Reply by Vladimir Vassilevsky●January 29, 20082008-01-29

"Rune Allnor" <allnor@tele.ntnu.no> wrote in message
news:8b082864-8ffe-4513-8cdb-4a7330703444@l1g2000hsa.googlegroups.com...

> On 29 Jan, 06:11, Jerry Avins <j...@ieee.org> wrote:
> > Vladimir Vassilevsky wrote:

> > > The FIR filters are optimized for the passband ripple/stopband
> > > attenuation rather then cutoff/slope. When designing a FIR with many
> > > stages it is important to know how the ripples of the different stages
> > > are added altogether. If we assume the worst case the design may not

be

> > > very optimal.
> >
> > > For the multirate FIR, the transfer function is something like:
> >
> > > P(Z)P(Z^n1)P(Z^n2)...
> >
> > > This results in the nastiness and I don't know if Parks-Mcclellan can

be

> > > applied to this problem. If it is applicable, I would just search
> > > through all ratios.
> >
> > The number of taps might be so chosen that the ripple peaks of one
> > filter fill in the valleys of the other.

The periods don't match unless specifically designed for that.

> Based on vague reminiscence of long-lost memories, this resembles
> a perfect reconstruction filter bank? Are you suggesting a
> multirate filter with extra decimation/interpolation steps
> interleaved?

All that I said is if the goal is a decimation/interpolation by the high
factor with the tough requirements to the passband flatness and to the
stopband attenuation, then the filter stages should be jointly optimized.
The formulae based on the cutoff slopes only give the rough idea of where
could be the decimation/interpolation ratios.
Vladimir Vassilevsky
DSP and Mixed Signal Consultant
www.abvolt.com

Reply by Rune Allnor●January 29, 20082008-01-29

On 29 Jan, 06:11, Jerry Avins <j...@ieee.org> wrote:

> Vladimir Vassilevsky wrote:
>
> > Jerry Avins wrote:
>
> >> A systematic approach to optimizing two stages is a first step to
> >> finding a more general procedure.
>
> > Unfortunately, no.
>
> > The FIR filters are optimized for the passband ripple/stopband
> > attenuation rather then cutoff/slope. When designing a FIR with many
> > stages it is important to know how the ripples of the different stages
> > are added altogether. If we assume the worst case the design may not be
> > very optimal.
>
> > For the multirate FIR, the transfer function is something like:
>
> > P(Z)P(Z^n1)P(Z^n2)...
>
> > This results in the nastiness and I don't know if Parks-Mcclellan can be
> > applied to this problem. If it is applicable, I would just search
> > through all ratios.
>
> The number of taps might be so chosen that the ripple peaks of one
> filter fill in the valleys of the other.

Based on vague reminiscence of long-lost memories, this resembles
a perfect reconstruction filter bank? Are you suggesting a
multirate filter with extra decimation/interpolation steps
interleaved?
Rune

Reply by DSPGURU●January 29, 20082008-01-29

On Jan 29, 12:11�am, Jerry Avins <j...@ieee.org> wrote:

> Vladimir Vassilevsky wrote:
>
> > Jerry Avins wrote:
>
> >> A systematic approach to optimizing two stages is a first step to
> >> finding a more general procedure.
>
> > Unfortunately, no.
>
> > The FIR filters are optimized for the passband ripple/stopband
> > attenuation rather then cutoff/slope. When designing a FIR with many
> > stages it is important to know how the ripples of the different stages
> > are added altogether. If we assume the worst case the design may not be
> > very optimal.
>
> > For the multirate FIR, the transfer function is something like:
>
> > P(Z)P(Z^n1)P(Z^n2)...
>
> > This results in the nastiness and I don't know if Parks-Mcclellan can be
> > applied to this problem. If it is applicable, I would just search
> > through all ratios.
>
> The number of taps might be so chosen that the ripple peaks of one
> filter fill in the valleys of the other. For three stages, one would
> want a three-phase offset. I can't guess the best approach, but I'm
> confident that exploring the solution space would provide insights we
> don't now have.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> �����������������������������������������������������������������������- Hide quoted text -
>
> - Show quoted text -

Yes Jerry,
It might prove insight if you have never done. I have done.
Regards,
Kamar Ruptan
DSP Guru

Reply by DSPGURU●January 29, 20082008-01-29

On Jan 28, 10:45�pm, Jerry Avins <j...@ieee.org> wrote:

> DSPGURU wrote:
> > On Jan 28, 9:45 pm, Jerry Avins <j...@ieee.org> wrote:
> >> DSPGURU wrote:
> >>> On Jan 28, 9:29 pm, "bharat pathak" <bha...@arithos.com> wrote:
> >>>>> do any of you know an equation that gives us the
> >>>>> optimum value for I1 (from which we can obtain I2)
> >>>>> that minimizes the total number of taps in the two
> >>>>> interpolation filters?
> >>>>> Thanks,
> >>>>> [-Rick-]
> >>>> Rick,
> >>>> � � For the equation see my other post on Two stage interpolation-Optimum
> >>>> order.
> >>>> Bharat Pathak
> >>>> Arithos Designswww.arithos.com
> >>> Hello my DSP Brothers,
> >>> Why is focus at two stages? Why not more?
> >>> To optimise all reddy under-optimal approach make any sense?
> >> A systematic approach to optimizing two stages is a first step to
> >> finding a more general procedure.
>
> >> Jerry
> >> --
> >> Engineering is the art of making what you want from things you can get.
> >> �����������������������������������������������������������������������- Hide quoted text -
>
> >> - Show quoted text -
>
> > Dr Avin,
>
> > Might be first step down path that go nowhere. �If real application
> > should just do it design starting closer to answer not as great a trip
> > away as can be. �Close form not required, maybe not possible as get
> > much bigger than too stages.
>
> > Ok, if only gymnastics of brain.
>
> Closed form will not be needed if an effective partitioning procedure
> can be developed. For example, if it becomes evident that the optimum
> two-way split is I1 = I2 = sqrt(I), then a good three-way split is
> likely to be I1 = I2 = I3 = cube-root(I). If, on the other hand, the
> best two-way split involves unequal I's (possibly because the filters
> operate at different rates), then the formula that works there will
> likely also lead to an efficient three-way split.
>
> Once efficient splits can be generated easily, the way is open to
> explore the relation between the number of splits and the size of the
> interpolation.
>
> Almost having a diploma makes you an apprentice, not a guru. You are
> accustomed to learning neat formulas out of textbooks, but you haven't
> yet realized that the messy problems aren't discussed in those texts.
> You have the privilege of witnessing here a process by which those messy
> problems come to be understood, then simplified in practice, and finally
> reduced to formulas suitable for student "gurus".
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> �����������������������������������������������������������������������- Hide quoted text -
>
> - Show quoted text -

Dr Jerry,
It seems Vlad and I both not agree with you. You make lot of
assumptions about me. Maybe I professor jerking your chain.
Regards,
Kamar Ruptan
DSP Guru

Reply by Jerry Avins●January 29, 20082008-01-29

Vladimir Vassilevsky wrote:

>
>
> Jerry Avins wrote:
>
>> A systematic approach to optimizing two stages is a first step to
>> finding a more general procedure.
>
> Unfortunately, no.
>
> The FIR filters are optimized for the passband ripple/stopband
> attenuation rather then cutoff/slope. When designing a FIR with many
> stages it is important to know how the ripples of the different stages
> are added altogether. If we assume the worst case the design may not be
> very optimal.
>
> For the multirate FIR, the transfer function is something like:
>
> P(Z)P(Z^n1)P(Z^n2)...
>
> This results in the nastiness and I don't know if Parks-Mcclellan can be
> applied to this problem. If it is applicable, I would just search
> through all ratios.

The number of taps might be so chosen that the ripple peaks of one
filter fill in the valleys of the other. For three stages, one would
want a three-phase offset. I can't guess the best approach, but I'm
confident that exploring the solution space would provide insights we
don't now have.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Reply by Vladimir Vassilevsky●January 29, 20082008-01-29

Jerry Avins wrote:

> A systematic approach to optimizing two stages is a first step to
> finding a more general procedure.

Unfortunately, no.
The FIR filters are optimized for the passband ripple/stopband
attenuation rather then cutoff/slope. When designing a FIR with many
stages it is important to know how the ripples of the different stages
are added altogether. If we assume the worst case the design may not be
very optimal.
For the multirate FIR, the transfer function is something like:
P(Z)P(Z^n1)P(Z^n2)...
This results in the nastiness and I don't know if Parks-Mcclellan can be
applied to this problem. If it is applicable, I would just search
through all ratios.
Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

Reply by Jerry Avins●January 28, 20082008-01-28

DSPGURU wrote:

> On Jan 28, 9:45 pm, Jerry Avins <j...@ieee.org> wrote:
>> DSPGURU wrote:
>>> On Jan 28, 9:29 pm, "bharat pathak" <bha...@arithos.com> wrote:
>>>>> do any of you know an equation that gives us the
>>>>> optimum value for I1 (from which we can obtain I2)
>>>>> that minimizes the total number of taps in the two
>>>>> interpolation filters?
>>>>> Thanks,
>>>>> [-Rick-]
>>>> Rick,
>>>> For the equation see my other post on Two stage interpolation-Optimum
>>>> order.
>>>> Bharat Pathak
>>>> Arithos Designswww.arithos.com
>>> Hello my DSP Brothers,
>>> Why is focus at two stages? Why not more?
>>> To optimise all reddy under-optimal approach make any sense?
>> A systematic approach to optimizing two stages is a first step to
>> finding a more general procedure.
>>
>> Jerry
>> --
>> Engineering is the art of making what you want from things you can get.
>> �����������������������������������������������������������������������- Hide quoted text -
>>
>> - Show quoted text -
>
> Dr Avin,
>
> Might be first step down path that go nowhere. If real application
> should just do it design starting closer to answer not as great a trip
> away as can be. Close form not required, maybe not possible as get
> much bigger than too stages.
>
> Ok, if only gymnastics of brain.

Closed form will not be needed if an effective partitioning procedure
can be developed. For example, if it becomes evident that the optimum
two-way split is I1 = I2 = sqrt(I), then a good three-way split is
likely to be I1 = I2 = I3 = cube-root(I). If, on the other hand, the
best two-way split involves unequal I's (possibly because the filters
operate at different rates), then the formula that works there will
likely also lead to an efficient three-way split.
Once efficient splits can be generated easily, the way is open to
explore the relation between the number of splits and the size of the
interpolation.
Almost having a diploma makes you an apprentice, not a guru. You are
accustomed to learning neat formulas out of textbooks, but you haven't
yet realized that the messy problems aren't discussed in those texts.
You have the privilege of witnessing here a process by which those messy
problems come to be understood, then simplified in practice, and finally
reduced to formulas suitable for student "gurus".
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Reply by bharat pathak●January 28, 20082008-01-28

>
>Can combines ups and downs in special order to signal BW is preserve.
>
>Maybe something like up 2, up 2, down 3, up 2, up 2, up 2, down 7, up
>2, up, 5 down 7?
>
>Kamar Ruptan
>DSP Guru helping the Supreme DSP Guru
>

Hi DSP Guru,
I liked your approach of up 2, up 2, down 3, up 2 ....
It reminded me of so many other things (also apart from the usual
DSP). One such thing I got reminded was the game of ping-pong. And
secondly i was thinking maybe this is how the instructions would
follow when 2 blind people date (just kidding).
Rather on a serious note, I want to know how do you come up with
some suggestions like this? Do you model it in matlab
or you just think about it? Also I want to know about the school
where you studied DSP so in case if I need to brush up my skills
it would be beneficial. Also can you tell us who your teacher was?
Also if you can tell which are your most favorite DSP books it will
help. one i suppose is rabeener and crushierre (i searched on amazon
but there is no book with these authors, I got the spelling from
your previous post).
Bharat

Reply by DSPGURU●January 28, 20082008-01-28

On Jan 28, 9:45�pm, Jerry Avins <j...@ieee.org> wrote:

> DSPGURU wrote:
> > On Jan 28, 9:29 pm, "bharat pathak" <bha...@arithos.com> wrote:
> >>> do any of you know an equation that gives us the
> >>> optimum value for I1 (from which we can obtain I2)
> >>> that minimizes the total number of taps in the two
> >>> interpolation filters?
> >>> Thanks,
> >>> [-Rick-]
> >> Rick,
>
> >> � � For the equation see my other post on Two stage interpolation-Optimum
> >> order.
>
> >> Bharat Pathak
>
> >> Arithos Designswww.arithos.com
>
> > Hello my DSP Brothers,
>
> > Why is focus at two stages? Why not more?
>
> > To optimise all reddy under-optimal approach make any sense?
>
> A systematic approach to optimizing two stages is a first step to
> finding a more general procedure.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> �����������������������������������������������������������������������- Hide quoted text -
>
> - Show quoted text -

Dr Avin,
Might be first step down path that go nowhere. If real application
should just do it design starting closer to answer not as great a trip
away as can be. Close form not required, maybe not possible as get
much bigger than too stages.
Ok, if only gymnastics of brain.
Regards,
Kamar Ruptan
DSP Guru

Reply by Jerry Avins●January 28, 20082008-01-28

DSPGURU wrote:

> On Jan 28, 9:29 pm, "bharat pathak" <bha...@arithos.com> wrote:
>>> do any of you know an equation that gives us the
>>> optimum value for I1 (from which we can obtain I2)
>>> that minimizes the total number of taps in the two
>>> interpolation filters?
>>> Thanks,
>>> [-Rick-]
>> Rick,
>>
>> For the equation see my other post on Two stage interpolation-Optimum
>> order.
>>
>> Bharat Pathak
>>
>> Arithos Designswww.arithos.com
>
> Hello my DSP Brothers,
>
> Why is focus at two stages? Why not more?
>
> To optimise all reddy under-optimal approach make any sense?

A systematic approach to optimizing two stages is a first step to
finding a more general procedure.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������