Is there a "DIGITAL" equivalent of "Q"?
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From: Clay on 29 Apr 2010 12:22 On Apr 28, 4:34 pm, glen herrmannsfeldt <g...(a)ugcs.caltech.edu> wrote: > Clay <c...(a)claysturner.com> wrote: > > (snip) > > > Certainly if you can describe your problem in terms of poles, zeroes, > > and filter order (i.e., "s" equations), a digital designer can then > > create an approximation to it. > > A common example concerns the A,B,C, or D weighting filters in > > acoustics. They are described using analog terms. And a few here have > > talked about how to go from there to digital approximations. So when > > you arrive at your filter, then the same approaches can be used to > > find digital approximations to your filter. > > At the following link, you will see some common "s" equations used for > > audio filters. > >http://en.wikipedia.org/wiki/A-weighting > > I wonder if it would be reasonable to have standard digital > filters for these. That would obviously require that they > be defined for specific sample rates, though. > > Well, maybe standard filters at 44.1kHz and 48kHz would be enough. > > -- glen Glen, The sample rate question is one of two potential problems I see for digital equivalents. Since some use the analog versions as gospel - they are cited in certains specs and regulations, so how close does a digital version need to be to a "standard" analog version to be accepted as equivalent? Maybe if someone compiled a table of digital representations for several of these filters using various levels of approximation and for some of the more common sample rates, there's a chance that they could become a standard. I'm sure if someone researched the original papers that resulted in these curves and found the experimental uncertainties, that could be used to guide the order of approximation and become a basis for the efficacy of the approximations. FWIW, Clay
From: Clay on 29 Apr 2010 12:32 On Apr 28, 10:56 pm, Mark <makol...(a)yahoo.com> wrote: > > > So you are talking about a one pole (one complex pole pair) filter? > > > How does a pole pair -- complex or otherwise -- become one pole? Even a > > pair of coincident poles will have a shape different from a single pole.. > > > Jerry > > -- > > ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ > Jerry, > > yes I agree with you 100%. > > My background is analog and RF and it has been and still is common > practice for analog RF guys to call a filter with 3 LC tuned circuits > a "3 pole filter" even though as you point out this is technically > incorrect and is actually a filter with 3 complex pole pairs. > > It took me a while to sort all this out when I was trying to expand my > background from analog RF to include a bit of DSP as well. > > So depending on who you are talking to, the vernacular for a tuned > circuit is "a pole" (technically wrong) or more correctly a "complex > pole pair". > > I can tell you from experience if you say to some folks, this filter > has 3 complex pole pairs, they will look at you funny and say oh you > mean it has 3 poles...... I say yeah, that's it... :-) > > thanks > Mark Of course calling this "3 poles" is at odds with the transfer equation being a 6th order polynomial. It is through the requirement that the polynomial's coefficients being real valued that the roots occur in conjugate pairs. How many noncombinable reactive elements are in your "3 pole" filter? From a physics point of view there are 6 places the energy is stored. I think that the people who insist on calling this a 3 pole filter are being sloppy and inconsistant in their terminology. What would these guys call a simple rc filter - a 1/2 pole filter? I hope not! my 2 cents worth. Clay
From: glen herrmannsfeldt on 29 Apr 2010 14:51 Clay <clay(a)claysturner.com> wrote: (snip, I wrote) >> I wonder if it would be reasonable to have standard digital >> filters for these. ?That would obviously require that they >> be defined for specific sample rates, though. ? > The sample rate question is one of two potential problems I see for > digital equivalents. Since some use the analog versions as gospel - > they are cited in certains specs and regulations, so how close does a > digital version need to be to a "standard" analog version to be > accepted as equivalent? Well, there is still the tolerance on the analog compenents. Resistors with 1% tolerance aren't hard to find, maybe a little harder for capacitors. Is there a suggestion that the analog version should do better than with 1% tolerance components? > Maybe if someone compiled a table of digital representations for > several of these filters using various levels of approximation and for > some of the more common sample rates, there's a chance that they could > become a standard. Well, the suggestion was for the standards people to do it. > I'm sure if someone researched the original papers > that resulted in these curves and found the experimental > uncertainties, that could be used to guide the order of approximation > and become a basis for the efficacy of the approximations. That is one I hadn't though about. It seems from the Wikipedia article that A weighting was defined based on the low amplitude senstivity of the ear, and so is already wrong at higher amplitude. It seems, then, that experimental uncertainties are already out the window for higher amplitudes, but what is really needed is a standard. -- glen
From: Mark on 29 Apr 2010 15:32 On Apr 29, 12:32 pm, Clay <c...(a)claysturner.com> wrote: > On Apr 28, 10:56 pm, Mark <makol...(a)yahoo.com> wrote: > > > > > > > > > So you are talking about a one pole (one complex pole pair) filter? > > > > How does a pole pair -- complex or otherwise -- become one pole? Even a > > > pair of coincident poles will have a shape different from a single pole. > > > > Jerry > > > -- > > > ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ > > Jerry, > > > yes I agree with you 100%. > > > My background is analog and RF and it has been and still is common > > practice for analog RF guys to call a filter with 3 LC tuned circuits > > a "3 pole filter" even though as you point out this is technically > > incorrect and is actually a filter with 3 complex pole pairs. > > > It took me a while to sort all this out when I was trying to expand my > > background from analog RF to include a bit of DSP as well. > > > So depending on who you are talking to, the vernacular for a tuned > > circuit is "a pole" (technically wrong) or more correctly a "complex > > pole pair". > > > I can tell you from experience if you say to some folks, this filter > > has 3 complex pole pairs, they will look at you funny and say oh you > > mean it has 3 poles...... I say yeah, that's it... :-) > > > thanks > > Mark > > Of course calling this "3 poles" is at odds with the transfer equation > being a 6th order polynomial. It is through the requirement that the > polynomial's coefficients being real valued that the roots occur in > conjugate pairs. How many noncombinable reactive elements are in your > "3 pole" filter? From a physics point of view there are 6 places the > energy is stored. I think that the people who insist on calling this a > 3 pole filter are being sloppy and inconsistant in their terminology. > What would these guys call a simple rc filter - a 1/2 pole filter? I > hope not! > > the usual context where "pole" is mis-used is RF bandpass LC filters (not lowpass) where the term pole is misused refering to "resonator" or "tuned circuit" or "tank circuit". I agree... it is wrong. Mark
From: Tauno Voipio on 29 Apr 2010 15:55
On 29.4.10 10:32 , Mark wrote: > On Apr 29, 12:32 pm, Clay<c...(a)claysturner.com> wrote: >> On Apr 28, 10:56 pm, Mark<makol...(a)yahoo.com> wrote: >> >> >> >> >> >>>>> So you are talking about a one pole (one complex pole pair) filter? >> >>>> How does a pole pair -- complex or otherwise -- become one pole? Even a >>>> pair of coincident poles will have a shape different from a single pole. >> >>>> Jerry >>>> -- >> >>> ���������������������������������������������������������������������� >>> Jerry, >> >>> yes I agree with you 100%. >> >>> My background is analog and RF and it has been and still is common >>> practice for analog RF guys to call a filter with 3 LC tuned circuits >>> a "3 pole filter" even though as you point out this is technically >>> incorrect and is actually a filter with 3 complex pole pairs. >> >>> It took me a while to sort all this out when I was trying to expand my >>> background from analog RF to include a bit of DSP as well. >> >>> So depending on who you are talking to, the vernacular for a tuned >>> circuit is "a pole" (technically wrong) or more correctly a "complex >>> pole pair". >> >>> I can tell you from experience if you say to some folks, this filter >>> has 3 complex pole pairs, they will look at you funny and say oh you >>> mean it has 3 poles...... I say yeah, that's it... :-) >> >>> thanks >>> Mark >> >> Of course calling this "3 poles" is at odds with the transfer equation >> being a 6th order polynomial. It is through the requirement that the >> polynomial's coefficients being real valued that the roots occur in >> conjugate pairs. How many noncombinable reactive elements are in your >> "3 pole" filter? From a physics point of view there are 6 places the >> energy is stored. I think that the people who insist on calling this a >> 3 pole filter are being sloppy and inconsistant in their terminology. >> What would these guys call a simple rc filter - a 1/2 pole filter? I >> hope not! >> >> > > the usual context where "pole" is mis-used is RF bandpass LC filters > (not lowpass) where the term pole is misused refering to "resonator" > or "tuned circuit" or "tank circuit". > > I agree... it is wrong. > > Mark The naming of pole count for bandpass filters may be coming from the design procedure where a low-pass prototype is constructed with the number of poles (3 for a 3 resonator filter). The low-pass prototype is then transferred to the center frequency by resonating each capacitor with an inductance and each coil with a capacitor, ignoring the extra poles brought in. -- Tauno Voipio (MSEE, and OH2UG) tauno voipio (at) iki fi |