Band Pass & Stop Band Filter Coef Transform from Low Pass

Hello,
as I am not an expert I am asking help to transform the IIR Coefficients
of a Low Pass Butterworth 6 poles filter to Band Pass and Stop.
I coded my application in C and after performing the computation of the
normalized coefficient with normalized frequency of 1 Hz, I performed the
low pass to low pass transform and the low pass to high pass transform
obtaining the new coefficients. (To that I used a commercial library but in
it I am not able to find the others transform). Then I performed the
filtering of data with success. After I need to transform the normalized
coefficients to band pass and band stop but I have no idea of how to do
it.
Does anybody can help me with C code, examples, everything can help me, to
transform the low pass normalized coefficients to band pass and stop ?
Thanks in advance

On Oct 27, 12:08=A0pm, "pdvmipv" <luigino.pagan...@agustawestland.com>
wrote:
> Hello,
> as I am not an expert I am asking help to transform the IIR Coefficients
> of a Low Pass Butterworth 6 poles filter to Band Pass and Stop.
> I coded my application in C and after performing the computation of the
> normalized coefficient with normalized frequency of 1 Hz, I performed the
> low pass to low pass transform and the low pass to high pass transform
> obtaining the new coefficients. (To that I used a commercial library but =
in
> it I am not able to find the others transform). Then I performed the
> filtering of data with success. After I need to transform the normalized
> coefficients to band pass and band stop but I have no idea of how to do
> it.
> Does anybody can help me with C code, examples, everything can help me, t=
o
> transform the low pass normalized coefficients to band pass and stop ?
> Thanks in advance

The book "Discrete-Time Signal Processing" by Oppenheim and Schafer
has the transformation equations for converting lowpass to bandpass
and highpass and bandstop filters. I have the 1989 version and the
details you want start on page 430.

IHTH,
Clay

On 27 Okt, 17:08, "pdvmipv" <luigino.pagan...@agustawestland.com>
wrote:
> Hello,
> as I am not an expert I am asking help to transform the IIR Coefficients
> of a Low Pass Butterworth 6 poles filter to Band Pass and Stop.
> I coded my application in C and after performing the computation of the
> normalized coefficient with normalized frequency of 1 Hz, I performed the
> low pass to low pass transform and the low pass to high pass transform
> obtaining the new coefficients. (To that I used a commercial library but in
> it I am not able to find the others transform). Then I performed the
> filtering of data with success. After I need to transform the normalized
> coefficients to band pass and band stop but I have no idea of how to do
> it.
> Does anybody can help me with C code, examples, everything can help me, to
> transform the low pass normalized coefficients to band pass and stop ?
> Thanks in advance

The book by Proakis and Manolakis has the transforms, but be
warned that the editions up to and including the 3rd contain
typos. The typos were corrected for the 4th edition.

Rune

>On 27 Okt, 17:08, "pdvmipv" <luigino.pagan...@agustawestland.com>
>wrote:
>> Hello,
>> as I am not an expert I am asking help to transform the IIR
Coefficients
>> of a Low Pass Butterworth 6 poles filter to Band Pass and Stop.
>> I coded my application in C and after performing the computation of
the
>> normalized coefficient with normalized frequency of 1 Hz, I performed
the
>> low pass to low pass transform and the low pass to high pass transform
>> obtaining the new coefficients. (To that I used a commercial library
but in
>> it I am not able to find the others transform). Then I performed the
>> filtering of data with success. After I need to transform the
normalized
>> coefficients to band pass and band stop but I have no idea of how to
do
>> it.
>> Does anybody can help me with C code, examples, everything can help me,
to
>> transform the low pass normalized coefficients to band pass and stop ?
>> Thanks in advance
>
>The book by Proakis and Manolakis has the transforms, but be
>warned that the editions up to and including the 3rd contain
>typos. The typos were corrected for the 4th edition.
>
>Rune
>

If anybody have already performed such a transformation and have a C code
or in other language please send it to me. I have already took a look at
the first book but as I am not an expert I do not understand how to
implement the transfomation with a programming language. Thanks in advance

On 27 Okt, 20:12, "pdvmipv" <luigino.pagan...@agustawestland.com>
wrote:
> >On 27 Okt, 17:08, "pdvmipv" <luigino.pagan...@agustawestland.com>
> >wrote:
> >> Hello,
> >> as I am not an expert I am asking help to transform the IIR
> Coefficients
> >> of a Low Pass Butterworth 6 poles filter to Band Pass and Stop.
> >> I coded my application in C and after performing the computation of
> the
> >> normalized coefficient with normalized frequency of 1 Hz, I performed
> the
> >> low pass to low pass transform and the low pass to high pass transform
> >> obtaining the new coefficients. (To that I used a commercial library
> but in
> >> it I am not able to find the others transform). Then I performed the
> >> filtering of data with success. After I need to transform the
> normalized
> >> coefficients to band pass and band stop but I have no idea of how to
> do
> >> it.
> >> Does anybody can help me with C code, examples, everything can help me,
> to
> >> transform the low pass normalized coefficients to band pass and stop ?
> >> Thanks in advance
>
> >The book by Proakis and Manolakis has the transforms, but be
> >warned that the editions up to and including the 3rd contain
> >typos. The typos were corrected for the 4th edition.
>
> >Rune
>
> If anybody have already performed such a transformation and have a C code
> or in other language please send it to me. I have already took a look at
> the first book but as I am not an expert I do not understand how to
> implement the transfomation with a programming language.

The trick is to keep the filter on a biquad representation
(as a set of fractions of 2nd order polynomials) and not
multiply out the whole expressions. If you do that, the
transforms are trivial - albeit tedious.

Rune

>On 27 Okt, 20:12, "pdvmipv" <luigino.pagan...@agustawestland.com>
>wrote:
>> >On 27 Okt, 17:08, "pdvmipv" <luigino.pagan...@agustawestland.com>
>> >wrote:
>> >> Hello,
>> >> as I am not an expert I am asking help to transform the IIR
>> Coefficients
>> >> of a Low Pass Butterworth 6 poles filter to Band Pass and Stop.
>> >> I coded my application in C and after performing the computation of
>> the
>> >> normalized coefficient with normalized frequency of 1 Hz, I
performed
>> the
>> >> low pass to low pass transform and the low pass to high pass
transform
>> >> obtaining the new coefficients. (To that I used a commercial
library
>> but in
>> >> it I am not able to find the others transform). Then I performed
the
>> >> filtering of data with success. After I need to transform the
>> normalized
>> >> coefficients to band pass and band stop but I have no idea of how
to
>> do
>> >> it.
>> >> Does anybody can help me with C code, examples, everything can help
me,
>> to
>> >> transform the low pass normalized coefficients to band pass and stop
?
>> >> Thanks in advance
>>
>> >The book by Proakis and Manolakis has the transforms, but be
>> >warned that the editions up to and including the 3rd contain
>> >typos. The typos were corrected for the 4th edition.
>>
>> >Rune
>>
>> If anybody have already performed such a transformation and have a C
code
>> or in other language please send it to me. I have already took a look
at
>> the first book but as I am not an expert I do not understand how to
>> implement the transfomation with a programming language.
>
>The trick is to keep the filter on a biquad representation
>(as a set of fractions of 2nd order polynomials) and not
>multiply out the whole expressions. If you do that, the
>transforms are trivial - albeit tedious.
>
>Rune
>

In fact it is what I do.
I Comupute the normalized IIR Coefficient for a 6 order butterworth filter
(Sample Rate 1Hz and Cutoff 1/2 pi=0.15915 Hz) giving the following biquad
filter coefficients (b0,b1,b2,a1,a2):
"1.267923e-01, 2.535845e-01, 1.267923e-01, -5.960975e-01, 1.032665e-01"
"1.441050e-01, 2.882099e-01, 1.441050e-01, -6.774909e-01, 2.539108e-01"
"1.887428e-01, 3.774856e-01, 1.887428e-01, -8.873498e-01, 6.423210e-01"
"5.619045e-309, 5.271038e-309, 0.000000e+00, 2.529616e-321,
-1.555730e+00"
"-1.567740e+00, 3.667700e-01, 6.191000e-01, 9.555300e-01, -3.902100e-01"
"8.353800e-01, -1.138500e-01, -7.781000e-02, -1.499000e-01, 9.041000e-02"

Then I have two functions to transform from low pass to low pass and low
pass to high pass. I do not have the source code of such a functions. But
what I am not able to do are the others trasnformations: band pass and stop
band.
Starting from the array of the above normalized coefficients what are the
steps to perform the transformation of the coefficient in order to filter,

for example, a signal sampled at 512 sample per seconds with band stop
cutoff freqs of fc1 40 Hz, fc2 80 Hz and similary a band pass filter with
the same low and high cutoff frequencies ?

Thanks

On 28 Okt, 09:15, "pdvmipv" <luigino.pagan...@agustawestland.com>
wrote:

> Starting from the array of the above normalized coefficients what are the
> steps to perform the transformation of the coefficient in order to filter,

- Find the transforms in a textbook.
- Analytically derive the transformed biquads.
- Implement the derived formulas in a programming
  language of your choise.
- Apply the functions to your prototype filter.
- Use the resulting coefficients when filtering
  your data.

Rune

Rune Allnor <allnor@tele.ntnu.no> wrote in news:813a6fda-6508-4557-9999-
b92243778e1f@z2g2000yqm.googlegroups.com:

> On 28 Okt, 09:15, "pdvmipv" <luigino.pagan...@agustawestland.com>
> wrote:
> 
>> Starting from the array of the above normalized coefficients what are the
>> steps to perform the transformation of the coefficient in order to filter,
> 
> - Find the transforms in a textbook.
> - Analytically derive the transformed biquads.
> - Implement the derived formulas in a programming
>   language of your choise.
> - Apply the functions to your prototype filter.
> - Use the resulting coefficients when filtering
>   your data.
> 
> Rune
> 

Or buy a filter program that does everything for you. I ise QEDesign from 
Momentum Data Systems (www.mds.com)

Al Clark
www.danvillesignal.com

>Rune Allnor <allnor@tele.ntnu.no> wrote in news:813a6fda-6508-4557-9999-
>b92243778e1f@z2g2000yqm.googlegroups.com:
>
>> On 28 Okt, 09:15, "pdvmipv" <luigino.pagan...@agustawestland.com>
>> wrote:
>> 
>>> Starting from the array of the above normalized coefficients what are
the
>>> steps to perform the transformation of the coefficient in order to
filter,
>> 
>> - Find the transforms in a textbook.
>> - Analytically derive the transformed biquads.
>> - Implement the derived formulas in a programming
>>   language of your choise.
>> - Apply the functions to your prototype filter.
>> - Use the resulting coefficients when filtering
>>   your data.
>> 
>> Rune
>> 
>
>Or buy a filter program that does everything for you. I ise QEDesign from

>Momentum Data Systems (www.mds.com)
>
>Al Clark
>www.danvillesignal.com
>
I posted precise questions (C code, code examples, ecc) and I obtained
generic answers or suggestion to buy a library. Is this the spirit of the
forum ? Thanks anyway for the help. 

On 29 Okt, 11:41, "pdvmipv" <luigino.pagan...@agustawestland.com>
wrote:
> >Rune Allnor <all...@tele.ntnu.no> wrote in news:813a6fda-6508-4557-9999-
> >b92243778...@z2g2000yqm.googlegroups.com:
>
> >> On 28 Okt, 09:15, "pdvmipv" <luigino.pagan...@agustawestland.com>
> >> wrote:
>
> >>> Starting from the array of the above normalized coefficients what are
> the
> >>> steps to perform the transformation of the coefficient in order to
> filter,
>
> >> - Find the transforms in a textbook.
> >> - Analytically derive the transformed biquads.
> >> - Implement the derived formulas in a programming
> >> &#4294967295; language of your choise.
> >> - Apply the functions to your prototype filter.
> >> - Use the resulting coefficients when filtering
> >> &#4294967295; your data.
>
> >> Rune
>
> >Or buy a filter program that does everything for you. I ise QEDesign from
> >Momentum Data Systems (www.mds.com)
>
> >Al Clark
> >www.danvillesignal.com
>
> I posted precise questions (C code, code examples, ecc) and I obtained
> generic answers or suggestion to buy a library. Is this the spirit of the
> forum ?

Yes, it is. If you want help with understanding DSP, then
this is the place to ask questions. If you want canned code
or ready-to-use solutions, try somewhere else.

Rune