LPF butterworth filter question
in [DSP]
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From: zs on 21 May 2010 10:26 On máj. 21, 15:22, Jerry Avins <j...(a)ieee.org> wrote: > On 5/21/2010 8:19 AM, zs wrote: > > ... > > > I can't see what's your problem. Some more technical comments wouldn't > > take more time to post. > > If you show the gain on a linear scale instead of using decibels, what > Rune is trying to tell you will become immediately clear. Of course, you > will need to print the numbers out as a table. They would be impossible > to show as a graph even on an entire roll of newsprint. > > http://www.harvestofhistory.org/assets/object-images/main/Paper1.jpg > > Jerry > -- > "I view the progress of science as ... the slow erosion of the tendency > to dichotomize." --Barbara Smuts, U. Mich. > ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ Thank you for the meaningful comment. Of course I didn't mean to calculate and plot the magnitude response in decibels down to -infty. What I said is that IMHO it makes sense to calculate the response in the magnitude domain which is to be plotted on the screen (say from -1000 to 0 dB), in spite of the fact that actual response of the realized filter will be different. Zsolt
From: Mikolaj on 21 May 2010 11:43 On 21-05-2010 at 08:59:00 zs <zsolt.garamvolgyi(a)gmail.com> wrote: (...) > What I'm talking about is filter design and visualization: when > designing a filter, I think it's useful to see its actual response (...) And they are actual and precise. Fdatool generates digital filters coefficients. (...) > without taking 'secondary' effects into account. What do you mean, there is no secondary effects. They all are primary. (...) > (visualized) response being corrupted below -150 dB won't imply any > problems during realization, (...) Frequency response is just perfectly the same as later realization. (...) > but having a correct response in a larger > dynamic range gives insight on the filter design process: (...) Maybe you would like an analog filter. Then you should use proper tool for that. My best analog design tool is pen and paper. The all infinities I plot in my mind because I have only finite sheet of paper. > Zsolt -- Mikolaj
From: Jerry Avins on 21 May 2010 11:46 On 5/21/2010 10:26 AM, zs wrote: > On m�j. 21, 15:22, Jerry Avins<j...(a)ieee.org> wrote: >> On 5/21/2010 8:19 AM, zs wrote: >> >> ... >> >>> I can't see what's your problem. Some more technical comments wouldn't >>> take more time to post. >> >> If you show the gain on a linear scale instead of using decibels, what >> Rune is trying to tell you will become immediately clear. Of course, you >> will need to print the numbers out as a table. They would be impossible >> to show as a graph even on an entire roll of newsprint. >> >> http://www.harvestofhistory.org/assets/object-images/main/Paper1.jpg >> >> Jerry >> -- >> "I view the progress of science as ... the slow erosion of the tendency >> to dichotomize." --Barbara Smuts, U. Mich. >> ����������������������������������������������������������������������� > > Thank you for the meaningful comment. > > Of course I didn't mean to calculate and plot the magnitude response > in decibels down to -infty. What I said is that IMHO it makes sense to > calculate the response in the magnitude domain which is to be plotted > on the screen (say from -1000 to 0 dB), in spite of the fact that > actual response of the realized filter will be different. Stop babbling and start thinking. If the difference between a voltage representing -350 dB and -351 dB is represented by one pixel, how many pixels are between the the voltage that represents -350 dB 0 dB? Now extend the lower limit to -1000 dB. At 200 pixels per inch, how far apart are those points? Get real! By the way: Your filter is not a digital version of a Butterworth. It is a digital *approximation* that shows severe frequency warping as fs/2 is approached and is totally invalid above that frequency. Jerry -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. �����������������������������������������������������������������������
From: Steve Pope on 21 May 2010 12:11 Jerry Avins <jya(a)ieee.org> wrote: >On 5/21/2010 10:26 AM, zs wrote: >> On m�j. 21, 15:22, Jerry Avins<j...(a)ieee.org> wrote: >>> On 5/21/2010 8:19 AM, zs wrote: >>> >>> If you show the gain on a linear scale instead of using decibels, what >>> Rune is trying to tell you will become immediately clear. Of course, you >>> will need to print the numbers out as a table. They would be impossible >>> to show as a graph even on an entire roll of newsprint. >> Thank you for the meaningful comment. >> Of course I didn't mean to calculate and plot the magnitude response >> in decibels down to -infty. What I said is that IMHO it makes sense to >> calculate the response in the magnitude domain which is to be plotted >> on the screen (say from -1000 to 0 dB), in spite of the fact that >> actual response of the realized filter will be different. >Stop babbling and start thinking. If the difference between a voltage >representing -350 dB and -351 dB is represented by one pixel, how many >pixels are between the the voltage that represents -350 dB 0 dB? Now >extend the lower limit to -1000 dB. At 200 pixels per inch, how far >apart are those points? Get real! I think what the OP just said about is sensible. This is a 30th order Butterworth, hence is rolling off at 180 dB per octave, therefore one is able to plot the log of its magnitude response and see a smooth rolloff over several hundred dB as one goes a few octaves past the corner frequency. Get fdatool to spit out lattice coefficients (which they have some vaguely non-standard name for, I think "ARMA something"). Then the worst effects of coefficient roundoff error will mostly go away, and you can (by various techniques) compute a response. You will not need more than double-precision floating point to do this. If you instead try to realize it as a direct form, you likely do not have the precision. Steve
From: Jerry Avins on 22 May 2010 09:04
On 5/21/2010 12:11 PM, Steve Pope wrote: > Jerry Avins<jya(a)ieee.org> wrote: > >> On 5/21/2010 10:26 AM, zs wrote: > >>> On m�j. 21, 15:22, Jerry Avins<j...(a)ieee.org> wrote: > >>>> On 5/21/2010 8:19 AM, zs wrote: >>>> >>>> If you show the gain on a linear scale instead of using decibels, what >>>> Rune is trying to tell you will become immediately clear. Of course, you >>>> will need to print the numbers out as a table. They would be impossible >>>> to show as a graph even on an entire roll of newsprint. > >>> Thank you for the meaningful comment. > >>> Of course I didn't mean to calculate and plot the magnitude response >>> in decibels down to -infty. What I said is that IMHO it makes sense to >>> calculate the response in the magnitude domain which is to be plotted >>> on the screen (say from -1000 to 0 dB), in spite of the fact that >>> actual response of the realized filter will be different. > >> Stop babbling and start thinking. If the difference between a voltage >> representing -350 dB and -351 dB is represented by one pixel, how many >> pixels are between the the voltage that represents -350 dB 0 dB? Now >> extend the lower limit to -1000 dB. At 200 pixels per inch, how far >> apart are those points? Get real! > > I think what the OP just said about is sensible. This is a > 30th order Butterworth, hence is rolling off at 180 dB per octave, > therefore one is able to plot the log of its magnitude response > and see a smooth rolloff over several hundred dB as one goes > a few octaves past the corner frequency. ... Where does it say 30th order? The spec reads "Single section", and kai_the_ruler has so far ignored my request for clarification. Let's look at his casual request for good resolution down to -1000 dB. That's a voltage ratio of 10^50. If the smallest step in the linear scale that I suggest might provide him with insight is one pixel, and we plot with 200 pixels/inch*, then we need 5e47 inches of paper to plot the entire curve. That is a length best measured in astronomical units, the mean distance between earth and the sun. (I did the calculation. I was wrong about A.U. being suitable. The result is 8.4854e34 A.U. As near as I figure, that comes out to 1,344e27 light years.) How big is the universe? :-) Maybe A.U. is a suitable unit for 350 dB. Jerry _________________________________ * A photograph is considered to be in sharp focus if no circle of confusion is larger than .005". -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. ����������������������������������������������������������������������� |