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8/17/2019 Filtros IIR - Ejemplos de Diseño
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This chapter discusses various IIR flter design methods. The our standard
types o flters are used here:
low-pass flter;
high-pass flter;
band-pass flter; and
band-stop flter.
The design method used here is known as bilinear transormation.
The IIR flter design process can be split into several steps described in
hapter !.".# $esigning IIR flters by bilinear transormation. These are:
$efning flter specifcations;
%peciying the type o analog prototype flter;
omputing the flter order according to the flter specifcations and specifedanalog prototype flter;
omputing the transer unction o reerence analog prototype flter;
Transormation into analog flter by range scaling;
Transormation into digital flter by bilinear transormation; and
I the resulting flter doesn&t satisy the given specifcations or i it is possible
to decrease the flter order' then it is necessary to do it. The specifed flter
order is increased or decreased according to needs' and steps (' # and ) are
repeated ater that as many times as needed.
%ome steps are skipped in some cases. I the flter order is known' step ! is
skipped. I the type o reerence analog prototype flter is predetermined'
step " is skipped.
In every given e*ample' the IIR flter design process will be described
through these steps in order to make it easier or you to observe similarities
and di+erencies between various design methodes' analog prototype flters
and design o various types o flters as well.
,igure !-)- illustrates the design steps along with input and output data or
each o them.
,igure !-)-. %teps in designing digital IIR flter
The frst block reers to design o reerence analog prototype flter o
appropriate order. The output data is a reerence analog prototype flter
transer unction a/s0. Regardless o the type o reerence analog prototypeflter in use' the transer unction is given by:
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where:
1 is a constant;
2k is the k-th 2ero o the reerence analog prototype flter transer unction;
3 is a number o 2eros o the reerence analog prototype flter transer
unction;
pk is the k-th pole o the reerence analog prototype flter transer unction;
and
4 is a number o poles o the reerence analog prototype flter transer
unction and flter order as well.
Reerence analog prototype flter is always a low-pass flter. The ne*t step is
the transormation into an analog flter o appropriate type. The e*pression
used to transorm the reerence analog prototype flter transer unction
depends on the type o flter that needs to be obtained. The fnal result is
the transer unction /s0 given by:
where:
1 is a constant;
2k is the k-th 2ero o the reerence analog prototype flter transer unction;
3 is a number o 2eros o the reerence analog prototype flter transer
unction;
pk is the k-th pole o the reerence analog prototype flter transer unction;
and
4 is a number o poles o the reerence analog prototype flter transer
unction and flter order as well.5s seen' the transer unctions o reerence analog prototype flter and
analog flter are very similar. They di+er only in the value o constant 1'
the values o the transer unction poles and 2eros 2k and pk as well as in
the number o transer unction 2eros 3. The flter order is the same i the
analog flter is a low-pass or high-pass flter' whereas it is di+erent i the
analog flter is a band-pass or band-stop flter. In the later case' the analog
flter order /40 is twice that o the reerence analog prototype flter.
The ne*t step is the transormation into appropriate digital IIR flter using
bilinear transormation given by e*pression:
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,ilter $esigner Tool is used or testing and analysing the resulting IIR flters
in this chapter. 5ll data are calculated with the accuracy o ( decimal digits'which is su6cient or most e*amples.
!.). ,ilter design using 7utterworth flter
!.).. 8*ample
%tep :
Type o flter 9 low-pass flter
,ilter specifcations:
,ilter order 9 4";
%ampling reuency 9 s"1
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,irst it is necessary to compute the analog prototype flter cut-o+ reuency
>c.
The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
5s the 7utterworth reerence prototype flter has no 2eros' the e*pression
or transer unction is simpler:
%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' substituting the comple* variable s into the e*pression or analog
flter transer unction' the ollowing is obtained:
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where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
This general e*pression can be written in a simpler way in this e*ample:
5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
The flter order is predetermined.
There is no need to additionally change it.
,ilter reali2ation:
,igure !-)-" illustrates the direct reali2ation o designed IIR flter' whereas
,igure !-)-! illustrates the reuency response o the flter obtained using
,ilter $esigner Tool.
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,igure !-)-". $igital IIR flter direct reali2ation in this e*ample
,igure !-)-!. $igital IIR flter reuency characteristic in this e*ample
!.).." 8*ample "
%tep :
Type o flter 9 high-pass flter
,ilter specifcations:
,ilter order 9 4!;
%ampling reuency 9 s"1
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The 7utterworth reerence prototype flter transer unction has no 2eros'
only poles. These can be computed via e*pression:
5s 4 !' the values o poles are:
The reerence analog prototype flter transer unction is:
%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency
>c.
The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
5s the 7utterworth reerence prototype flter has no 2eros' the e*pression
or transer unction is simpler:
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%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' substituting the comple* variable s into the e*pression or analog
flter transer unction' the ollowing is obtained:
where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
This general e*pression can be written in a simpler way in this e*ample:
5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
The flter order is predetermined.
There is no need to additionally change it.
,ilter reali2ation:
,igure !-)-( illustrates the direct reali2ation o designed IIR flter.
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,igure !-)-(. $igital IIR flter direct reali2ation in this e*ample
,igure !-)-#. $igital IIR flter reuency characteristic in this e*ample
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!.)..! 8*ample !
%tep :
Type o flter 9 band-pass flter
,ilter specifcations:
,ilter order 9 4(;
%ampling reuency 9 s"1c.
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The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
5s the 7utterworth reerence prototype flter has no 2eros' the e*pression
or transer unction is simpler:
%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' by substituting the comple* variable s into the e*pression or
analog flter transer unction' the ollowing is obtained:
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where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
In this e*ample' the general e*pression can be written in a simpler way:
5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
,ilter order is predetermined.
There is no need to additionally change it.
,ilter reali2ation:
,igure !-)-) illustrates the direct reali2ation o designed IIR flter.
,igure !-)-). $igital IIR flter direct reali2ation in this e*ample
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,igure !-)-@. $igital IIR flter reuency characteristic in this e*ample
!.)..( 8*ample (
%tep :
Type o flter 9 band-stop flter
,ilter specifcations:
,ilter order 9 4(;
%ampling reuency 9 s"1
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Ahen designing an IIR band-stop flter' the reerence prototype flter order ishal that o the reuired IIR flter order. In this e*ample or 4 (' the order
o reerence prototype flter is "' so the values o poles are:
The reerence analog prototype flter transer unction is:
%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency
>c.
The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
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5s the 7utterworth reerence prototype flter has no 2eros' the e*pression
or transer unction is simpler:
%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' by substituting the comple* variable s into the e*pression or
analog flter transer unction' the ollowing is obtained:
where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
In this e*ample' the general e*pression can be written in a simpler way:
5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
,ilter order is predetermined.
There is no need to additionally change it.
,ilter reali2ation:
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,igure !-)-B illustrates the direct reali2ation o designed IIR flter.
,igure !-)-B. $igital IIR flter direct reali2ation in this e*ample
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,igure !-)-C. $igital IIR flter reuency characteristic in this e*ample
!.)." ,ilter design using hebyshev flter
!.).". 8*ample
%tep :
Type o flter 9 low-pass flter
,ilter specifcations:
%ampling reuency 9 s((112;
=assband cut-o+ reuency9 c#
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progressively until some pre-determined reuirements are satisfed. Det&s
assume that the initial flter order is (.
%tep (:
The hebyshev reerence prototype flter transer unction has no 2eros'
only poles. These can be computed via e*pression:
5s 4 (' the values o poles are:
The hebyshev flter transer unction is e*pressed as:
In this case' the value o constant 51 is:
51 1."(#@so that the hebyshev reerence analog prototype flter transer unction is:
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%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency>c.
The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
5s the hebyshev reerence prototype flter has no 2eros' the e*pression or
transer unction is simpler:
%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' by substituting the comple* variable s into the e*pression or
analog flter transer unction' the ollowing is obtained:
where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
This general e*pression can be written in a simpler way in this e*ample:
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5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
7y analy2ing the resulting flter using ,ilter $esigner Tool' it is obvious that
the attenuation amounting to !."d7 appro*imately at the reuency o
B
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It is necessary to additionally redefne the flter order until the predefned
reuirements are satisfed. The flter order is incremented by and is #
thereore. 5ll steps starting with step ! are iterated.
%tep!:
The flter order is incremented in the second iteration. 5 new flter order is #.
%tep (:
The hebyshev reerence prototype flter transer unction has no 2eros'
only poles. These can be computed via e*pression:
5s 4 #' the values o poles are:
The hebyhsev flter transer unction is e*pressed as:
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In this case' the value o constant 51 is:
51 9 1.""B
so the hebyshev reerence analog prototype flter transer unction is:
%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency
>c.
The analog flter transer unction is obtained rom the reerence analogprototype flter transer unction using e*pression:
5s the hebyshev reerence prototype flter has no 2eros' the e*pression or
transer unction is simpler:
%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' substituting the comple* variable s into the e*pression or analog
flter transer unction' the ollowing is obtained:
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where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
This general e*pression can be written in a simpler way in this e*ample:
5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
7y analy2ing the resulting flter using ,ilter $esigner Tool' it is obvious that
the attenuation amounting to (.)d7 appro*imately at the reuency o
B
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,igure !-)-. ,reuency characteristic o the resulting IIR flter
It is not necessary to urther increase the flter order as this one is
appropriate. %ometimes more iterations are needed to determine the flter
order. The whole procedure is the same' only it takes more time.
,ilter reali2ation:
,igure !-)-" illustrates the direct reali2ation o designed IIR flter' whereas
,igure !-)-! illustrates the reuency characteristic o the flter obtained
using ,ilter $esigner Tool.
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,igure !-)-". $igital IIR flter direct reali2ation
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5s 4 !' the values o poles are:
The hebyshev flter transer unction is e*pressed as:
In this case' the value o constant 51 is:51 9 1.(C!
The reerence analog prototype flter transer unction is:
%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency
>c.
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The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
5s the hebyshev reerence prototype flter has no 2eros' the e*pression or
transer unction is simpler:
5ter substitution o poles and >c into e*pression:
%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' substituting the comple* variable s into the e*pression or analog
flter transer unction' the ollowing is obtained:
where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
This general e*pression can be written in a simpler way in this e*ample:
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5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
The flter order is predetermined.
There is no need to additionally change it.
,ilter reali2ation:
,igure !-)-( illustrates the direct reali2ation o designed IIR flter.
,igure !-)-(. $irect reali2ation o digital IIR flter in this e*ample
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,igure !-)-#. ,reuency characteristic o digital IIR flter in this e*ample
!.)..! 8*ample !
%tep :
Type o flter 9 band-pass flter
,ilter specifcations:
,ilter order 9 4 (;
%ampling reuency 9 s "1
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Ahen designing an IIR band-pass flter' the reerence prototype flter orderis hal that o the reuired IIR flter order. In this e*ample or 4 (' the
order o reerence prototype flter is "' so the values o poles are:
The hebyshev flter transer unction is e*pressed as:
In this e*ample' the value o constant 51 is:
51 1.CB")
The reerence analog prototype flter transer unction is:
%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency>c.
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The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
5s the hebyshev reerence prototype flter has no 2eros' the e*pression or
transer unction is simpler:
%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' substituting the comple* variable s into the e*pression or analog
flter transer unction' the ollowing is obtained:
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where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
In this e*pression' the general e*pression can be written in a simpler way:
5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
,ilter order is predetermined.
There is no need to additionally change it.
,ilter reali2ation:
,igure !-)-) illustrates direct reali2ation o designed IIR flter.
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,ilter !-)-). $irect reali2ation o digital IIR flter in this e*ample
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,igure !-)-@. ,reuency characteristic o digital IIR flter in this e*ample
!.)..( 8*ample (
%tep :
Type o flter 9 band-stop flter,ilter specifcations:
,ilter order 9 4 (;
%ampling reuency 9 s "1
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In this e*ample' the value o constant 51 is:
51 1.CB")
The reerence analog prototype flter transer unction is:
%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency
>c.
The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
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5s the hebyshev reerence prototype flter has no 2eros' the e*pression or
transer unction is simpler:
%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' substituting the comple* variable s into the e*pression or analog
flter transer unction' the ollowing is obtained:
where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
In this e*pression' the general e*pression can be written in a simpler way:
5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
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%tep @:
,ilter order is predetermined.
There is no need to additionally change it.
,ilter reali2ation
,igure !-)-B illustrates the direct reali2ation o designed IIR flter.
,igure !-)-B. $irect reali2ation o digital IIR flter in this e*ample
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,igure !-)-C. ,reuency characteristic o digital IIR flter in this e*ample
!.).! ,ilter design using inverse hebyshev flter
!.).!. 8*ample
%tep :
Type o flter 9low-pass flter
,ilter specifcations:
%ampling reuency 9 s ((112;
=assband cut-o+ reuency 9 c #
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,ilter order is not pre-determined' so it is necessary to choose an initial
solution rom which iterative method starts. The solution is redefned
progressively until some pre-determined reuirements are satisfed. Det&s
assume that the initial flter order is (.
%tep (:
The hebyshev reerence prototype flter transer unction has no 2eros'
only poles. These can be computed via e*pression:
5s 4 (' the values o poles are:
The inverse hebyhsev flter transer unction is e*pressed as:
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In this e*ample' the value o constant 1 is:
1 1.1
so that the hebyshev reerence analog prototype flter transer unction is:
%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency
>c.
The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
In this e*ample' the analog flter transer unction becomes:
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%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' substituting the comple* variable s into the e*pression or analog
flter transer unction' the ollowing is obtained:
where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
This general e*pression can be written in a simpler way in this e*ample:
5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
7y analy2ing the resulting flter using ,ilter $esigner Tool' it is obvious that
the attenuation amounting to #."d7 appro*imately at the reuency o
#
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,igure !-)-"1. ,reuency charactersitic o designed IIR flter
The attenuation at #
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5s 4 #' the values o poles are:
The hebyhsev flter transer unction is e*pressed as:
In this case' the value o constant 1 is:
1 9 1.1#
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so the inverse hebyshev reerence analog prototype flter transer unction
is:
%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency
>c.
The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
In this e*ample' the analog flter transer unction becomes:
%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' substituting the comple* variable s into the e*pression or analog
flter transer unction' the ollowing is obtained:
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where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
This general e*pression can be written in a simpler way in this e*ample:
5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
7y analysing the resulting flter using ,ilter $esigner Tool' it is obvious that
the attenuation at B
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,igure !-)-". ,reuency characteristic o IIR flter
It is not necessary to urther increase the flter order as this one is
approriate. %ometimes more iterations are needed to determine the flter
order. The whole procedure is the same' only it takes more time.
,ilter reali2ation:
,igure !-)-"" illustrates the direct reali2ation o designed IIR flter' whereas
,igure !-)-"! illustrates the reuency characteristic o the flter obtained
using ,ilter $esigner Tool.
,igure !-)-"". $irect reali2ation o digital IIR flter in this e*ample
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,igure !-)-"!. ,reuency characteristic o digital IIR flter in this e*ample
!.).." 8*ample "
%tep :
Type o flter 9 high-pass flter
,ilter specifcations:
,ilter order 9 4 !;
%ampling reuency 9 s "1
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The hebyshev reerence prototype flter transer unction has no 2eros'
only poles. These can be computed via e*pression:
5s 4 !' the values o poles are:
The inverse hebyshev flter transer unction is e*pressed as:
In this case' the value o constant 1 is:
1 -1.1!
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The reerence analog prototype flter transer unction is:
%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency
>c.
The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
In this e*ample' the transer unction is:
5ter substituting the poles and >c into e*pression:
%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' by substituting the comple* variable s into the e*pression or
analog flter transer unction' the ollowing is obtained:
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where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
This general e*pression can be written in a simpler way in this e*ample:
5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
The flter order is predetermined. There is no need to additionally change it.
,ilter reali2ation:
,igure !-)-"( illustrates the direct reali2ation o designed IIR flter.
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,igure !-)-"(. $irect reali2ation o digital IIR flter in this e*ample
,igure !-)-"#. ,reuency characteristic o digital IIR flter in this e*ample
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!.)..! 8*ample !
%tep :
Type o flter 9 band-pass flter
,ilter specifcation:
,ilter order 9 4 (;
%ampling reuency 9 s "1
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In this e*ample' the value o constant 1 is:
1 1.1
The reerence analog prototype flter transer unction is:
%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency
>c.
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The analog flter transer unction is obtained rom the reerence analog
prototype flter transer unction using e*pression:
,or this e*ample' the analog flter transer unction is:
%tep ):
The transormation into a digital flter through bilinear transormation:
?enerally' substituting the comple* variable s into the e*pression or analog
flter transer unction' the ollowing is obtained:
where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.
In this e*ample' the general e*pression can be written in a simpler way:
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5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
,ilter order is predetermined.
There is no need to additionally change it.
,ilter reali2ation:
,igure !-)-") illustrates direct reali2ation o designed IIR flter.
,igure !-)-"). $irect reali2ation o digital IIR flter in this e*ample
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,igure !-)-"@. ,reuency characteristic o digital IIR flter in this e*ample
!.)..( 8*ample (
%tep :
Type o flter 9 band-stop flter
,ilter specifcation:
,ilter order 9 4(;
%ampling reuency 9 s"1
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The inverse hebyshev reerence prototype flter transer unction has no
2eros' only poles. These can be computed via e*pression:
Ahen designing an IIR band-stop flter' the reerence prototype flter order is
hal that o the reuired IIR flter order. In this e*ample or 4 (' the order
o reerence prototype flter is "' so the values o poles are:
The inverse hebyshev flter transer unction is e*pressed as:
In this e*ample' the value o constant 1 is:
1 1.1
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The reerence analog prototype flter transer unction is:
%tep #:
,irst it is necessary to compute the analog prototype flter cut-o+ reuency
>c.
The analog flter transer unction is obtained rom the reerence analogprototype flter transer unction using e*pression:
In this e*ample' the analog flter transer unction is:
%tep ):
The transormation into a digital flter through bilinear transormation:
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?enerally' substituting the comple* variable s into the e*pression or analog
flter transer unction' the ollowing is obtained:
where:
2k are the 2eros o analog flter transer unction; and
pk are the poles o analog flter transer unction.In this e*pression' the general e*pression can be written in a simpler way:
5 more condensed orm o the previous e*pression is:
The result is the IIR flter transer unction.
%tep @:
,ilter order is predetermined.
There is no need to additionally change it.
,ilter reali2ation:
,igure !-)-"B illustrates the direct reali2ation o designed IIR flter.
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,igure !-)-"B. $irect reali2ation o digital IIR flter in this e*ample
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,igure !-)-"C. ,reuency characteristic o digital IIR flter in this e*ample
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Table o ontents
lose
Introduction
. Introduction to $igital ,ilter $esign
. 7asic concepts o digital fltering
.".Types o digital flters
". ,inite Impulse Response /,IR0 ,ilter
mailto:?subject=I%20wanted%20to%20share%20this%20post%20with%20you%20from%20Digital%20Filter%20Design&body=3.6%20Examples%20-%20http%3A%2F%2Flearn.mikroe.com%2Febooks%2Fdigitalfilterdesign%2Fchapter%2Fexamples-2%2Fhttp://learn.mikroe.com/ebooks/digitalfilterdesign/table-of-contentshttp://learn.mikroe.com/ebooks/digitalfilterdesign/chapter/examples-2/http://learn.mikroe.com/ebooks/digitalfilterdesign/front-matter/introduction/http://learn.mikroe.com/ebooks/digitalfilterdesign/chapter/basic-concepts-of-digital-filtering/http://learn.mikroe.com/ebooks/digitalfilterdesign/chapter/types-of-digital-filters/http://learn.mikroe.com/ebooks/digitalfilterdesign/table-of-contentshttp://learn.mikroe.com/ebooks/digitalfilterdesign/chapter/examples-2/http://learn.mikroe.com/ebooks/digitalfilterdesign/front-matter/introduction/http://learn.mikroe.com/ebooks/digitalfilterdesign/chapter/basic-concepts-of-digital-filtering/http://learn.mikroe.com/ebooks/digitalfilterdesign/chapter/types-of-digital-filters/mailto:?subject=I%20wanted%20to%20share%20this%20post%20with%20you%20from%20Digital%20Filter%20Design&body=3.6%20Examples%20-%20http%3A%2F%2Flearn.mikroe.com%2Febooks%2Fdigitalfilterdesign%2Fchapter%2Fexamples-2%2F
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". Introduction
"." ,inite impulse response /,IR0 flter design methods
".! Aindow unctions
".( 8*amples ".# ,inite word-length e+ects
!. Infnite Impulse Response /IIR0 ,ilters
!. Introduction
!." Infnite impulse response /IIR0 flter design
!.! Reerence 5nalog =rototype ,ilter
!.( 5nalog prototype flter to analog flter transormation
!.# 7ilinear transormation
!.) 8*amples
!.) 8*amples by 3ikro8lektronika is licensed under a reative ommons
5ttribution (.1 International Dicense' e*cept where otherwise noted.
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Ahat a top gun fghter-Ket pilot has in common with a good embedded
developer
# $5J% 5?F
e*iwear on