The Delay of Minimum Phase FIR filter

Dear all,
I would like to ask is there any way to have analytical estimation value of
delay of minimum phase FIR filter based on the following assumptions:

1. we regard the position of largest magnitude coefficient as the delay, so
for linear symmetric FIR filter the delay = (N+1)/2, where N is number of
coefficient.

2. If we use same measure for minimum-phase FIR delay, how can we estimate
or analytically know the delay of a particular minimum-phase FIR filter in
terms of number of samples? 

In most literature I searched, it says for minimum phase FIR, the maximum
coefficient "near" the beginning of impulse response. but I am not happy
about the description of "near". Is there anyway I can found out exact
expression of delay value? Or is there any paper people can point to me to
read about?

Many thanks for help.

On Fri, 17 May 2013 16:53:15 -0500, "wyonghao" <42396@dsprelated>
wrote:

>Dear all,
>I would like to ask is there any way to have analytical estimation value of
>delay of minimum phase FIR filter based on the following assumptions:
>
>1. we regard the position of largest magnitude coefficient as the delay, so
>for linear symmetric FIR filter the delay = (N+1)/2, where N is number of
>coefficient.
>
>2. If we use same measure for minimum-phase FIR delay, how can we estimate
>or analytically know the delay of a particular minimum-phase FIR filter in
>terms of number of samples? 
>
>In most literature I searched, it says for minimum phase FIR, the maximum
>coefficient "near" the beginning of impulse response. but I am not happy
>about the description of "near". Is there anyway I can found out exact
>expression of delay value? Or is there any paper people can point to me to
>read about?
>
>Many thanks for help.

Remember, an impulse response is the response to an impulse input, and
the coefficients in a FIR are the impulse response.   So if you saw
the coefficient set come out of the filter in response to an impulse,
what feature in the coefficient set would you use to define the moment
of the impulse "output" of the filter?   Most people would say the
maximum value of the tallest lobe for a reasonably-shaped impulse
response.

From that you might be able to determine your own interpretation of
what "near" the beginning of the impulse response means for
minimum-phase filter.


Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

On 5/17/2013 4:53 PM, wyonghao wrote:
> Dear all,
> I would like to ask is there any way to have analytical estimation value of
> delay of minimum phase FIR filter based on the following assumptions:

Wrong assumptions.

> 1. we regard the position of largest magnitude coefficient as the delay, so
> for linear symmetric FIR filter the delay = (N+1)/2, where N is number of
> coefficient.

Here is linear phase filter for you:  [1  0  -1]

> 2. If we use same measure for minimum-phase FIR delay, how can we estimate
> or analytically know the delay of a particular minimum-phase FIR filter in
> terms of number of samples?

Here is minumum phase filter for you: H(t) = exp(-t)

> In most literature I searched, it says for minimum phase FIR, the maximum
> coefficient "near" the beginning of impulse response. but I am not happy
> about the description of "near".

I am not happy either because this is nonsense.

> Is there anyway I can found out exact
> expression of delay value? Or is there any paper people can point to me to
> read about?

Define what do you mean by "delay".


Vladimir Vassilevsky
DSP and Mixed Signal Designs
www.abvolt.com

On May 17, 5:53&#4294967295;pm, "wyonghao" <42396@dsprelated> wrote:
> Dear all,
> I would like to ask is there any way to have analytical estimation value of
> delay of minimum phase FIR filter based on the following assumptions:
>
> 1. we regard the position of largest magnitude coefficient as the delay, so
> for linear symmetric FIR filter the delay = (N+1)/2, where N is number of
> coefficient.
>
> 2. If we use same measure for minimum-phase FIR delay, how can we estimate
> or analytically know the delay of a particular minimum-phase FIR filter in
> terms of number of samples?
>
> In most literature I searched, it says for minimum phase FIR, the maximum
> coefficient "near" the beginning of impulse response. but I am not happy
> about the description of "near". Is there anyway I can found out exact
> expression of delay value? Or is there any paper people can point to me to
> read about?
>

you need to be more explicit by what you mean by "delay" in number 2
above.  what is the "same measure"?  is it where the major lobe is?

r b-j

Hello
>>Define what do you mean by "delay".
Vladimir Vassilevsky
------------------
>you need to be more explicit by what you mean by "delay" in number 2
>above.  what is the "same measure"?  is it where the major lobe is?
-------------------
>r b-j

Let me explain my definition of "delay" of FIR filters. 

It is commonly agreed that cross correlation (CC) method is used for
estimate delay: taking CC, then looking for the time position of the
maximum value. CC can be also used for estimating impulse response as well,
actually I saw a prove that the cross correlation is equivalent to impulse
response (IR) for a linear system and the IR of FIR is its coefficients.

Therefore, I assume the position of the maximum value or "where the major
lobe is" can be defined as delay of the FIR filter which is equivalent to
group delay. 

Ok, for minimum phase FIR, the group delay is not constant, but I am only
looking for a time delay which "most of information or signal behavior" is
passed through the filter system. 

So I want to use the "where the major lobe is" to define the delay of
minimum phase FIR as well. the symmetric linear phase FIR with N
coefficient can be estimated as roughly N/2 or (N+1)/2. I would like to
have something similar to minimum phase FIR filter for example (1/10)*N or
(1/20)*N, so before we actually designed a minimum filter, we can estimate
the number of order (there are many way to do that) and the delay as well.

Hope I explained my thought clearly. and hope you dsp gurus can enlighten
me on that.

You can only extract this "approximate" delay if your filter has flat group delay over a large portion of the spectrum, and only deviates from this near the cutoff. So you are pretty much restricted to classical lowpass/highpass types of filters. If your filter has a lot of peaks and dips, the min-phase group delay will never be constant enough to make the approximation you would like to make.

How are you going about designing your min-phase FIR? In general, if you feed your specifications into an IIR design program, and look at the group delay and position of the peak impulse, I would expect that a min phase FIR designed to the same specs could not do any better.


Bob

On Sat, 18 May 2013 05:01:20 -0500, "wyonghao" <42396@dsprelated>
wrote:

>Ok, for minimum phase FIR, the group delay is not constant, but I am only
>looking for a time delay which "most of information or signal behavior" is
>passed through the filter system. 

Search for "Central Time" and "RMS Duration".

Greg

On Sat, 18 May 2013 05:01:20 -0500, "wyonghao" <42396@dsprelated>
wrote:

>Hello
>>>Define what do you mean by "delay".
>Vladimir Vassilevsky
>------------------
>>you need to be more explicit by what you mean by "delay" in number 2
>>above.  what is the "same measure"?  is it where the major lobe is?
>-------------------
>>r b-j
>
>Let me explain my definition of "delay" of FIR filters. 
>
>It is commonly agreed that cross correlation (CC) method is used for
>estimate delay: taking CC, then looking for the time position of the
>maximum value. CC can be also used for estimating impulse response as well,
>actually I saw a prove that the cross correlation is equivalent to impulse
>response (IR) for a linear system and the IR of FIR is its coefficients.
>
>Therefore, I assume the position of the maximum value or "where the major
>lobe is" can be defined as delay of the FIR filter which is equivalent to
>group delay. 
>
>Ok, for minimum phase FIR, the group delay is not constant, but I am only
>looking for a time delay which "most of information or signal behavior" is
>passed through the filter system. 
>
>So I want to use the "where the major lobe is" to define the delay of
>minimum phase FIR as well. the symmetric linear phase FIR with N
>coefficient can be estimated as roughly N/2 or (N+1)/2. I would like to
>have something similar to minimum phase FIR filter for example (1/10)*N or
>(1/20)*N, so before we actually designed a minimum filter, we can estimate
>the number of order (there are many way to do that) and the delay as well.
>
>Hope I explained my thought clearly. and hope you dsp gurus can enlighten
>me on that.

Here's a comparison between impulse responses for comparable
zero-phase and minimum-phase filters:

http://www.dsprelated.com/josimages_new/filters/img1286.png

from here:

http://www.dsprelated.com/dspbooks/filters/Linear_Phase_Really_Ideal.html

You can see the location of the peak at the largest lobe, which for
many applications and definitions may be used to assess the "delay"
from the input impulse to the output.   If you care about dispersion
or the sidelobe ringing for your particular application you may need
to adjust your definition of "delay" or whatever to best suit you.   

You can see in the zero-phase impulse response that there is also
sidelobe ringing there, and yet the common definition for "delay" in
that case is N/2, which is the location of the peak of the main lobe.

If you haven't designed the filter yet and want to estimate the delay,
you can take an educated guess, or you can do a few test designs and
get an idea of the results your design methodology could be expected
to yield. 

Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

On 5/18/2013 11:44 AM, Eric Jacobsen wrote:

> You can see the location of the peak at the largest lobe, which for
> many applications and definitions may be used to assess the "delay"
> from the input impulse to the output.

In many cases, impulse response of minimum phase filter has maximum at t 
= 0.  So, the delay = 0,  isn't it?

    If you care about dispersion
> or the sidelobe ringing for your particular application you may need
> to adjust your definition of "delay" or whatever to best suit you.

Windbag.

On 5/18/2013 5:01 AM, wyonghao wrote:

> Let me explain my definition of "delay" of FIR filters.
>
> It is commonly agreed that cross correlation (CC) method is used for
> estimate delay: taking CC,

Cross correlation of what? The result depends on the signal.

> Therefore, I assume the position of the maximum value or "where the major
> lobe is" can be defined as delay of the FIR filter which is equivalent to
> group delay.

No good idea.

> Ok, for minimum phase FIR, the group delay is not constant, but I am only
> looking for a time delay which "most of information or signal behavior" is
> passed through the filter system.

Once I had to define "delay" of IIR system in layman's terms for the 
sake of marketing department. I used "center of mass" of the impulse 
response.

Vladimir Vassilevsky
DSP and Mixed Signal Designs
www.abvolt.com