Is there a all-pass filters which group delay is negative

Hi,
As far as I know, the group delay of a all-pass filters always is a
positive number. Is there a all-pass filters which group delay is
negative？
Alan

On 9/7/2011 10:56 PM, zaitax wrote:
> Hi,
> As far as I know, the group delay of a all-pass filters always is a
> positive number. Is there a all-pass filters which group delay is
> negative？
> Alan

Group delay measures the time between when energy (or information) goes 
in and when it comes out. Your question amounts to asking if energy can 
come out before it went in. I'm rooting for you to be able to answer 
that on your own.

Jerry
-- 
Engineering is the art of making what you want from things you can get.

>On 9/7/2011 10:56 PM, zaitax wrote:
>> Hi,
>> As far as I know, the group delay of a all-pass filters always is a
>> positive number. Is there a all-pass filters which group delay is
>> negative？
>> Alan
>
>Group delay measures the time between when energy (or information) goes 
>in and when it comes out. Your question amounts to asking if energy can 
>come out before it went in. I'm rooting for you to be able to answer 
>that on your own.
>
>Jerry
>-- 
>Engineering is the art of making what you want from things you can get.
>

There are some negative group delay filter, Such as, peakingEQ has a
negative group delay peak when the gain is negative.

Jerry Avins <jya@ieee.org> wrote:
> On 9/7/2011 10:56 PM, zaitax wrote:

>> As far as I know, the group delay of a all-pass filters always is a
>> positive number. Is there a all-pass filters which group delay is
>> negative&#4294967295;??
>> Alan

> Group delay measures the time between when energy (or information) goes 
> in and when it comes out. Your question amounts to asking if energy can 
> come out before it went in. I'm rooting for you to be able to answer 
> that on your own.

Well, there are materials with negative group velocity (over
a specific frequency range).  For a given length, the group delay
will be negative.  More specifically, there are materials with
a negative index of refraction, usually just past a resonance.

(There are also materials with complex index of refraction.)

-- glen

On 9/7/11 11:47 PM, zaitax wrote:
>> On 9/7/2011 10:56 PM, zaitax wrote:
>>> Hi,
>>> As far as I know, the group delay of a all-pass filters always is a
>>> positive number. Is there a all-pass filters which group delay is
>>> negative？
>>> Alan
>>
>> Group delay measures the time between when energy (or information) goes
>> in and when it comes out. Your question amounts to asking if energy can
>> come out before it went in. I'm rooting for you to be able to answer
>> that on your own.
>>
>
> There are some negative group delay filter, Such as, peakingEQ has a
> negative group delay peak when the gain is negative.
>

you are correct.  and since it's group delay (not phase delay) and the 
derivative of phase is involved, it is never an ambiguity involving how 
the phase might be wrapped or unwrapped.

so yes, there is this mathematical parameter we call "group delay" that 
sometimes is negative, even with filters that are causal.  that is true.

but i'm with Jerry in rooting for you to answer this question yourself, 
and when you do, would you be so kind as to report your results?

because for APFs that are not FIRs (like some kinda delay or something 
like that), any IIR APF with real coefficients is gonna be a combination 
of 1st and 2nd order biquad APFs.  so all's you need to do is answer 
this question for the case of a general 1st-order APF and for a general 
resonant 2nd-order APF.  and, because of the "frequency warping" mapping 
of the bilinear transform, you can do this for 1st and 2nd-order 
*analog* APFs and whatever conclusion you get there will also be true 
for digital (even though the phase has a one-to-one mapping and the 
derivative will not have that, at least we know that if the analog phase 
is smooth and strictly decreasing, that property will be preserved with 
the bilinear transform).

just thinking about it, i can tell you that no 1st-order APF will have 
negative group delay.

there is no loss of generality to normalize the resonant frequency.  so 
you need to show that for any positive Q greater than 1/2 (if Q < 1/2, 
it ain't a resonant APF), that the derivative of the phase vs. frequency 
curve is always negative.  i don't think that will be hard to do.

so we cut your work out for you, but you have to sew the pieces together.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On Sep 8, 2:56&nbsp;pm, "zaitax" <zaitax@n_o_s_p_a_m.qq.com> wrote:
> Hi,
> As far as I know, the group delay of a all-pass filters always is a
> positive number. Is there a all-pass filters which group delay is
> negative&#65311;
> Alan

Sort of, negative group-delay is possible over a limited freq range.


Hardy

>On 9/7/11 11:47 PM, zaitax wrote:
>>> On 9/7/2011 10:56 PM, zaitax wrote:
>>>> Hi,
>>>> As far as I know, the group delay of a all-pass filters always is a
>>>> positive number. Is there a all-pass filters which group delay is
>>>> negative？
>>>> Alan
>>>
>>> Group delay measures the time between when energy (or information)
goes
>>> in and when it comes out. Your question amounts to asking if energy
can
>>> come out before it went in. I'm rooting for you to be able to answer
>>> that on your own.
>>>
>>
>> There are some negative group delay filter, Such as, peakingEQ has a
>> negative group delay peak when the gain is negative.
>>
>
>you are correct.  and since it's group delay (not phase delay) and the 
>derivative of phase is involved, it is never an ambiguity involving how 
>the phase might be wrapped or unwrapped.
>
>so yes, there is this mathematical parameter we call "group delay" that 
>sometimes is negative, even with filters that are causal.  that is true.
>
>but i'm with Jerry in rooting for you to answer this question yourself, 
>and when you do, would you be so kind as to report your results?
>
>because for APFs that are not FIRs (like some kinda delay or something 
>like that), any IIR APF with real coefficients is gonna be a combination 
>of 1st and 2nd order biquad APFs.  so all's you need to do is answer 
>this question for the case of a general 1st-order APF and for a general 
>resonant 2nd-order APF.  and, because of the "frequency warping" mapping 
>of the bilinear transform, you can do this for 1st and 2nd-order 
>*analog* APFs and whatever conclusion you get there will also be true 
>for digital (even though the phase has a one-to-one mapping and the 
>derivative will not have that, at least we know that if the analog phase 
>is smooth and strictly decreasing, that property will be preserved with 
>the bilinear transform).
>
>just thinking about it, i can tell you that no 1st-order APF will have 
>negative group delay.
>
>there is no loss of generality to normalize the resonant frequency.  so 
>you need to show that for any positive Q greater than 1/2 (if Q < 1/2, 
>it ain't a resonant APF), that the derivative of the phase vs. frequency 
>curve is always negative.  i don't think that will be hard to do.
>
>so we cut your work out for you, but you have to sew the pieces together.
>
>-- 
>
>r b-j                  rbj@audioimagination.com
>
>"Imagination is more important than knowledge."
>
>
>

If Q is negative, then the group delay will be negative too, but it will
become a unstable all-pass filter. If unstable filter can be realized, that
could be fine.

So I don't know where to begin about negative group delay all pass filter,
as no 1st-order APF have negative group delay.

>On Sep 8, 2:56=C2=A0pm, "zaitax" <zaitax@n_o_s_p_a_m.qq.com> wrote:
>> Hi,
>> As far as I know, the group delay of a all-pass filters always is a
>> positive number. Is there a all-pass filters which group delay is
>> negative=EF=BC=9F
>> Alan
>
>Sort of, negative group-delay is possible over a limited freq range.
>
>
>Hardy
>

The phase response of any allpass filter with real coefficients is a
monotonically decreasing function. Therefore the groupdelay is > 0 for all
frequencies.

i sayed:
...
 >> you need to show that for any positive Q greater than 1/2 (if Q <
 >> 1/2, it ain't a resonant APF), that the derivative of the phase vs.
 >> frequency curve is always negative.
...

On 9/8/11 2:31 AM, zaitax wrote:
 >
 > If Q is negative,

lessee, "If Q is negative", is that compatible with "Q greater than 1/2"?

 > then the group delay will be negative too, but it will
 > become a unstable all-pass filter. If unstable filter can be
 > realized, that could be fine.

you can realize an unstable filter, all-pass or not.  when you operate 
such a filter, what do you expect to happen?  could be "fine".

 > So I don't know where to begin about negative group delay all pass
 > filter, as no 1st-order APF have negative group delay.

sheesh.  better hope that Vlad doesn't see this.  i think his Shift or 
Caps Lock keys must be getting worn.


On 9/8/11 3:10 AM, niarn wrote:
>
> The phase response of any allpass filter with real coefficients is a
> monotonically decreasing function. Therefore the groupdelay is>  0 for all
> frequencies.

watch out for zaitax's Q<0 APF.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On Sep 8, 5:07&#4294967295;pm, robert bristow-johnson <r...@audioimagination.com>
wrote:
> i sayed:
> ...
> &#4294967295;>> you need to show that for any positive Q greater than 1/2 (if Q <
> &#4294967295;>> 1/2, it ain't a resonant APF), that the derivative of the phase vs.
> &#4294967295;>> frequency curve is always negative.
> ...
>
> On 9/8/11 2:31 AM, zaitax wrote:
> &#4294967295;>
> &#4294967295;> If Q is negative,
>
> lessee, "If Q is negative", is that compatible with "Q greater than 1/2"?
>
> &#4294967295;> then the group delay will be negative too, but it will
> &#4294967295;> become a unstable all-pass filter. If unstable filter can be
> &#4294967295;> realized, that could be fine.
>
> you can realize an unstable filter, all-pass or not. &#4294967295;when you operate
> such a filter, what do you expect to happen? &#4294967295;could be "fine".
>
> &#4294967295;> So I don't know where to begin about negative group delay all pass
> &#4294967295;> filter, as no 1st-order APF have negative group delay.
>
> sheesh. &#4294967295;better hope that Vlad doesn't see this. &#4294967295;i think his Shift or
> Caps Lock keys must be getting worn.
>
> On 9/8/11 3:10 AM, niarn wrote:
>
>
>
> > The phase response of any allpass filter with real coefficients is a
> > monotonically decreasing function. Therefore the groupdelay is> &#4294967295;0 for all
> > frequencies.
>
> watch out for zaitax's Q<0 APF.
>
> --
>
> r b-j &#4294967295; &#4294967295; &#4294967295; &#4294967295; &#4294967295; &#4294967295; &#4294967295; &#4294967295; &#4294967295;r...@audioimagination.com
>
> "Imagination is more important than knowledge."

I have been burned more than once by a misunderstanding of the term
"group delay". In the case of a linear-phase FIR filter, the group
delay is 1/2 the filter length which happens to correspond to the peak
output of the filter with an impulsive input, which leads us all to
believe that this is true in general; but it's not. The "delay" part
of group delay has more to do with the envelope delay of
communications signals that consist of multiple frequencies clustered
in a very narrow bandwidth at a very high carrier frequency. I kind of
wish the term would dissapear for audio-type signals because it causes
so much confusion.

Bob