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What does "6db per octave" mean in the digital world?

Started by Unknown January 29, 2009
>banton wrote: >>>> The digital frequency response is warped. >>>> It doesn't look like a straight line going down >>>> with 6db per octave (which is what you see >>>> if you plot an analog response on a logarithmic scale - after >>>> the rolloff at the beginning), >>>> but it's a curve. >>>> Remember that the distance from the pole is what determines >>>> the amplitude. =A0And you go from freq 0 to pi in a halfcircle in >>>> the z-plane. =A0 >>>> >>>> gr >>>> Bjoern >>>> >>>>> Thanks a lot. >>> It isn't if you sample high enough though. >>> >>> Hardy >> >> What? The frequency response shape of a digital 1 pole filter looks >> the same, regardless of the sampling frequency. > >Not so. Warping depends on f/fs. > >Jerry >-- >Engineering is the art of making what you want from things you can get. >����������������������������������������������������������������������� >
Ok, I see what you mean. But still, you can't avoid the warping and get a straight line by raising the sampling rate. It's just that you get a bigger portion of the response to be less curved. At the end of the response approaching pi you will again get strong deviation from the analog response. Of course it's wrong what I said in my message before; the responses do not look the same at different Fs. The shape of a filter with cutoff at 0.5 pi will allways look the same, but 0.5 pi isn't the same cutoff freq if you change the sampling rate (I am stating the obvious, but that made me write my (wrong) statement). thanks, Bjoern
banton wrote:

   ...

> Ok, I see what you mean. > But still, you can't avoid the warping and get a straight line > by raising the sampling rate. > It's just that you get a bigger portion of the response to be > less curved. At the end of the response approaching pi you will > again get strong deviation from the analog response. > > Of course it's wrong what I said in my message before; > the responses do not look the same at different Fs. > The shape of a filter with cutoff at 0.5 pi will > allways look the same, but 0.5 pi isn't the same cutoff freq > if you change the sampling rate (I am stating the obvious, but > that made me write my (wrong) statement).
You see it now. I'm glad I helped you to think it out. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
On Jan 30, 10:02&#2013266080;pm, "banton" <bant...@web.de> wrote:
> >> The digital frequency response is warped. > >> It doesn't look like a straight line going down > >> with 6db per octave (which is what you see > >> if you plot an analog response on a logarithmic scale - after > >> the rolloff at the beginning), > >> but it's a curve. > >> Remember that the distance from the pole is what determines > >> the amplitude. =A0And you go from freq 0 to pi in a halfcircle in > >> the z-plane. =A0 > > >> gr > >> Bjoern > > >> >Thanks a lot. > > >It isn't if you sample high enough though. > > >Hardy > > What? &#2013266080;The frequency response shape of a digital 1 pole filter looks > the same, regardless of the sampling frequency. > > gr. > Bjoern
The higher you sample relative to the cut-off of your filter, the nearer it is to analogue. So it will have the right slope. Hardy
On Jan 31, 6:31&#2013266080;am, "banton" <bant...@web.de> wrote:
> >banton wrote: > >>>> The digital frequency response is warped. > >>>> It doesn't look like a straight line going down > >>>> with 6db per octave (which is what you see > >>>> if you plot an analog response on a logarithmic scale - after > >>>> the rolloff at the beginning), > >>>> but it's a curve. > >>>> Remember that the distance from the pole is what determines > >>>> the amplitude. =A0And you go from freq 0 to pi in a halfcircle in > >>>> the z-plane. =A0 > > >>>> gr > >>>> Bjoern > > >>>>> Thanks a lot. > >>> It isn't if you sample high enough though. > > >>> Hardy > > >> What? &#2013266080;The frequency response shape of a digital 1 pole filter looks > >> the same, regardless of the sampling frequency. > > >Not so. Warping depends on f/fs. > > >Jerry > >-- > >Engineering is the art of making what you want from things you can get. > > > > Ok, I see what you mean. > But still, you can't avoid the warping and get a straight line > by raising the sampling rate. > It's just that you get a bigger portion of the response to be > less curved. &#2013266080;At the end of the response approaching pi you will > again get strong deviation from the analog response. > > Of course it's wrong what I said in my message before; > the responses do not look the same at different Fs. &#2013266080; > The shape of a filter with cutoff at 0.5 pi will > allways look the same, but 0.5 pi isn't the same cutoff freq > if you change the sampling rate (I am stating the obvious, but > that made me write my (wrong) statement). > > thanks, > Bjoern
That's right but who cares? You always have a finite bandwidth you operate over. Hardy
x-no-archive:
> > Ok, I see what you mean. > But still, you can't avoid the warping and get a straight line > by raising the sampling rate. > It's just that you get a bigger portion of the response to be > less curved. &#2013266080;At the end of the response approaching pi you will > again get strong deviation from the analog response. > > Of course it's wrong what I said in my message before; > the responses do not look the same at different Fs. &#2013266080; > The shape of a filter with cutoff at 0.5 pi will > allways look the same, but 0.5 pi isn't the same cutoff freq > if you change the sampling rate (I am stating the obvious, but > that made me write my (wrong) statement). > >
I thought there was a technique to adjust the coeffefficents to pre- warp the response so that the response remains closer to "ideal" over a wider frequency range... But of course, as you say, when you actually get to Fs/2, it's all over. Mark
makolber@yahoo.com wrote:
> x-no-archive: >> Ok, I see what you mean. >> But still, you can't avoid the warping and get a straight line >> by raising the sampling rate. >> It's just that you get a bigger portion of the response to be >> less curved. At the end of the response approaching pi you will >> again get strong deviation from the analog response. >> >> Of course it's wrong what I said in my message before; >> the responses do not look the same at different Fs. >> The shape of a filter with cutoff at 0.5 pi will >> allways look the same, but 0.5 pi isn't the same cutoff freq >> if you change the sampling rate (I am stating the obvious, but >> that made me write my (wrong) statement). >> >> > > I thought there was a technique to adjust the coeffefficents to pre- > warp the response so that the response remains closer to "ideal" over > a wider frequency range... But of course, as you say, when you > actually get to Fs/2, it's all over.
Prewarping can move a single critical (read important) frequency to where it is needed, but it cannot straighten a curved response. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
On Jan 30, 6:13&#2013266080;pm, Jerry Avins <j...@ieee.org> wrote:
> makol...@yahoo.com wrote: > > x-no-archive: > >> Ok, I see what you mean. > >> But still, you can't avoid the warping and get a straight line > >> by raising the sampling rate. > >> It's just that you get a bigger portion of the response to be > >> less curved. &#2013266080;At the end of the response approaching pi you will > >> again get strong deviation from the analog response. > > >> Of course it's wrong what I said in my message before; > >> the responses do not look the same at different Fs. &#2013266080; > >> The shape of a filter with cutoff at 0.5 pi will > >> allways look the same, but 0.5 pi isn't the same cutoff freq > >> if you change the sampling rate (I am stating the obvious, but > >> that made me write my (wrong) statement). > > > I thought there was a technique to adjust the coeffefficents to pre- > > warp the response so that the response remains closer to "ideal" over > > a wider frequency range... &#2013266080; But of course, as you say, when you > > actually get to Fs/2, it's all over. > > Prewarping can move a single critical (read important) frequency to > where it is needed, but it cannot straighten a curved response. > > Jerry >
OK thank you I didn't know that.. But why would that be so? If you can choose coefficients to create any arbitray shape (within reason) then why could you not choose a set of coef that create a response that is curved in some crazy way such that AFTER warping was a nice -6 dB per octave shape over a limited range anyway... I I'm not saying you are wrong, I'm just trying to understand why.. Mark
makolber@yahoo.com wrote:
> On Jan 30, 6:13 pm, Jerry Avins <j...@ieee.org> wrote: >> makol...@yahoo.com wrote: >>> x-no-archive: >>>> Ok, I see what you mean. >>>> But still, you can't avoid the warping and get a straight line >>>> by raising the sampling rate. >>>> It's just that you get a bigger portion of the response to be >>>> less curved. At the end of the response approaching pi you will >>>> again get strong deviation from the analog response. >>>> Of course it's wrong what I said in my message before; >>>> the responses do not look the same at different Fs. >>>> The shape of a filter with cutoff at 0.5 pi will >>>> allways look the same, but 0.5 pi isn't the same cutoff freq >>>> if you change the sampling rate (I am stating the obvious, but >>>> that made me write my (wrong) statement). >>> I thought there was a technique to adjust the coeffefficents to pre- >>> warp the response so that the response remains closer to "ideal" over >>> a wider frequency range... But of course, as you say, when you >>> actually get to Fs/2, it's all over. >> Prewarping can move a single critical (read important) frequency to >> where it is needed, but it cannot straighten a curved response. >> >> Jerry >> > > OK thank you I didn't know that.. > > But why would that be so? If you can choose coefficients to create > any arbitray shape (within reason) then why could you not choose a set > of coef that create a response that is curved in some crazy way such > that AFTER warping was a nice -6 dB per octave shape over a limited > range anyway... I > > I'm not saying you are wrong, I'm just trying to understand why..
You can create nearly any arbitrary shape, but not with just a single pole. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
On Jan 31, 9:21&#2013266080;pm, Jerry Avins <j...@ieee.org> wrote:
> makol...@yahoo.com wrote: > > On Jan 30, 6:13 pm, Jerry Avins <j...@ieee.org> wrote: > >> makol...@yahoo.com wrote: > >>> x-no-archive: > >>>> Ok, I see what you mean. > >>>> But still, you can't avoid the warping and get a straight line > >>>> by raising the sampling rate. > >>>> It's just that you get a bigger portion of the response to be > >>>> less curved. &#2013266080;At the end of the response approaching pi you will > >>>> again get strong deviation from the analog response. > >>>> Of course it's wrong what I said in my message before; > >>>> the responses do not look the same at different Fs. &#2013266080; > >>>> The shape of a filter with cutoff at 0.5 pi will > >>>> allways look the same, but 0.5 pi isn't the same cutoff freq > >>>> if you change the sampling rate (I am stating the obvious, but > >>>> that made me write my (wrong) statement). > >>> I thought there was a technique to adjust the coeffefficents to pre- > >>> warp the response so that the response remains closer to "ideal" over > >>> a wider frequency range... &#2013266080; But of course, as you say, when you > >>> actually get to Fs/2, it's all over. > >> Prewarping can move a single critical (read important) frequency to > >> where it is needed, but it cannot straighten a curved response. > > >> Jerry > > > OK thank you I didn't know that.. > > > But why would that be so? &#2013266080;If you can choose coefficients to create > > any arbitray shape (within reason) then why could you not choose a set > > of coef that create a response that is curved in some crazy way such > > that AFTER warping was a nice -6 dB per octave shape over a limited > > range anyway... I > > > I'm not saying you are wrong, I'm just trying to understand why.. > > You can create nearly any arbitrary shape, but not with just a single pole. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;- Hide quoted text - > > - Show quoted text -
OK, but using some number of coeff, i can create a perhaps complicated response that after warping resembles a single pole -6 dB per octave over a reasonable range of frequencies, no? Mark
makolber@yahoo.com wrote:

   ...

> OK, but using some number of coeff, i can create a perhaps complicated > response that after warping resembles a single pole -6 dB per octave > over a reasonable range of frequencies, no?
The more complex you make the filter, the closer you can bring your approximate straight-line response to fs/2. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;