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

Started by 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.
>&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;&#65533;
>

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.
&#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, 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;
```