On Thu, 20 Jun 2013 15:53:32 -0700, robert bristow-johnson
<rbj@audioimagination.com> wrote:
[Snipped by Lyons]
>>
>> so Rick, is it considered "good" that your differentiator gain starts to
>> dive toward zero after you get to pi/4 (or 1/2 Nyquist)? it seems to me
>> that the simple forward difference differentiator does much better in
>> that regard.
Hi Robert,
Well, one characteristic of the forward difference
differentiator is that it amplifies high frequency
noise. So my differentiator's response goes to zero
at Fs/2 to eliminate that characteristic.
(Fs is the sample rate in Hz.)
I always get confused when people use the term
"Nyquist" when referring to frequency. I'm
often unsure of what they mean. Above you equate
pi/4 to 1/2 Nyquist. It seems to me that
pi --> Fs/2,
pi/2 --> Fs/4, and
pi/4 --> Fs/8.
>>
>> i am in need of a decent differentiator and when i think of applying the
>> bilinear transform (BLT) directly to the problem:
>>
>> H(z) = 2*(1 - z^-1)/(1 + z^-1)
>>
>> because of BLT frequency warping, the gain shoots up to +inf at Nyquist
>> (small wonder since there is a pole directly on z=-1), which is too much
>> correction (the opposite problem of Rick's differentiator).
Yep, that transfer function makes for a great
oscillator at Fs/2.
>>i would
>> really like to do this with a first order filter and i think if we can
>> just back off on that nasty quasi-stable pole:
>>
>> H(z) = 2*(1 - z^-1)/(1 - p*z^-1)
>>
>> we can get something that might work pretty good. pole p would be close
>> to -1, but clearly inside the unit circle.
>>
>> has anyone tried this (the latter transfer function) and what value of p
>> had you used?
>>
>> please get back in a hurry to prevent me from re-inventing the wheel. if
>> i end up reinventing the blankity-blank wheel, i'll tell you how round i
>> got it to be.
>>
>
>okay, so i got this wheel (actually 2 of them).
>
>if you use the simple transfer function above (the scaling of 2 doesn't
>matter, comes from the BLT), i figgered out that if you want the gain at
>Nyquist to be exactly twice the gain at half Nyquist, you want the pole
>p to be at p = -0.267949192.
For p = -0.267949192 I get:
Freq: Gain:
Fs/2 5.464
Fs/4 2.732
Fs/8 1.27
>
>or, if you want the gain at 1/2 Nyquist to be exactly twice the gain at
>1/4 Nyquist, then the pole should be p = -0.694566677 .
For p = -0.694566677 I get:
Freq: Gain:
Fs/2 13.1
Fs/4 2.32
Fs/8 0.975
>i like the latter one the best. it looks pretty good.
>
>gee, i wish some bright undergrad EE student that doesn't have anything
>to do, if he/she would've done this for us and save me time. it can
>still be generalized a little where we can come up for an expression of
>p that preserves this double-the-gain-for-doubling-the-frequency
>relationship for an arbitrary frequency between 0 and pi/2. it would be
>nice if someone might do that and report the results, because i ain't gonna.
>
>L8r,
See Ya,
[-Rick-]
No. 6: "Where am I?"
No. 2: "In the Village."
No. 6: "What do you want?"
No. 2: "Information."
No. 6: "Who are you?"
No. 2: "I am the new No. 2."
No. 6: "Who is No. 1?"
No. 2: "You are No. 6."
No. 6: "I am not a number. I am a free man!"
Reply by robert bristow-johnson●June 20, 20132013-06-20
On 6/20/13 12:32 PM, robert bristow-johnson wrote:
>
> okay, so it just happens that now this topic is getting important to me.
>
> On 6/9/13 12:54 PM, Rick Lyons wrote:
>> On Sat, 08 Jun 2013 23:24:01 -0400, Jerry Avins<jya@ieee.org> wrote:
>>
> ...
>>>>> On Thursday, June 6, 2013 7:11:53 PM UTC+12, Mimar wrote:
>>>>>>
>>>>>> could somebody give me an advice? At the moment I am solving
>>>>>> interesting problem. I have been using SW PLL with SOGI circuit to
>>>>>> obtain grid frequency
> ...
>>>
>>> Digital approximations to derivatives come in many forms. The simplest
>>> and most intuitive is simply y[n]=x[n-1]-x[n]. For many applications,
>>> y[n]=.5(x[n-2]-2.c[n-1]+x[n]) is better. The cost is an extra clock of
>>> latency. Rick Lyons improves on that with two more delay terms and the
>>> corresponding extra latency. I'm not certain that I'm at liberty to
>>> provide more details. I expect that he will.
>>>
> ...
>> If you're referring to the differentiator that
>> I think you are, then it's described in detail
>> at:
>>
>> http://www.dsprelated.com/showarticle/35.php
>>
>
> so Rick, is it considered "good" that your differentiator gain starts to
> dive toward zero after you get to pi/4 (or 1/2 Nyquist)? it seems to me
> that the simple forward difference differentiator does much better in
> that regard.
>
> i am in need of a decent differentiator and when i think of applying the
> bilinear transform (BLT) directly to the problem:
>
> H(z) = 2*(1 - z^-1)/(1 + z^-1)
>
> because of BLT frequency warping, the gain shoots up to +inf at Nyquist
> (small wonder since there is a pole directly on z=-1), which is too much
> correction (the opposite problem of Rick's differentiator). i would
> really like to do this with a first order filter and i think if we can
> just back off on that nasty quasi-stable pole:
>
> H(z) = 2*(1 - z^-1)/(1 - p*z^-1)
>
> we can get something that might work pretty good. pole p would be close
> to -1, but clearly inside the unit circle.
>
> has anyone tried this (the latter transfer function) and what value of p
> had you used?
>
> please get back in a hurry to prevent me from re-inventing the wheel. if
> i end up reinventing the blankity-blank wheel, i'll tell you how round i
> got it to be.
>
okay, so i got this wheel (actually 2 of them).
if you use the simple transfer function above (the scaling of 2 doesn't
matter, comes from the BLT), i figgered out that if you want the gain at
Nyquist to be exactly twice the gain at half Nyquist, you want the pole
p to be at p = -0.267949192.
or, if you want the gain at 1/2 Nyquist to be exactly twice the gain at
1/4 Nyquist, then the pole should be p = -0.694566677 .
i like the latter one the best. it looks pretty good.
gee, i wish some bright undergrad EE student that doesn't have anything
to do, if he/she would've done this for us and save me time. it can
still be generalized a little where we can come up for an expression of
p that preserves this double-the-gain-for-doubling-the-frequency
relationship for an arbitrary frequency between 0 and pi/2. it would be
nice if someone might do that and report the results, because i ain't gonna.
L8r,
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
Reply by robert bristow-johnson●June 20, 20132013-06-20
okay, so it just happens that now this topic is getting important to me.
On 6/9/13 12:54 PM, Rick Lyons wrote:
> On Sat, 08 Jun 2013 23:24:01 -0400, Jerry Avins<jya@ieee.org> wrote:
>
...
>>>> On Thursday, June 6, 2013 7:11:53 PM UTC+12, Mimar wrote:
>>>>>
>>>>> could somebody give me an advice? At the moment I am solving
>>>>> interesting problem. I have been using SW PLL with SOGI circuit to
>>>>> obtain grid frequency
...
>>
>> Digital approximations to derivatives come in many forms. The simplest
>> and most intuitive is simply y[n]=x[n-1]-x[n]. For many applications,
>> y[n]=.5(x[n-2]-2.c[n-1]+x[n]) is better. The cost is an extra clock of
>> latency. Rick Lyons improves on that with two more delay terms and the
>> corresponding extra latency. I'm not certain that I'm at liberty to
>> provide more details. I expect that he will.
>>
so Rick, is it considered "good" that your differentiator gain starts to
dive toward zero after you get to pi/4 (or 1/2 Nyquist). it seems to me
that the simple forward difference differentiator does much better in
that regard.
i am in need of a decent differentiator and when i think of applying the
bilinear transform (BLT) directly to the problem:
H(z) = 2*(1 - z^-1) / (1 + z^-1)
because of BLT frequency warping, the gain shoots up to +inf at Nyquist
(small wonder since there is a pole directly on z=-1), which is too much
correction (the opposite problem of Rick's differentiator). i would
really like to do this with a first order filter and i think if we can
just back off on that nasty quasi-stable pole:
H(z) = 2*(1 - z^-1) / (1 + p*z^-1)
we can get something that might work pretty good. pole p would be close
to -1, but clearly inside the unit circle.
has anyone tried this (the latter transfer function) and what value of p
had you used?
please get back in a hurry to prevent me from re-inventing the wheel.
if i end up reinventing the blankity-blank wheel, i'll tell you how
round i got it to be.
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
Reply by Rick Lyons●June 15, 20132013-06-15
On Tue, 11 Jun 2013 17:36:29 +0300, Tauno Voipio
<tauno.voipio@notused.fi.invalid> wrote:
[Snipped by Lyons]
>>
>> Hello Miroslav Martisek,
>> Please forgive me for my ignorance.
>> What do you mean by Bohemia?
>>
>> In the United States we have Bohemian
>> beer. But I confess, I don't know what
>> Bohemia or Bohemian means.
>>
>> [-Rick-]
>
>Hello Rick,
>
>Bohemia (German: B�hmenland) is the western part of current Czech
>Republic, the home of world's best beer.
>
>See: <https://en.wikipedia.org/wiki/Bohemia>
Hi Tauno,
Thanks for the info. As always, I continue
to learn all manner of interesting things from
you guys.
[-Rick-]
No. 6: "Where am I?"
No. 2: "In the Village."
No. 6: "What do you want?"
No. 2: "Information."
No. 6: "Who are you?"
No. 2: "I am the new No. 2."
No. 6: "Who is No. 1?"
No. 2: "You are No. 6."
No. 6: "I am not a number. I am a free man!"
Reply by Rick Lyons●June 15, 20132013-06-15
On Tue, 11 Jun 2013 12:38:28 +0000 (UTC), Miroslaw Kwasniak
<mirek@infrared.zind.ikem.pwr.wroc.pl> wrote:
Hi Miroslaw,
That's a neat web site. Thanks.
I spent some time in Germany many years ago,
and grew to love Pilsner Urquell.
As a souvenir I brought a bottle of the
"REAL" Budweiser" home with me.
[-Rick-]
No. 6: "Where am I?"
No. 2: "In the Village."
No. 6: "What do you want?"
No. 2: "Information."
No. 6: "Who are you?"
No. 2: "I am the new No. 2."
No. 6: "Who is No. 1?"
No. 2: "You are No. 6."
No. 6: "I am not a number. I am a free man!"
Reply by Rick Lyons●June 15, 20132013-06-15
On Tue, 11 Jun 2013 00:22:12 -0700 (PDT), gyansorova@gmail.com wrote:
>>
>> Hello Miroslav Martisek,
>> Please forgive me for my ignorance.
>> What do you mean by Bohemia?
>>
>> In the United States we have Bohemian
>> beer. But I confess, I don't know what
>> Bohemia or Bohemian means.
>>
>> [-Rick-]
>>
>
>A lifestyle, arty type Bohemian existence - from Europe.
>
>Bohemianism is the practice of an unconventional lifestyle, often
>in the company of like-minded people, with few permanent ties,
>involving musical, artistic, or literary pursuits. In this context,
> Bohemians may be wanderers, adventurers, or vagabonds.
>This use of the word bohemian first appeared in the English language
>in the nineteenth century[1] to describe the non-traditional lifestyles
>of marginalized and impoverished artists, writers, journalists,
>musicians, and actors in major European cities.
Hi gyansorova,
Ah ha. Thanks.
Bohemian sounds like a description of
Jerry Avins. :-)
I'll try to use the word "Bohemian" in a
conversation the next time I get a chance.
[-Rick-]
No. 6: "Where am I?"
No. 2: "In the Village."
No. 6: "What do you want?"
No. 2: "Information."
No. 6: "Who are you?"
No. 2: "I am the new No. 2."
No. 6: "Who is No. 1?"
No. 2: "You are No. 6."
No. 6: "I am not a number. I am a free man!"
Reply by Mimar●June 12, 20132013-06-12
>On 11.6.13 8:25 , Rick Lyons wrote:
>> On Mon, 10 Jun 2013 07:31:15 -0500, "Mimar" <94571@dsprelated> wrote:
>>
>>>> On Sat, 08 Jun 2013 23:24:01 -0400, Jerry Avins <jya@ieee.org> wrote:
>>>>
>>>>> On 6/7/2013 12:56 PM, Vladimir Vassilevsky wrote:
>>>>>> On 6/6/2013 4:11 PM, gyansorova@gmail.com wrote:
>>>>>>> On Thursday, June 6, 2013 7:11:53 PM UTC+12, Mimar wrote:
>>>>>>>>
>>>>>>>> could somebody give me an advice? At the moment I am solving
>>>>>>>> interesting problem. I have been using SW PLL with SOGI circuit
to
>>>>>>>> obtain grid frequency
>>>>>>
>>>>>>
>>>>>>>
>>>>>>> You could design a simple control loop with an integrator in the
>>>>>>> feedback path. This will give you band-limited differentiation ie
a
>>>>>>> slope of 6dB/octave.
>>>>>>
>>>>>> Good point. As the OP is using PLL, the output of phase detector is
>>>>>> derivative of frequency.
>>>>>>
>>>>>> VLV
>>>>> On 6/7/2013 12:56 PM, Vladimir Vassilevsky wrote:
>>>>>> On 6/6/2013 4:11 PM, gyansorova@gmail.com wrote:
>>>>>>> On Thursday, June 6, 2013 7:11:53 PM UTC+12, Mimar wrote:
>>>>>>>>
>>>>>>>> could somebody give me an advice? At the moment I am solving
>>>>>>>> interesting problem. I have been using SW PLL with SOGI circuit
to
>>>>>>>> obtain grid frequency
>>>>>>
>>>>>>
>>>>>>>
>>>>>>> You could design a simple control loop with an integrator in the
>>>>>>> feedback path. This will give you band-limited differentiation ie
a
>>>>>>> slope of 6dB/octave.
>>>>>>
>>>>>> Good point. As the OP is using PLL, the output of phase detector is
>>>>>> derivative of frequency.
>>>>>>
>>>>>> VLV
>>>>>
>>>>> It still needs filtering.
>>>>>
>>>>> Digital approximations to derivatives come in many forms. The
simplest
>>>>> and most intuitive is simply y[n]=x[n-1]-x[n]. For many
applications,
>>>>> y[n]=.5(x[n-2]-2.c[n-1]+x[n]) is better. The cost is an extra clock
of
>>>>> latency. Rick Lyons improves on that with two more delay terms and
the
>>>>> corresponding extra latency. I'm not certain that I'm at liberty to
>>>>> provide more details. I expect that he will.
>>>>>
>>>>> Jerry
>>>>
>>>> Hi Jerry,
>>>> If you're referring to the differentiator that
>>>> I think you are, then it's described in detail
>>>> at:
>>>>
>>>> http://www.dsprelated.com/showarticle/35.php
>>>>
>>>> See Ya',
>>>> [-Rick-]
>>>> No. 6: "What do you want?"
>>>> No. 2: "Information."
>>>> No. 6: "Who are you?"
>>>> No. 2: "I am the new No. 2."
>>>> No. 6: "Who is No. 1?"
>>>> No. 2: "You are No. 6."
>>>> No. 6: "I am not a number. I am a free man!"
>>>>
>>>
>>> Hello everybody,
>>>
>>> I have to say: "Thank you for your advices, some (= everyone :-)) of
them
>>> were very useful for me!"
>>>
>>> At the moment I am testing differentiator described by Rick Lyons in
>>> be work as we with my boss want. The output from differentiator is
attached
>>> to moving average filter (16th order). Resulting value of derivative
is
>>> stable now. Super :-). I think, this solution is the best of we could
>>> choose.
>>>
>>> Thanks a lot.
>>>
>>> Miroslav Martisek, Bohemia
>>
>> Hello Miroslav Martisek,
>> Please forgive me for my ignorance.
>> What do you mean by Bohemia?
>>
>> In the United States we have Bohemian
>> beer. But I confess, I don't know what
>> Bohemia or Bohemian means.
>>
>> [-Rick-]
>
>Hello Rick,
>
>Bohemia (German: B�hmenland) is the western part of current Czech
>Republic, the home of world's best beer.
>
>See: <https://en.wikipedia.org/wiki/Bohemia>
>
>--
>
>-Tauno
>
>Hello Rick,
Tauno said the truth, Bohemia is really the western part of Czech Republic
- country in the middle Europe. Namely, I am living in České Budějovice
(= Czech Budweis) now, where you can find the best beer in the world:
Budweiser Budvar (NO Anheuser-Busch "Budweiser" :-))).
Miroslav
>
Reply by Tauno Voipio●June 11, 20132013-06-11
On 11.6.13 8:25 , Rick Lyons wrote:
> On Mon, 10 Jun 2013 07:31:15 -0500, "Mimar" <94571@dsprelated> wrote:
>
>>> On Sat, 08 Jun 2013 23:24:01 -0400, Jerry Avins <jya@ieee.org> wrote:
>>>
>>>> On 6/7/2013 12:56 PM, Vladimir Vassilevsky wrote:
>>>>> On 6/6/2013 4:11 PM, gyansorova@gmail.com wrote:
>>>>>> On Thursday, June 6, 2013 7:11:53 PM UTC+12, Mimar wrote:
>>>>>>>
>>>>>>> could somebody give me an advice? At the moment I am solving
>>>>>>> interesting problem. I have been using SW PLL with SOGI circuit to
>>>>>>> obtain grid frequency
>>>>>
>>>>>
>>>>>>
>>>>>> You could design a simple control loop with an integrator in the
>>>>>> feedback path. This will give you band-limited differentiation ie a
>>>>>> slope of 6dB/octave.
>>>>>
>>>>> Good point. As the OP is using PLL, the output of phase detector is
>>>>> derivative of frequency.
>>>>>
>>>>> VLV
>>>> On 6/7/2013 12:56 PM, Vladimir Vassilevsky wrote:
>>>>> On 6/6/2013 4:11 PM, gyansorova@gmail.com wrote:
>>>>>> On Thursday, June 6, 2013 7:11:53 PM UTC+12, Mimar wrote:
>>>>>>>
>>>>>>> could somebody give me an advice? At the moment I am solving
>>>>>>> interesting problem. I have been using SW PLL with SOGI circuit to
>>>>>>> obtain grid frequency
>>>>>
>>>>>
>>>>>>
>>>>>> You could design a simple control loop with an integrator in the
>>>>>> feedback path. This will give you band-limited differentiation ie a
>>>>>> slope of 6dB/octave.
>>>>>
>>>>> Good point. As the OP is using PLL, the output of phase detector is
>>>>> derivative of frequency.
>>>>>
>>>>> VLV
>>>>
>>>> It still needs filtering.
>>>>
>>>> Digital approximations to derivatives come in many forms. The simplest
>>>> and most intuitive is simply y[n]=x[n-1]-x[n]. For many applications,
>>>> y[n]=.5(x[n-2]-2.c[n-1]+x[n]) is better. The cost is an extra clock of
>>>> latency. Rick Lyons improves on that with two more delay terms and the
>>>> corresponding extra latency. I'm not certain that I'm at liberty to
>>>> provide more details. I expect that he will.
>>>>
>>>> Jerry
>>>
>>> Hi Jerry,
>>> If you're referring to the differentiator that
>>> I think you are, then it's described in detail
>>> at:
>>>
>>> http://www.dsprelated.com/showarticle/35.php
>>>
>>> See Ya',
>>> [-Rick-]
>>> No. 6: "What do you want?"
>>> No. 2: "Information."
>>> No. 6: "Who are you?"
>>> No. 2: "I am the new No. 2."
>>> No. 6: "Who is No. 1?"
>>> No. 2: "You are No. 6."
>>> No. 6: "I am not a number. I am a free man!"
>>>
>>
>> Hello everybody,
>>
>> I have to say: "Thank you for your advices, some (= everyone :-)) of them
>> were very useful for me!"
>>
>> At the moment I am testing differentiator described by Rick Lyons in his
>> article (http://www.dsprelated.com/showarticle/35.php). It seems, it will
>> be work as we with my boss want. The output from differentiator is attached
>> to moving average filter (16th order). Resulting value of derivative is
>> stable now. Super :-). I think, this solution is the best of we could
>> choose.
>>
>> Thanks a lot.
>>
>> Miroslav Martisek, Bohemia
>
> Hello Miroslav Martisek,
> Please forgive me for my ignorance.
> What do you mean by Bohemia?
>
> In the United States we have Bohemian
> beer. But I confess, I don't know what
> Bohemia or Bohemian means.
>
> [-Rick-]
Hello Rick,
Bohemia (German: B�hmenland) is the western part of current Czech
Republic, the home of world's best beer.
See: <https://en.wikipedia.org/wiki/Bohemia>
--
-Tauno
Reply by Miroslaw Kwasniak●June 11, 20132013-06-11
Rick Lyons <R.Lyons@_bogus_ieee.org> wrote:
> Please forgive me for my ignorance.
> What do you mean by Bohemia?