LPF butterworth filter question
in [DSP]
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From: zs on 22 May 2010 14:31 On máj. 21, 17:46, Jerry Avins <j...(a)ieee.org> wrote: > On 5/21/2010 10:26 AM, zs wrote: > > > > > > > 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. > > 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! > Obviously, I'm talking about plotting the response in decibels as shown on the figure provided by the OP. Let's assume that the magnitude response approaches to zero at fs/2. Then the precision needed during the calculation of the filter response in order to plot it correctly is determined by the limits of the magnitude axis (e.g., 0 to -1000 dB). By 'correct' plotting I mean the response is not corrupted by the 'fuzz' in the magnitude domain between those limits. > 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 Ok, what is your definition of the 'digital version of a Butterworth' filter? As a 'digital Butterworth' I refer to an approximation of the analog Butterworth filter. > approached and is totally invalid above that frequency. > As the response of any discrete-time filter is periodic with fs, why would anyone expect any discrete-time approximation of an analog filter be correct above fs/2? The magnitude response of an analog Butterworth LPF tends to zero (= - infinity dB) as the freq. tends to infinity. The bilinear transform maps the entire (analog) frequency axis to the frequencies between fs/ 2 and -fs/2, therefore, the magnitude response of the digital filter tends to -infty dB at fs/2. If you transform the analog LPF by using a different method (e.g., impulse invariance), the digital response will be different. My point, which is not some magical thing that deserves such a long discussion, is that plotting the magnitude response under, say, -350 dB, which may require increased precision to calculate correctly, can IMHO (!) be useful because it contains more information on the filter design process than the fuzz seen on the figure of the OP. > Jerry > -- > "I view the progress of science as ... the slow erosion of the tendency > to dichotomize." --Barbara Smuts, U. Mich. > ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
From: Jerry Avins on 22 May 2010 15:06 On 5/22/2010 2:31 PM, zs wrote: > ... My point, which is not some magical thing that deserves > such a long discussion, is that plotting the magnitude response under, > say, -350 dB, which may require increased precision to calculate > correctly, can IMHO (!) be useful because it contains more information > on the filter design process than the fuzz seen on the figure of the > OP. I suspect that you'll have a different opinion when you've designed enough filters and set them to work. Jerry -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. �����������������������������������������������������������������������
From: zs on 22 May 2010 15:07 On máj. 22, 15:04, Jerry Avins <j...(a)ieee.org> wrote: > On 5/21/2010 12:11 PM, Steve Pope wrote: > > > > > > > Jerry Avins<j...(a)ieee.org> wrote: > > >> On 5/21/2010 10:26 AM, zs wrote: > > >>> On máj. 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 If Matlab is available to you, type 'fdatool' and design the filter with the given specifications. Zsolt
From: Jerry Avins on 22 May 2010 15:15 On 5/22/2010 3:07 PM, zs wrote: > On m�j. 22, 15:04, Jerry Avins<j...(a)ieee.org> wrote: >> On 5/21/2010 12:11 PM, Steve Pope wrote: >> >> >> >> >> >>> Jerry Avins<j...(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 > > If Matlab is available to you, type 'fdatool' and design the filter > with the given specifications. Including the specification "Single section"? Jerry -- "I view the progress of science as ... the slow erosion of the tendency to dichotomize." --Barbara Smuts, U. Mich. �����������������������������������������������������������������������
From: Steve Pope on 22 May 2010 15:36
zs <zsolt.garamvolgyi(a)gmail.com> wrote: >On m�j. 22, 15:04, Jerry Avins <j...(a)ieee.org> wrote: >> > 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 It doesn't. I must have been hallucinating again. >If Matlab is available to you, type 'fdatool' and design the filter >with the given specifications. Yep. S. |