Anti-Aliasing filter

If you are estimating time-delay bewteen two microphones would it be
better to use a Bessel filter for anti-aliasing rather than a
Butterworth due to the approximate linear phase.


Wang King

On 31 Mar, 08:24, gyansor...@gmail.com wrote:
> If you are estimating time-delay bewteen two microphones would it be
> better to use a Bessel filter for anti-aliasing rather than a
> Butterworth due to the approximate linear phase.

I must admit that I don't know Bessel filters very well,
but I *think* they have a magnitude response like

|H(w)| ~ 1/w.

So the almost-linear phase is bought at the expense of a
lower effective bandwidth, which is bad, since large
bandwidth is good to pin-point events in time.

If the above is correct, I think I would stick with the
Butterworth, or maybe a Chebyshev, but make sure to use
similar anti-alias filters on all channels.

Having done that, I would use cross correlations between
channels to estimate relative delays, possibly using the
phase response of relevant cross spectra to obtain fine
resolution of time delays.

Rune

Rune Allnor wrote:
> On 31 Mar, 08:24, gyansor...@gmail.com wrote:
>> If you are estimating time-delay bewteen two microphones would it be
>> better to use a Bessel filter for anti-aliasing rather than a
>> Butterworth due to the approximate linear phase.
> 
> I must admit that I don't know Bessel filters very well,
> but I *think* they have a magnitude response like
> 
> |H(w)| ~ 1/w.
> 
> So the almost-linear phase is bought at the expense of a
> lower effective bandwidth, which is bad, since large
> bandwidth is good to pin-point events in time.
> 
> If the above is correct, I think I would stick with the
> Butterworth, or maybe a Chebyshev, but make sure to use
> similar anti-alias filters on all channels.
> 
> Having done that, I would use cross correlations between
> channels to estimate relative delays, possibly using the
> phase response of relevant cross spectra to obtain fine
> resolution of time delays.

I would try to use a cheap and dirty (single RC?) filter and a sampling 
rate high enough to keep keep aliasing above the frequency of interest, 
then low-pass/decimate with a linear phase filter. The phase shift of an 
RC is 5.7 degrees a decade below 1/RC

If that's not practical, I'd remember that a pair of matched filters 
will delay the signals from the two microphone equally, so the problem 
of inconstant group delay might not be as severe as at first imagined.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Apr 1, 3:50 pm, Jerry Avins <j...@ieee.org> wrote:
> Rune Allnor wrote:
> > On 31 Mar, 08:24, gyansor...@gmail.com wrote:
> >> If you are estimating time-delay bewteen two microphones would it be
> >> better to use a Bessel filter for anti-aliasing rather than a
> >> Butterworth due to the approximate linear phase.
>
> > I must admit that I don't know Bessel filters very well,
> > but I *think* they have a magnitude response like
>
> > |H(w)| ~ 1/w.
>
> > So the almost-linear phase is bought at the expense of a
> > lower effective bandwidth, which is bad, since large
> > bandwidth is good to pin-point events in time.
>
> > If the above is correct, I think I would stick with the
> > Butterworth, or maybe a Chebyshev, but make sure to use
> > similar anti-alias filters on all channels.
>
> > Having done that, I would use cross correlations between
> > channels to estimate relative delays, possibly using the
> > phase response of relevant cross spectra to obtain fine
> > resolution of time delays.
>
> I would try to use a cheap and dirty (single RC?) filter and a sampling
> rate high enough to keep keep aliasing above the frequency of interest,
> then low-pass/decimate with a linear phase filter. The phase shift of an
> RC is 5.7 degrees a decade below 1/RC
>
> If that's not practical, I'd remember that a pair of matched filters
> will delay the signals from the two microphone equally, so the problem
> of inconstant group delay might not be as severe as at first imagined.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF

How do I design matched filters? I only know that a matched filter has
impulse response that is the time-reverse of the incoming signal. If
the signal was a pulse then fine but I have speech signals....

W=2EK

gyansorova@gmail.com wrote:

   ...

> How do I design matched filters? I only know that a matched filter has
> impulse response that is the time-reverse of the incoming signal. If
> the signal was a pulse then fine but I have speech signals....

I meant "matched filters" in the same way that an analog designer used 
matched resistors or a stereo builder matched speakers. In other words, 
as close to identical as practical. In digital implementations, that is 
"identical filters". The same (slight) phase shift in both microphone 
channels should not greatly interfere with delay estimation. Still, 
sample as fast as you can and decimate. Whatever filter type you use, 
that will minimize analog phase shift in the final band of interest.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Hi,
I have a question about anti-aliasing filters which I thought would fit in
this discussion thread.  
I have an RC circuit and my ultimate goal is to estimate the value of the
capacitor using least square estimation.  In order to carry out this
estimation I need to discretize the system transfer function and find the
ARMA model, however to do that I need to use an anti-aliasing filter first
to make the transfer function bandlimited.  
I tried using a Butterworth filter, which does very well is preserving the
magnitude response of the system however the phase is really not preserved
and since I'm trying to estimate the value of the capacitor in the system I
thought preserving the phase is important for my estimation purposes. 
However I am now not certain any more.
So my question is how do I know if preserving phase is important in an
application or not? and if it is what is the best anti-aliasing filter that
would preserve phase?
thanks 

orien1202 wrote:
> Hi,
> I have a question about anti-aliasing filters which I thought would fit in
> this discussion thread.  
> I have an RC circuit and my ultimate goal is to estimate the value of the
> capacitor using least square estimation.  In order to carry out this
> estimation I need to discretize the system transfer function and find the
> ARMA model, however to do that I need to use an anti-aliasing filter first
> to make the transfer function bandlimited.  
> I tried using a Butterworth filter, which does very well is preserving the
> magnitude response of the system however the phase is really not preserved
> and since I'm trying to estimate the value of the capacitor in the system I
> thought preserving the phase is important for my estimation purposes. 
> However I am now not certain any more.
> So my question is how do I know if preserving phase is important in an
> application or not? and if it is what is the best anti-aliasing filter that
> would preserve phase?

I'm thoroughly confused. Are you trying to guess the size of the 
capacitor in an R-C rolloff you can't examine? Do you want to design a 
filter and need to determine the appropriate capacitor value? Are you 
hunting mosquitoes with a shotgun? :-)

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

On 16 Jul, 23:30, "orien1202" <saharmonfa...@yahoo.ca> wrote:
> Hi,
> I have a question about anti-aliasing filters which I thought would fit in
> this discussion thread. &#4294967295;

That thread is a year and a half old. What's wrong with starting
a new thread?

> I have an RC circuit and my ultimate goal is to estimate the value of the
> capacitor using least square estimation.

Any particular RC cirquit, or just *some* RC cirquit?

>&#4294967295;In order to carry out this
> estimation I need to discretize the system transfer function and find the
> ARMA model,

What does ARMA models have to do with RC networks?

> however to do that I need to use an anti-aliasing filter first
> to make the transfer function bandlimited. &#4294967295;

If you want to sample the data, then yes, you need an anti-alias
filter.

> I tried using a Butterworth filter, which does very well is preserving the
> magnitude response of the system however the phase is really not preserved
> and since I'm trying to estimate the value of the capacitor in the system I
> thought preserving the phase is important for my estimation purposes.

For your information, the phase is lost in ARMA models.

> However I am now not certain any more.

Whenever you implement an RC network you necessarily mess
with both magnitude and phase.

> So my question is how do I know if preserving phase is important in an
> application or not?

Usually, it is not. Simply because it is impossible to
preserve phase in any useful cirquits. The best you can
hope for is to state what kind of phase degradation
is acceptable, and how much.

> and if it is what is the best anti-aliasing filter that
> would preserve phase?

Again, you need to find out what is acceptable in the end
applications. The phase is lost in ARMA models, so if that's
what you are going to find, there is no reason to worry
about phase in the anti-alias filter.

Rune

On Jul 16, 5:30&#4294967295;pm, "orien1202" <saharmonfa...@yahoo.ca> wrote:

and if it is what is the best anti-aliasing filter that
> would preserve phase?
> thanks

I am involved in many applications where preserving phase is
important. To preserve phase the type of anti-aliasing filter is not
that important, but how you implement it is. We use very stable
precision caps/resistors that have very low drift over time/
temperature, then model the inverse of the transfer function of the
anti-aliasing filter in software, then compensate for any phase errors
introduced by the filter. We also generally use a delta-sigma A/D for
phase important applications, as it simplifies the anti-aliasing
filter, and therefore the cost (since the precise resistors/caps are
not cheap or physically small)

"orien1202" <saharmonfared@yahoo.ca> wrote in
news:PpWdncfkZLIY9ePVnZ2dnUVZ_qPinZ2d@giganews.com: 

> Hi,
> I have a question about anti-aliasing filters which I thought would
> fit in this discussion thread.  
> I have an RC circuit and my ultimate goal is to estimate the value of
> the capacitor using least square estimation.  In order to carry out
> this estimation I need to discretize the system transfer function and
> find the ARMA model, however to do that I need to use an anti-aliasing
> filter first to make the transfer function bandlimited.  
> I tried using a Butterworth filter, which does very well is preserving
> the magnitude response of the system however the phase is really not
> preserved and since I'm trying to estimate the value of the capacitor
> in the system I thought preserving the phase is important for my
> estimation purposes. However I am now not certain any more.
> So my question is how do I know if preserving phase is important in an
> application or not? and if it is what is the best anti-aliasing filter
> that would preserve phase?
> thanks 

The Bessel filter produces linear phase-- i.e., a simple time delay.  Best 
practice is to filter all your channels through the same filter.

-- 
Scott
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