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From: Shen Zhi on 30 May 2010 04:47
Hi, friends!

Is there any good method for "Polynomial Decomposition" being used in
Filter Design?
For example, if I use Park-McClellan algorithm designing a 10-order FIR
filter,then want to decompose the polynomial into five 2-order filters, and
keep the overall magnitude response.
Does anyone has good suggestion or known some papers about this issue,
please tell me.


From: Rune Allnor on 30 May 2010 05:00
On 30 Mai, 10:47, "Shen Zhi" <markk...(a)hotmail.com> wrote:
> Hi, friends!
>
>   Is there any good method for "Polynomial Decomposition" being used in
> Filter Design?
> For example, if I use Park-McClellan algorithm designing a 10-order FIR
> filter,then want to decompose the polynomial into five 2-order filters, and
> keep the overall magnitude response.
>   Does anyone has good suggestion or known some papers about this issue,
> please tell me.

Any reason, other than numerical accuracy issues [*], why you
can't try polynomial rooting?

Rune

[*] Numerical accuracy issues might well be severe enough to
destroy your results, if the polynomial order is too high.
From: Jerry Avins on 30 May 2010 05:11
On 5/30/2010 4:47 AM, Shen Zhi wrote:
> Hi, friends!
>
> Is there any good method for "Polynomial Decomposition" being used in
> Filter Design?
> For example, if I use Park-McClellan algorithm designing a 10-order FIR
> filter,then want to decompose the polynomial into five 2-order filters, and
> keep the overall magnitude response.
> Does anyone has good suggestion or known some papers about this issue,
> please tell me.

Question: why do you want the roots? Aren't the coefficients that P-M
gives you all you really need? (Some FIR filters can reasonably have 100
taps. Would you still want to find the roots?)

Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
From: Shen Zhi on 30 May 2010 05:21
Haha, Rune!
I forget the roots of polynomial.
By the way, do you think any high order FIR filter could be decomposed into
many low order filters by the roots?
If yes, is that means we doesn't need to implement a high order FIR filter
but use many low order filters?

"Rune Allnor" <allnor(a)tele.ntnu.no>
??????:d512d56c-f38d-40b0-948b-b95fd7cce808(a)32g2000prq.googlegroups.com...
On 30 Mai, 10:47, "Shen Zhi" <markk...(a)hotmail.com> wrote:
> Hi, friends!
>
> Is there any good method for "Polynomial Decomposition" being used in
> Filter Design?
> For example, if I use Park-McClellan algorithm designing a 10-order FIR
> filter,then want to decompose the polynomial into five 2-order filters,
> and
> keep the overall magnitude response.
> Does anyone has good suggestion or known some papers about this issue,
> please tell me.

Any reason, other than numerical accuracy issues [*], why you
can't try polynomial rooting?

Rune

[*] Numerical accuracy issues might well be severe enough to
destroy your results, if the polynomial order is too high.


From: Shen Zhi on 30 May 2010 05:29
Hi, Jerry.
I'm thinking of differents effections or different magnitude response
errors, which comes from the limited wordlength quantiziton, between the
single high-order FIR filter and several its decomposed lower FIR filters.

"Jerry Avins" <jya(a)ieee.org> ??????:EYpMn.82856$gv4.41042(a)newsfe09.iad...
> On 5/30/2010 4:47 AM, Shen Zhi wrote:
>> Hi, friends!
>>
>> Is there any good method for "Polynomial Decomposition" being used in
>> Filter Design?
>> For example, if I use Park-McClellan algorithm designing a 10-order FIR
>> filter,then want to decompose the polynomial into five 2-order filters,
>> and
>> keep the overall magnitude response.
>> Does anyone has good suggestion or known some papers about this issue,
>> please tell me.
>
> Question: why do you want the roots? Aren't the coefficients that P-M
> gives you all you really need? (Some FIR filters can reasonably have 100
> taps. Would you still want to find the roots?)
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> �����������������������������������������������������������������������


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