduced from the samples. > > > Noise reduction is concerned with seperating noise and signal. For > > most real-world noise reduction applications, an LTI filter isn't > > sufficient. LTI filters only make sense for noise reduction if > > a) the noise is additive and > > b) noise and signal are in non-overlapping frequency bands. > > dunno if i completely agree, Andor.I don't think I completely agree either :-).> but i must admit that this takes > me back to grad school and is not stuff that i think about or work on > currently. > > as Dale said, "'optimal' with respect to what criteria? " > > if reconstructing the signal where scaling was important (and you > measure error with a Euclidian norm) then a Weiner filter is optimal > (if scaling isn't important, then it's a Matched filter), and assuming > it's been turned on a long time and the statastics of the noise do not >change, it's LTI.You are right. Clearly, there are optimal LTI solutions to increase SNR, given noise and signal statistics are known and constant. I am completely engrossed in a current audio denoising project. There, the main objective is to remove the noise (or increase SNR) without altering the signal part of the signal + noise mix. That is a different task than maximising SNR under the conditions of Wiener filtering, and in general it cannot be achieved using LTI filtering. Regards, Andor
Reply by ●April 21, 20072007-04-21
On Apr 21, 3:25 pm, Jerry Avins <j...@ieee.org> wrote:> > I keep trying to inject the idea that the origin of the noise -- before > sampling or during conversion to analog -- matters. Am I being politely > ignored because nobody wants to embarrass a genial old geezer, or isn't > anyone listening?i'm listening, but not understanding completely (it might be a semantic thing). i would say that the known *properties* of the noise (essentially its power spectrum) matter as well as the known properties of the signal (it would be nice to know its power spectrum also, of course we don't know its complete spectrum - magnitude and phase - because then we would know what the signal is and would have little need to extract it from noise). if a white noise got added to a signal with unknown (or assumed flat) spectrum, i don't think there is diddley-squat that you can do about reducing the effect of the noise at all. but if white noise is added to a signal that we have reason to believe is narrow bandwidth and we have an idea where this narrow bandwidth resides on the spectrum, there should be something we can do to help coax out the signal. but anyway, if these properties are known, what additional information do we get from knowing the origin? or, Jerry, is it that if we know the origin, we'll know its properties? L8r, r b-j
Reply by ●April 21, 20072007-04-21
robert bristow-johnson wrote: ...> but anyway, if these properties are known, what additional information > do we get from knowing the origin? or, Jerry, is it that if we know > the origin, we'll know its properties?If the samples are clean but the reconstructed signal is noisy, zqchen needs to build a quieter D/A conversion chain. If the signal is clean but the samples are noisy, he needs to build a quieter A/D chain. If the noise is so broadband that it aliases (could that be determined?) while the signal is properly bandlimited, the noise entered the system somewhere after the anti-alias filter. The properties of the noise matter only if it can't be removed at the source, and in that case standard noise-reduction techniques (that may be combined with the reconstruction filter) apply. Digital noise reduction methods like Wiener filters are to be used, it seems to me that a standard reconstruction filter has to come after that. I don't understand the processing sequence some of youse guys are advocating. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●April 22, 20072007-04-22
thank you all for your insightful comments. it's a question appeared in my mind when i read through the book. the book said the ideal low-pass filter may exactly reconstruct the signal, then i just think if it's the case in the presence of some noise. i felt it may be not so but i need some confirmation from experts. :)
