On 22/03/2011 16:23, Vladimir Vassilevsky wrote:> Who cares about worseless stupident/studiot homeworks. > It is because of the folks like that Chernobils and Fukushimas are > happening. >Chernobil and Fukushima problems are due to bad management - too many corners cut to save money, and too little management of what the engineers are doing. There are plenty of things that go wrong in this world due to incompetent or undertrained engineers - but with projects that size, the fault lies fully with the leadership. And if your point had a basis in fact, then clearly we should /all/ care about the student and his homework!
A question about DFT
Started by ●March 20, 2011
Reply by ●March 22, 20112011-03-22
Reply by ●March 22, 20112011-03-22
> Vladimir Vassilevsky schrieb:> > > Dave wrote: >> On Mar 21, 10:16 am, Vladimir Vassilevsky <nos...@nowhere.com> wrote: >> >>> hyd198471 wrote: >>> >>>> I have exercise to solve. >>> >>>> Giving is an analog signal, the spectra of discrete lines at a minimum >>>> distance deltaF = 2Hz >>>> The ratio of the largest to the smallest signal amplitude is 100:1. The >>>> signal is band limited to 5KHz. The signal spectrum is to be >>>> measured with >>>> a DFT Analyzer. Please set the sampling frequency fa, the number M of >>>> samples and the window function (blackman,Rectangular, Hamming or >>>> Hanning)suitably, so that all lines are detected with no doubt. >>> >>>> I figure it out the fa should be 10 KHz, but the number of samples and >>>> which type of window function should be used I don't know how to do it. >>>> Can someone help me? >>> >>> The resolution is determined only by signal to noise ratio. Windows, >>> DFTs, etc, are no more then minor technicalities. Since there is no >>> noise in your homework, you only need 5kHz/2Hz = 2500 samples to resolve >>> all of the components. >>> >>> VLV >> >> >> I don't know what weed you're smokin. Resolution is determined by the >> observation time of the signal. > > Resolution = distance_between_the_signals/noiseWhy does everbody in the world uses the word resolution in a different manner? Resolution is the ability to separate two sources in the spectral-, spatial-, time- or whatever domain you are using. This resolution is limited by statistical and deterministic errors of the estimation process. If noise goes to zero, the deterministic errors limit still the resolution. And the deterministic errors are influenced mainly by the window length and shape in case of a DFT based processing scheme.
Reply by ●March 22, 20112011-03-22
Dave <dspguy2@netscape.net> wrote: (snip, someone wrote)>> > I don't know what weed you're smokin. �Resolution is determined by the >> > observation time of the signal.(someone else wrote)>> Resolution = distance_between_the_signals/noise(snip)>> Zero noise = infinite resolution(snip)> Maybe before you start changing the titles on people's posts you > should go back to school and take a course on spectral estimation or > even take the first year DSP course.The discussion has come up before. If a signal is known to contain one sine, with unknown frequency, phase, and amplitude, then a small number, about three, noiseless points are enough to determine all three. With noise, more points are needed to average out the noise effects, and improve the ability to resolve the (single) frequency. In the case of a sum of a large number of sinusoids, the answer is very different. Two questions, two answers. -- glen
Reply by ●March 22, 20112011-03-22
On Mar 22, 2:29�pm, Sebastian Doht <seb_d...@lycos.com> wrote:> �> Vladimir Vassilevsky schrieb: > > > Dave wrote: > > >> Resolution is determined by the observation time of the signal. > > > Resolution = distance_between_the_signals/noise > > Why does everbody in the world uses the word resolution in a different > manner? > Resolution is the ability to separate two sources in the spectral-, > spatial-, time- or whatever domain you are using.how about the "amplitude domain"? the ability to separate two samples (or signals composed of these samples) of different amplitudes? i think i've heard the term "20-bit resolution". what does that mean? r b-j
Reply by ●March 22, 20112011-03-22
Sebastian Doht wrote:>>> I don't know what weed you're smokin. Resolution is determined by the >>> observation time of the signal. >> >> >> Resolution = distance_between_the_signals/noise > > > Why does everbody in the world uses the word resolution in a different > manner? > Resolution is the ability to separate two sources in the spectral-, > spatial-, time- or whatever domain you are using. This resolution is > limited by statistical and deterministic errors of the estimation > process. If noise goes to zero, the deterministic errors limit still the > resolution. And the deterministic errors are influenced mainly by the > window length and shape in case of a DFT based processing scheme.The resolution is a property of the signal and the noise. The deficiencies of particular algorithms have nothing to do with resolution. VLV
Reply by ●March 22, 20112011-03-22
Vladimir Vassilevsky schrieb:> > > Sebastian Doht wrote: > > >>>> I don't know what weed you're smokin. Resolution is determined by the >>>> observation time of the signal. >>> >>> >>> Resolution = distance_between_the_signals/noise >> >> >> Why does everbody in the world uses the word resolution in a different >> manner? >> Resolution is the ability to separate two sources in the spectral-, >> spatial-, time- or whatever domain you are using. This resolution is >> limited by statistical and deterministic errors of the estimation >> process. If noise goes to zero, the deterministic errors limit still >> the resolution. And the deterministic errors are influenced mainly by >> the window length and shape in case of a DFT based processing scheme. > > The resolution is a property of the signal and the noise. The > deficiencies of particular algorithms have nothing to do with resolution. > > VLVWell I understand it as a property of the designed system. If a radar uses only narrowband signals it can not achieve a superior range resolution. If a spectrum analyser only operates on block of 32 samples the frequency resolution will not be as required. But I think I understand your definition now. The resolution you specify is the one which could be reached by a "perfect" estimation. Something like a Cramer-Rao bound? When I choose an algorithm I first check that the basic assumptions are met, meaning that it can perform in the noise-free case as required before specifying anything in terms of required SNR. Best regards, Sebastian
Reply by ●March 22, 20112011-03-22
robert bristow-johnson schrieb:> On Mar 22, 2:29 pm, Sebastian Doht<seb_d...@lycos.com> wrote: >> > Vladimir Vassilevsky schrieb: >> >>> Dave wrote: >> >>>> Resolution is determined by the observation time of the signal. >> >>> Resolution = distance_between_the_signals/noise >> >> Why does everbody in the world uses the word resolution in a different >> manner? >> Resolution is the ability to separate two sources in the spectral-, >> spatial-, time- or whatever domain you are using. > > how about the "amplitude domain"? the ability to separate two samples > (or signals composed of these samples) of different amplitudes? > > i think i've heard the term "20-bit resolution". what does that mean? > > r b-jAnd that is where the real trouble starts ^^ Suppose for a moment a range value of a radar system is encoded with a 20-bit "resolution". Now there are two possible interpretations of what "resolution" defines and the manufactor will most likely put the one in the spec/manual that looks better.
Reply by ●March 22, 20112011-03-22
robert bristow-johnson <rbj@audioimagination.com> wrote: (snip)> how about the "amplitude domain"? the ability to separate two samples > (or signals composed of these samples) of different amplitudes?> i think i've heard the term "20-bit resolution". what does that mean?It makes most sense for amplitude (or sample) resolution on quantized samples. That is, quantized as 20 bit samples. It seems to me that it could also apply for sampled data with at least 2**20 samples, though that would seem rare. That is, the frequency resolution is the appropriate fraction of the Nyquist frequency. (Frequencies in the Fourier tranform require at least 20 bits.) -- glen
Reply by ●March 22, 20112011-03-22
On Wed, 23 Mar 2011 00:30:02 +0100, Sebastian Doht <seb_doht@lycos.com> wrote:>Vladimir Vassilevsky schrieb: >> >> >> Sebastian Doht wrote: >> >> >>>>> I don't know what weed you're smokin. Resolution is determined by the >>>>> observation time of the signal. >>>> >>>> >>>> Resolution = distance_between_the_signals/noise >>> >>> >>> Why does everbody in the world uses the word resolution in a different >>> manner? >>> Resolution is the ability to separate two sources in the spectral-, >>> spatial-, time- or whatever domain you are using. This resolution is >>> limited by statistical and deterministic errors of the estimation >>> process. If noise goes to zero, the deterministic errors limit still >>> the resolution. And the deterministic errors are influenced mainly by >>> the window length and shape in case of a DFT based processing scheme. >> >> The resolution is a property of the signal and the noise. The >> deficiencies of particular algorithms have nothing to do with resolution. >> >> VLV > >Well I understand it as a property of the designed system. If a radar >uses only narrowband signals it can not achieve a superior range >resolution. If a spectrum analyser only operates on block of 32 samples >the frequency resolution will not be as required. > >But I think I understand your definition now. The resolution you specify >is the one which could be reached by a "perfect" estimation. Something >like a Cramer-Rao bound? > >When I choose an algorithm I first check that the basic assumptions are >met, meaning that it can perform in the noise-free case as required >before specifying anything in terms of required SNR. > >Best regards, >SebastianBeing able to resolve two (or more) things just means being able to tell them apart, in a basic sense. So for the multiple tones case it means one thing, for levels into an ADC it means something else, for details in an image it means something else. Nothing in that basic definition has anything to do with *why* you may not be able to tell them apart, and noise is only one factor. As you mention, for a radar or similar system there are lots of other things to consider, like window shape, etc., etc. Eric Jacobsen http://www.ericjacobsen.org http://www.dsprelated.com/blogs-1//Eric_Jacobsen.php
Reply by ●March 23, 20112011-03-23
Sebastian Doht wrote:> Vladimir Vassilevsky schrieb: > >> >> >> Sebastian Doht wrote: >>>>> I don't know what weed you're smokin. Resolution is determined by the >>>>> observation time of the signal. >>>> >>>> Resolution = distance_between_the_signals/noise >>> >>> >>> Why does everbody in the world uses the word resolution in a different >>> manner? >>> Resolution is the ability to separate two sources in the spectral-, >>> spatial-, time- or whatever domain you are using. This resolution is >>> limited by statistical and deterministic errors of the estimation >>> process. If noise goes to zero, the deterministic errors limit still >>> the resolution. And the deterministic errors are influenced mainly by >>> the window length and shape in case of a DFT based processing scheme. >> >> >> The resolution is a property of the signal and the noise. The >> deficiencies of particular algorithms have nothing to do with resolution. >> > > Well I understand it as a property of the designed system. If a radar > uses only narrowband signals it can not achieve a superior range > resolution.GPS uses ~10 MHz wide signal however there are receivers which achieve sub-centimeter resolution.> If a spectrum analyser only operates on block of 32 samples > the frequency resolution will not be as required.It depends. What is done and how it is done.> But I think I understand your definition now. The resolution you specify > is the one which could be reached by a "perfect" estimation. Something > like a Cramer-Rao bound?Good example.> When I choose an algorithm I first check that the basic assumptions are > met, meaning that it can perform in the noise-free case as required > before specifying anything in terms of required SNR.There is a common fallacy that the frequency resolution is 1/T. Despite of being wrong, this statement is repeated everywhere. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
