filtering narrow-band signal preserving phase information

Hello,

I have a newbie question again on phase of signal. 
I want to know more on filtering signal with preserving phase information.

When is it important to preserve the phase information of a signal and how
do we do it using digital FIR filter? I am working on Matlab for my
application, but would it be possible to do "zero-phase" filtering in real
time system such as FPGA?
Could you give me some reference please?
Thanks!

Thomas

On Fri, 30 Nov 2012 10:20:01 -0600, gongdori wrote:

> Hello,
> 
> I have a newbie question again on phase of signal.
> I want to know more on filtering signal with preserving phase
> information.
> 
> When is it important to preserve the phase information of a signal and
> how do we do it using digital FIR filter? I am working on Matlab for my
> application, but would it be possible to do "zero-phase" filtering in
> real time system such as FPGA?
> Could you give me some reference please?
> Thanks!

Without knowing what you mean by "zero-phase" filtering, it is impossible 
to answer that part of your question.

Can you filter a signal while preserving phase _information_?  Yes, 
easily -- just use a symmetric FIR filter.  Can you filter _any_ signal 
while maintaining zero phase shift?  No, not in this real world we live 
in.

When you filter a signal with a causal* filter, _at minimum_ the phase 
shift in the frequency domain will be equal to the Hilbert transform of 
the magnitude response (or log magnitude?  I can't remember).  You can 
only get worse from there.

Filtering with a symmetric FIR will give you more phase lag, but will 
give you dead-constant time delay, without any frequency-dependent 
delays.  This meets your "preserve phase information" criteria quite 
nicely, but I'm not sure if it gets you what you want.

If you want to go further, you may want to tell us what you're actually 
trying to do, instead of picking out one part of it for independent 
inspection.

* "causal filter" means that the filter does not look ahead in time

-- 
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

>Hello,
>
>I have a newbie question again on phase of signal. 
>I want to know more on filtering signal with preserving phase
information.
>
>When is it important to preserve the phase information of a signal and
how
>do we do it using digital FIR filter? I am working on Matlab for my
>application, but would it be possible to do "zero-phase" filtering in
real
>time system such as FPGA?
>Could you give me some reference please?
>Thanks!
>
>Thomas
>

Are you aware of Matlab function called "filtfilt"? It filters signal then
reverses the filtered stream and filters it again in same filter. Result is
"zero phase" change. 
How can you translate that to real world, I don't know but you will need to
break the stream into chunks, store it and restitch it.

Kadhiem 

>Hello,
>
>I have a newbie question again on phase of signal. 
>I want to know more on filtering signal with preserving phase
information.
>
>When is it important to preserve the phase information of a signal and
how
>do we do it using digital FIR filter? I am working on Matlab for my
>application, but would it be possible to do "zero-phase" filtering in
real
>time system such as FPGA?
>Could you give me some reference please?
>Thanks!
>
>Thomas
>

Also note that phase is preserved if your filter response is linear as
pointed out to you by Tim. Thus it is no different from effect of any delay
e.g. through piece of wire.

Kadhiem

>>Hello,
>>
>>I have a newbie question again on phase of signal. 
>>I want to know more on filtering signal with preserving phase
>information.
>>
>>When is it important to preserve the phase information of a signal and
>how
>>do we do it using digital FIR filter? I am working on Matlab for my
>>application, but would it be possible to do "zero-phase" filtering in
>real
>>time system such as FPGA?
>>Could you give me some reference please?
>>Thanks!
>>
>>Thomas
>>
>
>Also note that phase is preserved if your filter response is linear as
>pointed out to you by Tim. Thus it is no different from effect of any
delay
>e.g. through piece of wire.
>
>Kadhiem
>


Thank you so much, Tim and Kadhiem. 
What I am trying to do is filtering everything but a narrow band frequency
hopping signal with preserving phase info of every burst and I'm doing it
in Matlab. 
After I read the replies, I dig up some text books which talks about group
delay and phase delay. Please correct me if I am wrong. :)

Since my filter is linear phase, I have fixed number of group delay. If I
have N+1 tap "Type I" filter, which is symmetric and odd tap, I would get
N/2 group delay. Thus, that is the number of initial samples I need to
throw out when I compute the filter output... Is that correct? 
Also, the group delay of the filter would be the same at all frequency, I
can apply what I mentioned to all frequency channels...right?


    

On 11/30/12 11:55 AM, Tim Wescott wrote:
> On Fri, 30 Nov 2012 10:20:01 -0600, gongdori wrote:
>
>> Hello,
>>
>> I have a newbie question again on phase of signal.
>> I want to know more on filtering signal with preserving phase
>> information.
>>
>> When is it important to preserve the phase information of a signal and
>> how do we do it using digital FIR filter? I am working on Matlab for my
>> application, but would it be possible to do "zero-phase" filtering in
>> real time system such as FPGA?

someone else mentioned FILTFILT.

there *is* a method of doing FILTFILT real-time, but it seems to me to 
be a pretty complicated mess in an FPGA.  you have to break the input 
into frames and filter each frame frontwards and backwards but you also 
have to do overlap-add.

there is an IEEE paper by Powell and Chau:

  http://users.cosylab.com/~msekoranja/tmp/00097998.pdf

some other paper about it

  http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=324751

and Avery Wang and Julius Smith came up with this idea of "Truncated" 
IIR filters which is a way to do this correctly, theoretically (powell & 
chau do not use truncated IIR filters, so there is a theoretical problem).

>> Could you give me some reference please?
>> Thanks!
>
> Without knowing what you mean by "zero-phase" filtering, it is impossible
> to answer that part of your question.

zero-phase filtering is linear-phase filtering with zero delay.  of 
course that cannot be strictly done in real time (except for the trivial 
wire or wire-with-gain) because a symmetrical h[n] that is centered 
about n=0 is non-causal.

with the right adjustment of offset, FILTFILT is zero-phase filtering 
so, with file processing (where you can look ahead to "future" samples) 
zero-phase filtering is possible.


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

>What I am trying to do is filtering everything but a narrow band
frequency
>hopping signal with preserving phase info of every burst and I'm doing it
>in Matlab. 
>After I read the replies, I dig up some text books which talks about
group
>delay and phase delay. Please correct me if I am wrong. :)
>
>Since my filter is linear phase, I have fixed number of group delay. If I
>have N+1 tap "Type I" filter, which is symmetric and odd tap, I would get
>N/2 group delay. Thus, that is the number of initial samples I need to
>throw out when I compute the filter output... Is that correct? 
>Also, the group delay of the filter would be the same at all frequency, I
>can apply what I mentioned to all frequency channels...right?
>

Yes for symmetric fir, group delay = order/2 (order = taps -1)
It is fixed constant for all frequencies if your fir filter is symmetric.
It represents a fixed time delay just like a piece of wire say delaying a
signal by few nano seconds. This wire delay will change phase but in a
linear way.

Kadhiem

On Fri, 30 Nov 2012 19:34:49 -0500, robert bristow-johnson wrote:

> On 11/30/12 11:55 AM, Tim Wescott wrote:
>> On Fri, 30 Nov 2012 10:20:01 -0600, gongdori wrote:
>>
>>> Hello,
>>>
>>> I have a newbie question again on phase of signal. I want to know more
>>> on filtering signal with preserving phase information.
>>>
>>> When is it important to preserve the phase information of a signal and
>>> how do we do it using digital FIR filter? I am working on Matlab for
>>> my application, but would it be possible to do "zero-phase" filtering
>>> in real time system such as FPGA?
> 
> someone else mentioned FILTFILT.
> 
> there *is* a method of doing FILTFILT real-time, but it seems to me to
> be a pretty complicated mess in an FPGA.  you have to break the input
> into frames and filter each frame frontwards and backwards but you also
> have to do overlap-add.
> 
> there is an IEEE paper by Powell and Chau:
> 
>   http://users.cosylab.com/~msekoranja/tmp/00097998.pdf
> 
> some other paper about it
> 
>   http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=324751
> 
> and Avery Wang and Julius Smith came up with this idea of "Truncated"
> IIR filters which is a way to do this correctly, theoretically (powell &
> chau do not use truncated IIR filters, so there is a theoretical
> problem).
> 
>>> Could you give me some reference please? Thanks!
>>
>> Without knowing what you mean by "zero-phase" filtering, it is
>> impossible to answer that part of your question.
> 
> zero-phase filtering is linear-phase filtering with zero delay.  of
> course that cannot be strictly done in real time (except for the trivial
> wire or wire-with-gain) because a symmetrical h[n] that is centered
> about n=0 is non-causal.
> 
> with the right adjustment of offset, FILTFILT is zero-phase filtering
> so, with file processing (where you can look ahead to "future" samples)
> zero-phase filtering is possible.

I'm too immersed in control systems: the notion of zero delay across the 
board just got shoved into the "can't be done" pigeon hole, without 
remembering my DSP terminology.

-- 
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

On 12/2/12 2:39 PM, Tim Wescott wrote:
> On Fri, 30 Nov 2012 19:34:49 -0500, robert bristow-johnson wrote:
>
>> On 11/30/12 11:55 AM, Tim Wescott wrote:
>>> On Fri, 30 Nov 2012 10:20:01 -0600, gongdori wrote:
>>>
>>>> Hello,
>>>>
>>>> I have a newbie question again on phase of signal. I want to know more
>>>> on filtering signal with preserving phase information.
>>>>
>>>> When is it important to preserve the phase information of a signal and
>>>> how do we do it using digital FIR filter? I am working on Matlab for
>>>> my application, but would it be possible to do "zero-phase" filtering
>>>> in real time system such as FPGA?
>>
>> someone else mentioned FILTFILT.
>>
>> there *is* a method of doing FILTFILT real-time, but it seems to me to
>> be a pretty complicated mess in an FPGA.  you have to break the input
>> into frames and filter each frame frontwards and backwards but you also
>> have to do overlap-add.
>>
>> there is an IEEE paper by Powell and Chau:
>>
>>    http://users.cosylab.com/~msekoranja/tmp/00097998.pdf
>>
>> some other paper about it
>>
>>    http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=324751
>>
>> and Avery Wang and Julius Smith came up with this idea of "Truncated"
>> IIR filters which is a way to do this correctly, theoretically (powell&
>> chau do not use truncated IIR filters, so there is a theoretical
>> problem).
>>
>>>> Could you give me some reference please? Thanks!
>>>
>>> Without knowing what you mean by "zero-phase" filtering, it is
>>> impossible to answer that part of your question.
>>
>> zero-phase filtering is linear-phase filtering with zero delay.  of
>> course that cannot be strictly done in real time (except for the trivial
>> wire or wire-with-gain) because a symmetrical h[n] that is centered
>> about n=0 is non-causal.
>>
>> with the right adjustment of offset, FILTFILT is zero-phase filtering
>> so, with file processing (where you can look ahead to "future" samples)
>> zero-phase filtering is possible.
>
> I'm too immersed in control systems: the notion of zero delay across the
> board just got shoved into the "can't be done" pigeon hole, without
> remembering my DSP terminology.
>

you're thinking about real, physical realizable systems doing useful 
things in real time interacting with other real components.

FILTFILT is a file processing program.  as such, the "present" sample is 
a conceptual construct (it's the sample that your "present sample" 
pointer is pointing to).  there is no problem with looking ahead to 
"future" samples.  or even to run time backwards.  i was talking about 
this sorta at the last AES and the way i put it is, in Unreal-Time 
processing (that is processing sound files to sound files), you get to 
sorta play God with time.  run it forward slow or fast, run it 
backwards, take a piece of time from here, another piece of time from 
there (sometimes we call these little pieces "grains").  it's like time 
is just another spacial dimension and you get to look at the timescape 
of the file like landscape.

of course, in a physically realizable real-time system, you cannot see 
future samples and the impulse response must be causal and you cannot do 
zero-phase filtering except for a simple gain applied to the present 
sample x[n].  if there are any past samples in the mix, you have no 
future samples to balance them with, so there can't be any past samples 
in a real-time zero-phase filter.

when you use the concept of FILTFILT in a real time system using the 
Powell/Chau technique, it actually has quite a bit of delay to do the 
necessary buffering and framing.  so it's not really zero-phase, but a 
linear phase system.  it's a true FIR if, instead of using a regular IIR 
filter (forward and backward, like in FILTFILT) if you use Truncated IIR 
filters (similar to the Wang and Smith idea).

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

 �i was talking about
> this sorta at the last AES and the way i put it is, in Unreal-Time
> processing (that is processing sound files to sound files), you get to
> sorta play God with time. �run it forward slow or fast, run it
> backwards, take a piece of time from here, another piece of time from
> there (sometimes we call these little pieces "grains"). �it's like time
> is just another spacial dimension and you get to look at the timescape
> of the file like landscape.

it's funny you mention that, i think that IS how God "sees" existence.

God can view time like in an audio editor, all of time is there right
before him (or her).

Just like we can see space to the left and space to the right, he can
see time before and time after all at the same um time.

Mark