Cascade IIR Filters

Discussion:

Cascade IIR Filters

(too old to reply)

Anju

2004-04-20 20:10:00 UTC

Hi! Ken,
here's what am trying to do..i should be able to generate the
coefficients of a Nth order filter just by using a 2nd order and/or a
1st order...is it possible??..

Anju

Hi! Abhay,
Thanks for ur reply.I tried that already but it would
defeat the very purpose of cascading filters because u need to

get

the direct coefficients first then use zp2sos to get the

cascade

form...what am trying to do is for eg. if i need the

coefficients

a 4th order butterworth filter, i should be able to cascade 2

2nd

order filters...is it possible???....
Anju

hi! All,
i would like some info on implementing cascade form

IIR

filters...does matlab support it???...as far as i can

understand

butter,cheby1,cheby2,bessel,ellip generate

coefficients in the

direct
form...how do i implement the cascade form...
TIA
Anju

Hi
You might like to use commands like tf2zp and zp2sos to

get it

into

cascaded form IIR.
[z,p,k]=tf2zp(b,a);
sys=zp2sos(z,p,k)
A. Kumar

I do not see how this defeats the very purpose of cascading
filters. Perhaps
you need to explain what is the very purpose of cascading filters.
I always
understood that one designs the filter for the response you want
and onlt
then does one restructures it for the implementation... as Abhay
has
suggested.

Anju

2004-04-20 16:24:15 UTC

Permalink

Hi! Abhay,
Thanks for ur reply.I tried that already but it would
defeat the very purpose of cascading filters because u need to get
the direct coefficients first then use zp2sos to get the cascade
form...what am trying to do is for eg. if i need the coefficients of
a 4th order butterworth filter, i should be able to cascade 2 2nd
order filters...is it possible???....

Anju

hi! All,
i would like some info on implementing cascade form IIR
filters...does matlab support it???...as far as i can

understand

butter,cheby1,cheby2,bessel,ellip generate coefficients in the
direct
form...how do i implement the cascade form...
TIA
Anju

Hi
You might like to use commands like tf2zp and zp2sos to get it into
cascaded form IIR.
[z,p,k]=tf2zp(b,a);
sys=zp2sos(z,p,k)
A. Kumar

Ken Davis

2004-04-20 16:48:01 UTC

Permalink

hi! All,
i would like some info on implementing cascade form IIR
filters...does matlab support it???...as far as i can

understand

butter,cheby1,cheby2,bessel,ellip generate coefficients in the
direct
form...how do i implement the cascade form...
TIA
Anju

Hi
You might like to use commands like tf2zp and zp2sos to get it into
cascaded form IIR.
[z,p,k]=tf2zp(b,a);
sys=zp2sos(z,p,k)
A. Kumar

I do not see how this defeats the very purpose of cascading filters. Perhaps
you need to explain what is the very purpose of cascading filters. I always
understood that one designs the filter for the response you want and onlt
then does one restructures it for the implementation... as Abhay has
suggested.

Abhay Kumar

2004-04-20 15:04:15 UTC

Permalink

hi! All,
i would like some info on implementing cascade form IIR
filters...does matlab support it???...as far as i can understand
butter,cheby1,cheby2,bessel,ellip generate coefficients in the
direct
form...how do i implement the cascade form...
TIA
Anju

Hi

You might like to use commands like tf2zp and zp2sos to get it into
cascaded form IIR.
something like:
[z,p,k]=tf2zp(b,a);
sys=zp2sos(z,p,k)

A. Kumar

Ken Davis

2004-04-21 12:45:16 UTC

Permalink

Post by Anju
Hi! Ken,
here's what am trying to do..i should be able to generate the
coefficients of a Nth order filter just by using a 2nd order and/or a
1st order...is it possible??..
Anju

Hi! Abhay,
Thanks for ur reply.I tried that already but it would
defeat the very purpose of cascading filters because u need to

get

the direct coefficients first then use zp2sos to get the

cascade

form...what am trying to do is for eg. if i need the

coefficients

a 4th order butterworth filter, i should be able to cascade 2

2nd

order filters...is it possible???....
Anju

hi! All,
i would like some info on implementing cascade form

IIR

filters...does matlab support it???...as far as i can

understand

butter,cheby1,cheby2,bessel,ellip generate

coefficients in the

direct
form...how do i implement the cascade form...
TIA
Anju

Hi
You might like to use commands like tf2zp and zp2sos to

get it

into

cascaded form IIR.
[z,p,k]=tf2zp(b,a);
sys=zp2sos(z,p,k)
A. Kumar

I do not see how this defeats the very purpose of cascading
filters. Perhaps
you need to explain what is the very purpose of cascading filters.
I always
understood that one designs the filter for the response you want and onlt
then does one restructures it for the implementation... as Abhay has
suggested.

You haven't answered my question. You can design 2nd order sections and
cascade them (by multiplying their transfer functions) or you can break an
n-th order filter into second order sections. What else could you want?

Jason Schickler

2004-04-21 13:33:07 UTC

Permalink

Hey guys,

I think what you want to do is design the filter directly in ZPK and
then convert to SOS to avoid the numerical errors that come from
converting to the transfer function.

You should be able to do something like this:

[z,p,k] = butter(10, .4);

When you request 3 outputs from BUTTER it returns the zeros, poles
and gains and never converts to a transfer function which eliminates
a good amount of round-off error.

Now you can use zp2sos without fear.

[sos, g] = zp2sos(z,p,k);

And if you have a recent version of Signal Processing Toolbox, you
can pass this into an object and then to FVTool.

Hd = dfilt.df2sos(sos, g);
fvtool(Hd);

You can also see the improvement by passing the TF version of the
same butterworth filter to FVTool

[b, a] = butter(10, .4);
Hd2 = dfilt.df2(b, a);
fvtool(Hd, Hd2)

Jason