Linear phase IIR filter

Hello,

I am currently designing a decimating filter for a sigma delta 
converter. I am searching a small decimating filter. I heard about 
approximately linear phase iir filter.

Where can I find some implementation examples?

Thanks you in advance

Thoma

Check

http://www.dspguru.com/info/faqs/fir/props.htm

In article <445db9b9$0$29588$636a55ce@news.free.fr>, thoma <pas@d.adresse> 
wrote:
>Hello,
>
>I am currently designing a decimating filter for a sigma delta 
>converter. I am searching a small decimating filter. I heard about 
>approximately linear phase iir filter.
>
>Where can I find some implementation examples?
>
>Thanks you in advance
>
>Thoma

John Herman wrote:
>
> http://www.dspguru.com/info/faqs/fir/props.htm

for some reason, my domain name server says there is no dspguru.com .
geez, i hope that Grant didn't shut it down.

> In article <445db9b9$0$29588$636a55ce@news.free.fr>, thoma <pas@d.adresse>
> wrote:
> >
> >I am currently designing a decimating filter for a sigma delta
> >converter. I am searching a small decimating filter. I heard about
> >approximately linear phase iir filter.

there are three things that i can understand being what you are
refering to.  first of all, there are no *exactly* linear phase IIR
filters.  But:

1. there are Bessel filters (analog s-plane) that have very flat group
delay for nearly all frequencies of interest.  but their selectivity is
not so good.  probably a commercial package like what comes from
Momentum Data would be able to design it.  maybe there's a MATLAB
toolbox function that will.

2. with all-pass filters, you can smooth out the humps, in the
group-delay (or phase-delay) response of a reasonably well-behaved
analog filter (such as a Butterworth or maybe Tchebyshev or inverse
Tchebyshev, but certainly not Elliptical), but i don't know of a good
automated design procedure of where to put the resonant frequency and Q
of the APF to get the flattest response.  if you're making a digital
filter, first bilinear transform the analog design to digital and then
try to fit an APF to flatten out the group delay.

3. there are the so-called "Truncated IIR" filters (TIIR) which are
actually FIR filters but designed in such a way as an IIR with another
delayed IIR that clips off the tail (making it an FIR).  this doesn't
make them constant delay, but you can break apart the input into a pair
of "ping-pong" buffers, and run the filtered data through identical
TIIR filters *backwards" (this makes it phase linear) and then
reconstructing with overlap-add.  big awful design process.

(just for sematics:  "linear phase" = "constant group delay" or
"constant phase delay".)

r b-j

In article <1147034634.336519.223150@i39g2000cwa.googlegroups.com>, "robert bristow-johnson" <rbj@audioimagination.com> wrote:
>
>John Herman wrote:
>>
>> http://www.dspguru.com/info/faqs/fir/props.htm
>
>for some reason, my domain name server says there is no dspguru.com .
>geez, i hope that Grant didn't shut it down.
>
dspguru.com =  66.75.164.90

The reason I pointed th OP tp DSP Guru was that they were talking about FIR 
filters.  For decimation and linear phase, there isn't an IIR filter that can 
compete in terms of operation count or constant delay characteristics

On 7 May 2006 13:43:54 -0700, "robert bristow-johnson"
<rbj@audioimagination.com> wrote:

>2. with all-pass filters, you can smooth out the humps, in the
>group-delay (or phase-delay) response of a reasonably well-behaved
>analog filter (such as a Butterworth or maybe Tchebyshev or inverse
>Tchebyshev, but certainly not Elliptical), 

I have in my possession a set of TTE passive analog 5th order elliptic
"delay compensated" lowpass filters that are within a few degrees of
linear phase from DC to just above the cutoff frequency (~20 kHz).  I
purchased these filters for a project in 1993.  I contacted TTE a few
years ago to find out how they were constructed, but they indicated that
they no longer sell the type and could not provide any design info.

Maybe one of these days I should break open the encapsulation and see
what kind of magic topology and components they used.

Greg

John Herman wrote:
> In article <1147034634.336519.223150@i39g2000cwa.googlegroups.com>, "robert bristow-johnson" <rbj@audioimagination.com> wrote:
> >
> >John Herman wrote:
> >>
> >> http://www.dspguru.com/info/faqs/fir/props.htm
> >
> >for some reason, my domain name server says there is no dspguru.com .
> >geez, i hope that Grant didn't shut it down.
> >
> dspguru.com =  66.75.164.90

now it says that the connection was refused by 66.75.164.90.  maybe
Grant doesn't like me and won't let my IP get in there.

> The reason I pointed th OP tp DSP Guru was that they were talking about FIR
> filters.  For decimation and linear phase, there isn't an IIR filter that can
> compete in terms of operation count or constant delay characteristics.

especially since an FIR can be perfectly linear phase and an IIR can't.

but, seriously John, you might want to Google "Avery Wang", "Julius
Smith", and "TIIR" and look up this thing called Truncated IIR filters.
 they are really FIR but implemented with IIRs and a delay line.  the
CIC would be a simple non-trivial example.  at least from what i read
(and i thunk that i understood it pretty well) they can do a pretty
sharp phase linear LPF with cutoff at low frequencies for a lot less
MACs than a normal transversal FIR.  might not beat "fast convolution"
using the FFT.


Greg Berchin wrote:
> On 7 May 2006 13:43:54 -0700, "robert bristow-johnson"
> <rbj@audioimagination.com> wrote:
>
> >2. with all-pass filters, you can smooth out the humps, in the
> >group-delay (or phase-delay) response of a reasonably well-behaved
> >analog filter (such as a Butterworth or maybe Tchebyshev or inverse
> >Tchebyshev, but certainly not Elliptical),
>
> I have in my possession a set of TTE passive analog 5th order elliptic
> "delay compensated" lowpass filters that are within a few degrees of
> linear phase from DC to just above the cutoff frequency (~20 kHz).  I
> purchased these filters for a project in 1993.  I contacted TTE a few
> years ago to find out how they were constructed, but they indicated that
> they no longer sell the type and could not provide any design info.
>
> Maybe one of these days I should break open the encapsulation and see
> what kind of magic topology and components they used.

wow.  to make such an aminal outa R's, L's, and C's seems like a
formidable task.  one thing is that a few degrees of phase mean a lot
of time at low frequencies.  i wonder what the group delay or phase
delay would look like.

my recollection of the group delay or Elliptical filters was the same
as that of Grover and Deller ( http://www.redcedar.com/revaes.htm )
which was something like "Drunk fly on cross-country skis in tornado".

it would be truly interesting to know the circuit, figger out the
transfer function, and see what they did.

r b-j

analog delay compensated filters are usually filters in cascade with
all pass filters.  The all pass filters have nearly flat frequency
reposnse but add delay at certain frequencies.  The uncompensated low
pass filters usually has the most delay near the cutoff.  The all pass
filters are added to add delay to the lower frequency regions so that
the delay is more nearly constant throughout the passband....  look up
all pass filter and group delay compensation  for more info...

Mark

Is the title something like "Tail Cancelling IIR Filters"?  If it is, I read 
it.  The operation count seems a little high.  That may not matter to the OP, 
though.

In article <1147050425.962807.183400@i39g2000cwa.googlegroups.com>, "robert 
bristow-johnson" <rbj@audioimagination.com> wrote:
>John Herman wrote:
>but, seriously John, you might want to Google "Avery Wang", "Julius
>Smith", and "TIIR" and look up this thing called Truncated IIR filters.
> they are really FIR but implemented with IIRs and a delay line.  the
>CIC would be a simple non-trivial example.  at least from what i read
>(and i thunk that i understood it pretty well) they can do a pretty
>sharp phase linear LPF with cutoff at low frequencies for a lot less
>MACs than a normal transversal FIR.  might not beat "fast convolution"
>using the FFT.
>

>r b-j
>

robert bristow-johnson wrote:

...
> there are three things that i can understand being what you are
> refering to.  first of all, there are no *exactly* linear phase IIR
> filters.

You meant: There are no *exactly* linear phase _causal_ IIR filters.

> But:
>
> 1. there are Bessel filters (analog s-plane) that have very flat group
> delay for nearly all frequencies of interest.  but their selectivity is
> not so good.  probably a commercial package like what comes from
> Momentum Data would be able to design it.  maybe there's a MATLAB
> toolbox function that will.
>
> 2. with all-pass filters, you can smooth out the humps, in the
> group-delay (or phase-delay) response of a reasonably well-behaved
> analog filter (such as a Butterworth or maybe Tchebyshev or inverse
> Tchebyshev, but certainly not Elliptical), but i don't know of a good
> automated design procedure of where to put the resonant frequency and Q
> of the APF to get the flattest response.  if you're making a digital
> filter, first bilinear transform the analog design to digital and then
> try to fit an APF to flatten out the group delay.
>
> 3. there are the so-called "Truncated IIR" filters (TIIR) which are
> actually FIR filters but designed in such a way as an IIR with another
> delayed IIR that clips off the tail (making it an FIR).  this doesn't
> make them constant delay, but you can break apart the input into a pair
> of "ping-pong" buffers, and run the filtered data through identical
> TIIR filters *backwards" (this makes it phase linear) and then
> reconstructing with overlap-add.  big awful design process.

4. The "filtfilt" technique: Forwards and backwards filtering with any
filter (IIR, FIR, TIIR,...) squares magnitude response and cancels
phase response. The Powell and Chau implementation of this technique is
true IIR (only the pre-response is finite, the post-response is
infinite) and approximate linear-phase.

Regards,
Andor

Andor wrote:
> robert bristow-johnson wrote:
> 
> ...
>> there are three things that i can understand being what you are
>> refering to.  first of all, there are no *exactly* linear phase IIR
>> filters.
> 
> You meant: There are no *exactly* linear phase _causal_ IIR filters.
> 
You meant: There are no *exactly* linear phase _causal_ and _stable_ IIR
filters. ;)
> 
*snip*
> Regards,
> Andor

-- 
Jani Huhtanen
Tampere University of Technology, Pori