> Rick Lyons wrote:
>> On Tue, 14 Nov 2006 15:14:18 -0500, Jerry Avins <jya@ieee.org> wrote:
>>
>>> Vladimir Vassilevsky wrote:
>>>>
>>>> Jerry Avins wrote:
>>>>
>>>>
>>>>> A formula for a derivative that gives good results up to quarter of
>>>>> the sample rate is not easy to devise. Don't be misled into
>>>>> thinking it's trivial.
>>>> But this is trivial. The differentiator is a linear phase filter
>>>> which has response proportional to the frequency. A filter like that
>>>> can be designed to any given accuracy.
>>> The operative word is "designed". Most implementors merely imagine
>>> one and use it without checking the performance (or phase
>>> characteristics). That the delay through the filter be a whole number
>>> of samples requires an odd number of taps. In turn, that implies that
>>> the amplitude at f be the same as the response at Fs/2 - f. For a
>>> differentiator, the response is zero at f = 0. An off number of taps
>>> ensures that the response is also zero at Fs/2, which is hardly ideal.
>>>
>>> Jerry
>>
>> Hi Jer,
>> maybe the differentiator at
>> http://www.elecdesign.com/Articles/Index.cfm?AD=1&ArticleID=13358
>>
>> would be useful to ma.
>
> Rick,
>
> I recognize that design as the one we corresponded about some months
> ago. Being linear phase, it lacks the 90-degree phase shift that is an
> important part of some applications in control loops. The delay elements
> being two unit delays each show that this is a half-band structure, with
> all the attendant constraints and advantages. These symmetric
> differentiators can't do better than get to pi/2 in the limit, and yours
> is pretty close to that.
>
> As good as this is, there's still room for a few improvements.
Rick,
I should have gone over the equations instead of relying on memory. Your
new differentiator is antisymmetric and exhibits the required quadrature
phase shift Sorry about that!
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Jerry Avins●November 19, 20062006-11-19
Rick Lyons wrote:
> On Tue, 14 Nov 2006 15:14:18 -0500, Jerry Avins <jya@ieee.org> wrote:
>
>> Vladimir Vassilevsky wrote:
>>>
>>> Jerry Avins wrote:
>>>
>>>
>>>> A formula for a derivative that gives good results up to quarter of
>>>> the sample rate is not easy to devise. Don't be misled into thinking
>>>> it's trivial.
>>> But this is trivial. The differentiator is a linear phase filter which
>>> has response proportional to the frequency. A filter like that can be
>>> designed to any given accuracy.
>> The operative word is "designed". Most implementors merely imagine one
>> and use it without checking the performance (or phase characteristics).
>> That the delay through the filter be a whole number of samples requires
>> an odd number of taps. In turn, that implies that the amplitude at f be
>> the same as the response at Fs/2 - f. For a differentiator, the response
>> is zero at f = 0. An off number of taps ensures that the response is
>> also zero at Fs/2, which is hardly ideal.
>>
>> Jerry
>
> Hi Jer,
> maybe the differentiator at
>
> http://www.elecdesign.com/Articles/Index.cfm?AD=1&ArticleID=13358
>
> would be useful to ma.
Rick,
I recognize that design as the one we corresponded about some months
ago. Being linear phase, it lacks the 90-degree phase shift that is an
important part of some applications in control loops. The delay elements
being two unit delays each show that this is a half-band structure, with
all the attendant constraints and advantages. These symmetric
differentiators can't do better than get to pi/2 in the limit, and yours
is pretty close to that.
As good as this is, there's still room for a few improvements.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Rick Lyons●November 19, 20062006-11-19
On Tue, 14 Nov 2006 15:14:18 -0500, Jerry Avins <jya@ieee.org> wrote:
>Vladimir Vassilevsky wrote:
>>
>>
>> Jerry Avins wrote:
>>
>>
>>> A formula for a derivative that gives good results up to quarter of
>>> the sample rate is not easy to devise. Don't be misled into thinking
>>> it's trivial.
>>
>> But this is trivial. The differentiator is a linear phase filter which
>> has response proportional to the frequency. A filter like that can be
>> designed to any given accuracy.
>
>The operative word is "designed". Most implementors merely imagine one
>and use it without checking the performance (or phase characteristics).
>That the delay through the filter be a whole number of samples requires
>an odd number of taps. In turn, that implies that the amplitude at f be
>the same as the response at Fs/2 - f. For a differentiator, the response
>is zero at f = 0. An off number of taps ensures that the response is
>also zero at Fs/2, which is hardly ideal.
>
>Jerry
> Jerry Avins wrote:
>
>> ma wrote:
>>
>>> Interesting, where can I find more information on this subject?
>>
>>
>> Ray is the man. http://www.dspguru.com/info/faqs/cordic.htm
>>
>> Jerry
>
> Thanks Jerry. I have a tutorial paper on CORDIC for FPGAs on my
> website. It is the most hit page on my website, and has been cited in
> several dozen papers that I am aware of. Look under the publications
> page. http://www.andraka.com/papers.htm
A (it turns out outdated) link to that page is in the DSPguru page I cited.
jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Thanks Jerry. I have a tutorial paper on CORDIC for FPGAs on my
website. It is the most hit page on my website, and has been cited in
several dozen papers that I am aware of. Look under the publications
page. http://www.andraka.com/papers.htm
Reply by Jerry Avins●November 15, 20062006-11-15
ma wrote:
> Interesting, where can I find more information on this subject?
Ray is the man. http://www.dspguru.com/info/faqs/cordic.htm
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by ma●November 15, 20062006-11-15
Interesting, where can I find more information on this subject?
Regards
"Ray Andraka" <ray@andraka.com> wrote in message
news:rtH6h.49645$WD6.2480@newsfe13.lga...
> ma wrote:
>> There are two cons of using atan:
>> 1- It is very expensive ( processing ) to use it in software.
>> 2- I am not sure if I can use it in FPGA at all.
>>
>> so I am looking for other ways to do this. Still couldn't find a good
>> book or paper or ... on digital FM demodulation. Any suggestion?
>>
>> Regards
>>
>>
>
>
> Atan2 is actually pretty easy to do on the FPGA using CORDIC. I just did
> a digital AM/FM demod last month for Virtex2Pro using a CORDIC rotator to
> extract the ATAN2 and magnitude (for AM).
Reply by Ray Andraka●November 15, 20062006-11-15
ma wrote:
> There are two cons of using atan:
> 1- It is very expensive ( processing ) to use it in software.
> 2- I am not sure if I can use it in FPGA at all.
>
> so I am looking for other ways to do this. Still couldn't find a good book
> or paper or ... on digital FM demodulation. Any suggestion?
>
> Regards
>
>
Atan2 is actually pretty easy to do on the FPGA using CORDIC. I just
did a digital AM/FM demod last month for Virtex2Pro using a CORDIC
rotator to extract the ATAN2 and magnitude (for AM).
Reply by ma●November 15, 20062006-11-15
Hello,
Where did you add any note? I couldn't find them!
Regards
<johns@3db-labs.com> wrote in message
news:1163589428.543670.3620@b28g2000cwb.googlegroups.com...
>
> ma wrote:
>> There are two cons of using atan:
>> 1- It is very expensive ( processing ) to use it in software.
>> 2- I am not sure if I can use it in FPGA at all.
>>
>> so I am looking for other ways to do this. Still couldn't find a good
>> book
>> or paper or ... on digital FM demodulation. Any suggestion?
>>
>> Regards
>>
>>
>>
>> <johns@3db-labs.com> wrote in message
>> news:1163558037.394548.107480@i42g2000cwa.googlegroups.com...
>> >
>> > Jerry Avins wrote:
>> >> ma wrote:
>> >> > "Jerry Avins" <jya@ieee.org> wrote in message
>> >> > news:M5qdnU3kH4I4f8TYnZ2dnUVZ_vSdnZ2d@rcn.net...
>> >> >> ma wrote:
>> >> >>> Thanks,
>> >> >>> lets look at the problem from other side.
>> >> >>> What is W? Is it the demodulated signal? If we are in digital
>> >> >>> space
>> >> >>> then
>> >> >>> this equation should change to:
>> >> >>>
>> >> >>> I * (q(n)- q(n-1)) - q * (I(n)- I(n-1))
>> >> >>> W(n)= ---------------------------------------
>> >> >>> I(n) ^2 + q(n) ^2
>> >> >> That doesn't work. There are delays in your differences but not in
>> >> >> the
>> >> >> corresponding I and Q. All quantities need to be refer to the same
>> >> >> instant.
>> >> >
>> >> > How can I calculate this without using I(n-1) and q(n-1) ?
>> >>
>> >> I can think of several ways. You probably can too if you think about
>> >> what you want to accomplish, rather than starting with the math that
>> >> you
>> >> hope accomplishes it. One of them is
>> >>
>> >> I(n-1)*[Q(n) - Q[(n-2)] + Q(n-1)*[I(n) - I(n-2)]
>> >> w(n-1)= ------------------------------------------------------
>> >> I(n-1)*I(n-1) + Q(n-1)*Q(n-1)
>> >>
>> >> In other words, compute your "derivatives" symmetrically about the
>> >> time
>> >> they apply to, and use the I and Q measured at that time.
>> >>
>> >> Another way is ridiculously increasing the sample rate so timing
>> >> errors
>> >> measured in sample times don't matter.
>> >>
>> >> A formula for a derivative that gives good results up to quarter of
>> >> the
>> >> sample rate is not easy to devise. Don't be misled into thinking it's
>> >> trivial.
>> >>
>> >
>> > Exactly why one should weigh the pros and cons against the other method
>> > I gave, especially if the atan2 function is available in a library.
>> >
>> > John
>> >
>
Reply by ●November 15, 20062006-11-15
ma wrote:
> There are two cons of using atan:
> 1- It is very expensive ( processing ) to use it in software.
> 2- I am not sure if I can use it in FPGA at all.
>
> so I am looking for other ways to do this. Still couldn't find a good book
> or paper or ... on digital FM demodulation. Any suggestion?
>
> Regards
>
>
>
> <johns@3db-labs.com> wrote in message
> news:1163558037.394548.107480@i42g2000cwa.googlegroups.com...
> >
> > Jerry Avins wrote:
> >> ma wrote:
> >> > "Jerry Avins" <jya@ieee.org> wrote in message
> >> > news:M5qdnU3kH4I4f8TYnZ2dnUVZ_vSdnZ2d@rcn.net...
> >> >> ma wrote:
> >> >>> Thanks,
> >> >>> lets look at the problem from other side.
> >> >>> What is W? Is it the demodulated signal? If we are in digital space
> >> >>> then
> >> >>> this equation should change to:
> >> >>>
> >> >>> I * (q(n)- q(n-1)) - q * (I(n)- I(n-1))
> >> >>> W(n)= ---------------------------------------
> >> >>> I(n) ^2 + q(n) ^2
> >> >> That doesn't work. There are delays in your differences but not in the
> >> >> corresponding I and Q. All quantities need to be refer to the same
> >> >> instant.
> >> >
> >> > How can I calculate this without using I(n-1) and q(n-1) ?
> >>
> >> I can think of several ways. You probably can too if you think about
> >> what you want to accomplish, rather than starting with the math that you
> >> hope accomplishes it. One of them is
> >>
> >> I(n-1)*[Q(n) - Q[(n-2)] + Q(n-1)*[I(n) - I(n-2)]
> >> w(n-1)= ------------------------------------------------------
> >> I(n-1)*I(n-1) + Q(n-1)*Q(n-1)
> >>
> >> In other words, compute your "derivatives" symmetrically about the time
> >> they apply to, and use the I and Q measured at that time.
> >>
> >> Another way is ridiculously increasing the sample rate so timing errors
> >> measured in sample times don't matter.
> >>
> >> A formula for a derivative that gives good results up to quarter of the
> >> sample rate is not easy to devise. Don't be misled into thinking it's
> >> trivial.
> >>
> >
> > Exactly why one should weigh the pros and cons against the other method
> > I gave, especially if the atan2 function is available in a library.
> >
> > John
> >