jim wrote:> > Fred Marshall wrote:...>>Here are a couple of points: >> >>You said: >> >>It seems perfectly reasonable to call the single >>frequency, by inspection, of a time limited non-periodic signal >>as simply its frequency. >> >>I respond: >> >>In the real AND arm-waving world it is reasonable. You gate the output of a >>very stable sinusoidal generator for a short time. The "frequency" of the >>sinusoid is clear. >>But the frequency of the sinusoid and the spectrum of the signal are very >>different things. >>There can be no doubt that the sharp edges of the gated sinusoid contribute >>rich spectral content that is measurable. So, a perfect spectrum analyzer >>will see that energy. > > > No not true. This is only true if your gating and sampling functions are > "brain dead" which admittedly they most often are. But there is no > reason it has to be that way (well there might be reasons in some > specific cases but speaking in general). If there is a mechanism for > detecting repetition in the signal and modifying the sample rate and > length of samples analyzed to match then your objections completely > evaporate.What isn't true, that the spectrum of a signal is unaltered by selecting a piece of it? That the spectrum of a snippet depends on what one knows about the rest of the signal? Tune in WWV or one of its derivatives (WWVx). There will be a tone for most of a minute with clicks to mark the seconds.(The tone is 440.000 or 600.000 Hz in alternate minutes.) Near the end of a minute the tone stops, and a voice says, "When the tone returns, the time will be ..." and for a while there is only tick ... tick ... tick ..., once a second. Put the audio on a scope. See that the ticks are in fact five complete cycles of 1000.000 Hz, beginning on a second, accurate to nanoseconds at the transmitter. Does the tick resemble a 1 KHz tone in any way but visually?> Randy's question is based on the assumption that there exists knowledge > of what exists outside the 1024 samples. The reasoning goes something > like this: what are the chances that the 1024 represents a complete > cycle of a repeating wave form in the real world? Well the chances are > excellent if the system were to be designed for that.I doubt very much that Randy claims that private knowledge can change the result of the measurement. I hope he responds for himself. ... Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
spectral estimation question
Started by ●April 2, 2006
Reply by ●April 4, 20062006-04-04
Reply by ●April 4, 20062006-04-04
"Jerry Avins" <jya@ieee.org> wrote in message news:7qKdnZ_lvvED4q_ZRVn-ug@rcn.net...> Fred Marshall wrote: > > ... > >> Totally lost..... > > You, or Ron? :-( > > Jerry > --*I* was lost in what I was reading there.
Reply by ●April 4, 20062006-04-04
Jerry Avins wrote:> > Tune in WWV or one of its derivatives (WWVx). There will be a tone for > most of a minute with clicks to mark the seconds.(The tone is 440.000 o=r> 600.000 Hz in alternate minutes.) Near the end of a minute the tone > stops, and a voice says, "When the tone returns, the time will be ..." > and for a while there is only tick ... tick ... tick ..., once a second==2E> Put the audio on a scope. See that the ticks are in fact five complet=e> cycles of 1000.000 Hz, beginning on a second, accurate to nanoseconds a=t> the transmitter. Does the tick resemble a 1 KHz tone in any way but > visually?Do you mean could you tell the difference between that particular tick and one similarly constructed with 500Hz wave form. Yes you probably could. But that only makes you wrong about some completely irrelevant and unrelated point. Your scope (if its not very old) is an example of what I was saying. It adjusts the window and sample rate to match the input signal.> => > Randy's question is based on the assumption that there exists k=nowledge> > of what exists outside the 1024 samples. The reasoning goes something=> > like this: what are the chances that the 1024 represents a complete > > cycle of a repeating wave form in the real world? Well the chances ar=e> > excellent if the system were to be designed for that. > => I doubt very much that Randy claims that private knowledge can change > the result of the measurement. I hope he responds for himself.Well I doubt that also and I have no idea why you brought it up. = Randy started with the premise that if we view the DFT as filter bank it turns out to be a not the best. My point is that isn't necessarily true. Under the right circumstances it could be the best set of filters. -jim> => ... > => Jerry > -- > Engineering is the art of making what you want from things you can get.=> =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=AF ----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----
Reply by ●April 4, 20062006-04-04
jim wrote:> > Jerry Avins wrote: > >>Tune in WWV or one of its derivatives (WWVx). There will be a tone for >>most of a minute with clicks to mark the seconds.(The tone is 440.000 or >>600.000 Hz in alternate minutes.) Near the end of a minute the tone >>stops, and a voice says, "When the tone returns, the time will be ..." >>and for a while there is only tick ... tick ... tick ..., once a second. >> Put the audio on a scope. See that the ticks are in fact five complete >>cycles of 1000.000 Hz, beginning on a second, accurate to nanoseconds at >>the transmitter. Does the tick resemble a 1 KHz tone in any way but >>visually? > > > Do you mean could you tell the difference between that particular tick > and one similarly constructed with 500Hz wave form. Yes you probably > could. But that only makes you wrong about some completely irrelevant > and unrelated point. > > Your scope (if its not very old) is an example of what I was saying. It > adjusts the window and sample rate to match the input signal.That doesn't make the tick sound like a tone. One KHz is a small pert of its spectrum.>>> Randy's question is based on the assumption that there exists knowledge >>>of what exists outside the 1024 samples. The reasoning goes something >>>like this: what are the chances that the 1024 represents a complete >>>cycle of a repeating wave form in the real world? Well the chances are >>>excellent if the system were to be designed for that. >> >>I doubt very much that Randy claims that private knowledge can change >>the result of the measurement. I hope he responds for himself. > > > Well I doubt that also and I have no idea why you brought it up. > > Randy started with the premise that if we view the DFT as filter bank > it turns out to be a not the best. My point is that isn't necessarily > true. Under the right circumstances it could be the best set of filters.I misunderstood. (I still don't see what you meant to write, but no matter.) ... Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 4, 20062006-04-04
"Mark" <makolber@yahoo.com> wrote in message news:1144159202.823653.173700@e56g2000cwe.googlegroups.com...> > Randy Yates wrote: >> Jerry Avins <jya@ieee.org> writes: >> >> > Ron N. wrote: >> >> Randy Yates wrote: >> >> >> >>>OK, here's one of those "This should be simple..." questions. >> >>> >> >>>We know that many (all?) methods of spectral estimation of >> >>>discrete-time data rely fundamentally on the DFT (the N-point DFT). >> >>> >> >>>However, the output of a specific bin of the DFT can be viewed as a >> >>>bandpass filter. This DFT bandpass filter is not particularly "good," >> >>>i.e., it has high side lobes and poor stop-band rejection. >> >>> > > > There has been a lot of discussion about the assumed finite time > duration of the input time domain data fundamentally implying a limited > resolution in the output in the frequency domain. Also if we assume > the input data is repetitive we can improve the output frequency > resolution. OK Good. Yes we can improve the resolution of the DFT by > making each bin narrower. > > But I was hoping to see some discussion about improving the SHAPE > FACTOR of the DFT bin filters, i.e. making the skirts steeper for a > given passband bandwidth. I think that was what Randy was getting at > with his original question. > > The SHAPE FACTOR of the DFT bins is fixed. But if we were making > individual filters instead of using the DFT, we could use "better" > filters ...here better does not just mean narrower, but instead > better means with a better SHAPE FACTOR. >Mark, Good question. The answer is: "it depends". Here's a case that I worked on recently: Given a signal rich in harmonic content at a known frequency(ies) and mixed with background noise - detect the presence of the signal with limited processing resources (as always). Response time isn't critical - measured in seconds, not milliseconds. A natural filter for this purpose is a fixed-frequency comb filter. It's a good choice because it can be a FIR filter with very few "taps" that are nonzero. In fact, the prototype filter will be a sequence of unit samples in time - which convert to a sequence of unit samples in frequency. Just put the unit samples in frequency at the fundamental and all the harmonics. Obviously the sample interval of the signal and the equal underlying delay value of the filter will be relatively short to meet the Nyquist criterion with system margin added. This means that the frequency sampling interval of the nonzero filter structure (not the entire filter) is f0 - the fundamental. This means that the time separation of unit samples in the unit sample response of the filter is 1/f0. And, nicely, the filter has lots of zero coefficients. But the "bins" have roughly the same sinx/x shape that corresponds to the length of the filter in time from the first nonzero coefficient to the last. Narrow but with a fair amount of spectral spreading. So, one is tempted to window the filter unit sample response to supress the sidelobes - and this will work. Taking it a step further, what if you don't know the frequency perfectly and want to do a good job of capturing it over some possible range of frequencies? This suggests that the unit samples in frequency become maybe groups of 3 or 4 unit samples. How to achieve that easily and get good transitions and sidelobes with acceptable ripple in the passbands? One method would be to convolve the frequency response with the response of a very good lowpass filter that's 3 or 4 "bins" wide. This is the same as windowing the time response of course. The window function you might use is interesting - particularly if you want to have zero response at f=0. So, there's a shape factor example. Back to basic physics: Usually (symmetrical) filters are constructed as sums of cosines. But it need not be done this way and it's nice to think of the construction differently sometimes. A sum of sincs or Dirichlet kernels is another way. Just like reconstruction in time using sincs, we can have construction in frequency using sincs. The width of the sinc is inversely proportional to the length of the filter just as the width of a sinc in time is inversely proportional to the bandwidth. So, if we're building a filter response we are stuck with transition widths that are determined by the width of those sincs. That makes visualization really simple doesn't it? The sincs are separated from one another by the spacing of their zero crossings. They can't be closer together or the superposition of them becomes a new sum of sincs that *are* spaced this way. In this latter case we may start with a sum of frequency samples over limited support (i.e. bandlimited) and find the added sincs that are closer together within that support imply nonzero sincs outside that range - well actually an infinite number of them I believe. So, yes, we can create filter banks with improved shape factor but the filter passbands have to be wider than the underlying sinc. And, if our shape factor allows the transition bands to be wider then there is real energy available to spread around in reducing ripple and stopband attenuation. Fred
Reply by ●April 4, 20062006-04-04
Jerry Avins wrote:> > jim wrote: > > > > Jerry Avins wrote:> >> Put the audio on a scope. See that the ticks are in fact five complete > >>cycles of 1000.000 Hz, beginning on a second, accurate to nanoseconds at > >>the transmitter. Does the tick resemble a 1 KHz tone in any way but > >>visually? > > > > > > Do you mean could you tell the difference between that particular tick > > and one similarly constructed with 500Hz wave form. Yes you probably > > could. But that only makes you wrong about some completely irrelevant > > and unrelated point. > >> > That doesn't make the tick sound like a tone.But it does make it sound like a tone. That is you can hear the difference in spectral content of your 'tick' versus my proposed 'tock'. No that doesn't make it a tone because your mind classifies "tone" as something that lasts awhile. But there is a resemblance which was what you asked about and I responded too. -jim ----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==---- http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups ----= East and West-Coast Server Farms - Total Privacy via Encryption =----
Reply by ●April 4, 20062006-04-04
jim wrote:> > Jerry Avins wrote: > >>jim wrote: >> >>>Jerry Avins wrote: > > >>>> Put the audio on a scope. See that the ticks are in fact five complete >>>>cycles of 1000.000 Hz, beginning on a second, accurate to nanoseconds at >>>>the transmitter. Does the tick resemble a 1 KHz tone in any way but >>>>visually? >>> >>> >>>Do you mean could you tell the difference between that particular tick >>>and one similarly constructed with 500Hz wave form. Yes you probably >>>could. But that only makes you wrong about some completely irrelevant >>>and unrelated point. >>> > > >>That doesn't make the tick sound like a tone. > > > But it does make it sound like a tone. That is you can hear the > difference in spectral content of your 'tick' versus my proposed 'tock'. > No that doesn't make it a tone because your mind classifies "tone" as > something that lasts awhile. But there is a resemblance which was what > you asked about and I responded too.It seems that we hear differently. All the side energy interferes with my perception of pitch. Jerry
Reply by ●April 4, 20062006-04-04
Randy Yates wrote:> Jerry Avins <j...@ieee.org> writes:> > Ron N. wrote: > >> Randy Yates wrote:> >>>OK, here's one of those "This should be simple..." questions.> >>>We know that many (all?) methods of spectral estimation of > >>>discrete-time data rely fundamentally on the DFT (the N-point DFT).> >>>However, the output of a specific bin of the DFT can be viewed as a > >>>bandpass filter. This DFT bandpass filter is not particularly "good," > >>>i.e., it has high side lobes and poor stop-band rejection.There has been a lot of discussion about the assumed finite time duration of the input time domain data fundamentally implying a limited resolution in the output in the frequency domain. Also if we assume the input data is repetitive we can improve the output frequency resolution. OK Good. Yes we can improve the resolution of the DFT by making each bin narrower. But I was hoping to see some discussion about improving the SHAPE FACTOR of the DFT bin filters, i.e. making the skirts steeper for a given passband bandwidth. I think that was what Randy was getting at with his original question. The SHAPE FACTOR of the DFT bins is fixed. But if we were making individual filters instead of using the DFT, we could use "better" filters ...here better does not just mean narrower, but instead better means with a better SHAPE FACTOR. thanks Mark
Reply by ●April 4, 20062006-04-04
Mark wrote:> Randy Yates wrote: > >>Jerry Avins <j...@ieee.org> writes: > > >>>Ron N. wrote: >>> >>>>Randy Yates wrote: > > > >>>>>OK, here's one of those "This should be simple..." questions. > > > >>>>>We know that many (all?) methods of spectral estimation of >>>>>discrete-time data rely fundamentally on the DFT (the N-point DFT). > > > >>>>>However, the output of a specific bin of the DFT can be viewed as a >>>>>bandpass filter. This DFT bandpass filter is not particularly "good," >>>>>i.e., it has high side lobes and poor stop-band rejection. > > > > > There has been a lot of discussion about the assumed finite time > duration of the input time domain data fundamentally implying a limited > > resolution in the output in the frequency domain. Also if we assume > the input data is repetitive we can improve the output frequency > resolution. OK Good. Yes we can improve the resolution of the DFT by > making each bin narrower. > > But I was hoping to see some discussion about improving the SHAPE > FACTOR of the DFT bin filters, i.e. making the skirts steeper for a > given passband bandwidth. I think that was what Randy was getting at > with his original question. > > > The SHAPE FACTOR of the DFT bins is fixed. But if we were making > individual filters instead of using the DFT, we could use "better" > filters ...here better does not just mean narrower, but instead > better means with a better SHAPE FACTOR.This doesn't really make sense. A bin has no width; there is only spacing. The idea of width has just enough connection to what is real to make it an appealing and sometimes useful analogy, but that's as far as it goes. A frequency that does not match a bin precisely will influence other bins, not necessarily neighbors to the closest match. Just as the DFT can be pressed into service for aperiodic signals, it can also be pressed into service as a filter bank. As you have observed, it is not the tool one would choose if a better were available. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 4, 20062006-04-04
Mark skrev:> Randy Yates wrote: > > Jerry Avins <jya@ieee.org> writes: > > > > > Ron N. wrote: > > >> Randy Yates wrote: > > >> > > >>>OK, here's one of those "This should be simple..." questions. > > >>> > > >>>We know that many (all?) methods of spectral estimation of > > >>>discrete-time data rely fundamentally on the DFT (the N-point DFT). > > >>> > > >>>However, the output of a specific bin of the DFT can be viewed as a > > >>>bandpass filter. This DFT bandpass filter is not particularly "good," > > >>>i.e., it has high side lobes and poor stop-band rejection. > > >>> > > > There has been a lot of discussion about the assumed finite time > duration of the input time domain data fundamentally implying a limited > resolution in the output in the frequency domain. Also if we assume > the input data is repetitive we can improve the output frequency > resolution. OK Good. Yes we can improve the resolution of the DFT by > making each bin narrower. > > But I was hoping to see some discussion about improving the SHAPE > FACTOR of the DFT bin filters, i.e. making the skirts steeper for a > given passband bandwidth. I think that was what Randy was getting at > with his original question. > > The SHAPE FACTOR of the DFT bins is fixed. But if we were making > individual filters instead of using the DFT, we could use "better" > filters ...here better does not just mean narrower, but instead > better means with a better SHAPE FACTOR.I don't understand this. I might agree with the bandpass filter as a useful *analogy* for the DFT bin, but I am not comfortable with a discussion about the DFT that is based on the properties of the analogy and not the DFT. The properties of the DFT are well-known. The DFT is an abstract tool that has been around for a couple of centuries, at least since the time of Gauss. Being an abstract tool, the DFT should be discussed in abstract terms. Once the terms "finite data records" and "DFT" appear in the same sentence, the term "window function" usually appears in the next. If people have a problem with that, the only possible solution is to avoid bringing the DFT into the discussion in the first place. As for power spectrum analysis, that can be achieved by using wavelets or (sub)octave-band filters, as lots of people do in practical applications. It might be very interesting to discuss the merits of different filters in that setting. as far as I am concerned, it is futile to discus filters as a method to improve on the DFT. Rune
