On Thu, 07 Jun 2012 20:25:41 +0000, Eric Jacobsen wrote:

> On Thu, 7 Jun 2012 01:30:02 -0700 (PDT), HardySpicer
> <gyansorova@gmail.com> wrote:
> 
>>On Jun 7, 7:42=A0pm, HardySpicer <gyansor...@gmail.com> wrote:
>>> What is the best filter for a pulse in white noise? I remember in the
>>> depths of the past reading something about a filter with a reverse-
>>> time impulse response of the pulse which you convolve it with, but
>>> this is just an integrator.
>>>
>>> Hardy
>>
>>ok it's a matched filter. How do you implement this - say in analogue? I
>>imagine just a leaky integrator?
>>
>>Hardy
> 
> An integrator, specifically an integrate-and-dump filter, is the matched
> filter for receiving a rectangular pulse.    Is this what you're asking
> about?
> 
> If so, such an integrator is not that hard to build with analog
> components.
> 
> 
> Eric Jacobsen
> Anchor Hill Communications
> www.anchorhill.com

I assumed - perhaps Hardy could fill us in - that we don't have the 
synchronization needed for this; and that he was looking for a cheap 
approximation, maybe something a bit better than a  leaky integrator (one 
reactive component) but not necessarily approaching something in some 
sense "optimal".

A quite-low-Q bandpass filter (two reactive components) would be the next 
step up in approaching a rectangular-looking impulse response.  Just take 
the FT of the time domain response, do a Pade approximation on the 
transform (carefully choosing how many terms you want) and design your 
circuit from there.  Others have already mentioned methods for generating 
more DSP-ish methods.

I've used a similar (analog) technique in designing an ECG waveform 
discriminator, though that was years ago.  In that system the various 
signal distortion mechanisms were wrapped into the theoretical ECG 
waveform before the approximation step.  The final result was a 
considerable improvement in rejecting motion artifacts and other noise 
contributions, and sufficiently simple and low-power for the application.

On Fri, 08 Jun 2012 01:24:55 -0400, robert bristow-johnson
<rbj@audioimagination.com> wrote:

>On 6/7/12 11:53 PM, dvsarwate wrote:
>> On Jun 7, 2:57 pm, robert bristow-johnson<r...@audioimagination.com>
>> wrote:
>>
>>>
>>> in the digital world, we just use an FIR with impulse response that is
>>> proportional to the time-reversed copy of the pulse we're trying to
>>> detect.  with simple additive white noise, that is pretty much the end
>>> result of what a matched filter is in the digital domain.
>>
>>
>> So, if the pulse is rectangular, the FIR has impulse
>> response H(z) = 1 + z^-1 + z^-2 + ... z^-n ?
>
>which is a moving-sum (a scaled moving-average) and can be implemented 
>with an integrator and delay (of n samples) and subtractor, instead of 
>adding up all those terms.  isn't this what Eric means by "integrate and 
>dump"?

No, usually an I&D filter in a comm system is implemented strictly as
an integrator that accumulates for the symbol period, is sampled, and
then reset to integrate again for the next symbol period.

This requires synchronization with the symbol period.   If the time of
arrival of the pulse is unknown for a single-pulse detection system,
then you can subtract off old samples as you suggest or run N I&D
filters in parallel with different delays.

>On 6/7/12 11:50 PM, dvsarwate wrote:
>> On Jun 7, 8:40 pm, robert bristow-johnson<r...@audioimagination.com>
>> wrote:
>>
>>>
>>> Eric, is an integrate-and-dump filter one that has a rectangular pulse
>>> for its impulse response?  just not sure about terminology.
>>
>>
>> An integrate-and-dump (or better yet, an
>> integrate-sample-and.THEN.dump.,not.before)
>> "filter" is not a linear time-invariant
>> system but a time-varying system.
>
>that's what i kinda thought.  but what triggers the dump?  just the 
>arrival of time nT (where n is an integer)?

In a comm system the timing recovery loop steers the integrator period
to align with the symbol period.   

>what if the pulse we're trying to detect straddles the time nT?

An I&D is only matched to a pulse with a duration matching the
integration time.  So, as mentioned, you can either subtract off old
samples as the window slides along (for a digital implementation) or
run N filters in parallel with time offsets small enough to get
whatever time resolution is required.

It's not all that elegant, but the point is that an I&D filter is the
match (in a matched filter sense) to a rectangular pulse.   It sounded
like that was appropriate for the problem at hand but I'm not sure.

Hardy mentioned that DC offset is a concern, which it may be if the
pulse is very long.

>-- 
>
>r b-j                  rbj@audioimagination.com
>
>"Imagination is more important than knowledge."
>
>

Eric Jacobsen
Anchor Hill Communications
www.anchorhill.com

On 6/7/12 11:53 PM, dvsarwate wrote:
> On Jun 7, 2:57 pm, robert bristow-johnson<r...@audioimagination.com>
> wrote:
>
>>
>> in the digital world, we just use an FIR with impulse response that is
>> proportional to the time-reversed copy of the pulse we're trying to
>> detect.  with simple additive white noise, that is pretty much the end
>> result of what a matched filter is in the digital domain.
>
>
> So, if the pulse is rectangular, the FIR has impulse
> response H(z) = 1 + z^-1 + z^-2 + ... z^-n ?

which is a moving-sum (a scaled moving-average) and can be implemented 
with an integrator and delay (of n samples) and subtractor, instead of 
adding up all those terms.  isn't this what Eric means by "integrate and 
dump"?


On 6/7/12 11:50 PM, dvsarwate wrote:
> On Jun 7, 8:40 pm, robert bristow-johnson<r...@audioimagination.com>
> wrote:
>
>>
>> Eric, is an integrate-and-dump filter one that has a rectangular pulse
>> for its impulse response?  just not sure about terminology.
>
>
> An integrate-and-dump (or better yet, an
> integrate-sample-and.THEN.dump.,not.before)
> "filter" is not a linear time-invariant
> system but a time-varying system.

that's what i kinda thought.  but what triggers the dump?  just the 
arrival of time nT (where n is an integer)?

what if the pulse we're trying to detect straddles the time nT?

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On Jun 7, 2:57&#4294967295;pm, robert bristow-johnson <r...@audioimagination.com>
wrote:

>
> in the digital world, we just use an FIR with impulse response that is
> proportional to the time-reversed copy of the pulse we're trying to
> detect. &#4294967295;with simple additive white noise, that is pretty much the end
> result of what a matched filter is in the digital domain.


So, if the pulse is rectangular, the FIR has impulse
response H(z) = 1 + z^-1 + z^-2 + ... z^-n ?

Dilip Sarwate

On Jun 7, 8:40&#4294967295;pm, robert bristow-johnson <r...@audioimagination.com>
wrote:

>
> Eric, is an integrate-and-dump filter one that has a rectangular pulse
> for its impulse response? &#4294967295;just not sure about terminology.

An integrate-and-dump (or better yet, an
integrate-sample-and.THEN.dump.,not.before)
"filter" is not a linear time-invariant
system but a time-varying system.  If it
integrates over T-second periods (e.g.
integrate over (0+,T-), sample at T, dump
at T+, and lather-rinse-repeat similarly
every T seconds, then it will respond to
an impulse at t = 0 with a rectangular pulse
lasting from 0++ to T. It will respond
to an impulse at t = 0.25T with a rectangular
pulse that lasts from t = 0.25T+ to T, etc.

Dilip Sarwate

On Jun 8, 8:25&#4294967295;am, eric.jacob...@ieee.org (Eric Jacobsen) wrote:
> On Thu, 7 Jun 2012 01:30:02 -0700 (PDT), HardySpicer
>
> <gyansor...@gmail.com> wrote:
> >On Jun 7, 7:42=A0pm, HardySpicer <gyansor...@gmail.com> wrote:
> >> What is the best filter for a pulse in white noise? I remember in the
> >> depths of the past reading something about a filter with a reverse-
> >> time impulse response of the pulse which you convolve it with, but
> >> this is just an integrator.
>
> >> Hardy
>
> >ok it's a matched filter. How do you implement this - say in analogue?
> >I imagine just a leaky integrator?
>
> >Hardy
>
> An integrator, specifically an integrate-and-dump filter, is the
> matched filter for receiving a rectangular pulse. &#4294967295; &#4294967295;Is this what
> you're asking about?
>
> If so, such an integrator is not that hard to build with analog
> components.
>
> Eric Jacobsen
> Anchor Hill Communicationswww.anchorhill.com

aye. But an integrator tends to wander off at the slightest hint of
dc, hence the leaky integrator ie a big resistor across the capacitor.


Hardy

On 6/7/12 4:25 PM, Eric Jacobsen wrote:
> On Thu, 7 Jun 2012 01:30:02 -0700 (PDT), HardySpicer
> <gyansorova@gmail.com>  wrote:
>
>> On Jun 7, 7:42=A0pm, HardySpicer<gyansor...@gmail.com>  wrote:
>>> What is the best filter for a pulse in white noise? I remember in the
>>> depths of the past reading something about a filter with a reverse-
>>> time impulse response of the pulse which you convolve it with, but
>>> this is just an integrator.
>>
>> ok it's a matched filter. How do you implement this - say in analogue?
>> I imagine just a leaky integrator?
>
> An integrator, specifically an integrate-and-dump filter, is the
> matched filter for receiving a rectangular pulse.    Is this what
> you're asking about?

Eric, is an integrate-and-dump filter one that has a rectangular pulse 
for its impulse response?  just not sure about terminology.

>
> If so, such an integrator is not that hard to build with analog
> components.

what do you use for an analog delay element?  some RC-ladder APF thingie 
or CCD?


__

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On Thu, 07 Jun 2012 00:42:41 -0700, HardySpicer wrote:

> What is the best filter for a pulse in white noise? I remember in the
> depths of the past reading something about a filter with a reverse- time
> impulse response of the pulse which you convolve it with, but this is
> just an integrator.

If the duration of the pulse is known then you want a filter with an 
impulse response is on _for that duration_.  If you don't know _when_ the 
pulse is going to happen (i.e. radar), then the filter is hard to 
implement and you need to think about spending lots of $$ (for fancy 
things like delay lines) or you need to think about approximating the 
response (with a 1st, 2nd, or 3rd order lowpass filter, probably).

If the _time_ of the pulse is known as well as it's duration, then an 
integrate-and-dump will work, as mentioned.

-- 
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 6/7/2012 12:42 AM, HardySpicer wrote:
> What is the best filter for a pulse in white noise? I remember in the
> depths of the past reading something about a filter with a reverse-
> time impulse response of the pulse which you convolve it with, but
> this is just an integrator.
>
>
> Hardy

"Best" depends on the objectve:

a matched filter is best for peak detection / i.e. presence.

something else might be best for getting a clean eye pattern as in PAM - 
particularly with respect to location of zero crossings of the filter 
output.

Fred

On Thu, 7 Jun 2012 01:30:02 -0700 (PDT), HardySpicer
<gyansorova@gmail.com> wrote:

>On Jun 7, 7:42=A0pm, HardySpicer <gyansor...@gmail.com> wrote:
>> What is the best filter for a pulse in white noise? I remember in the
>> depths of the past reading something about a filter with a reverse-
>> time impulse response of the pulse which you convolve it with, but
>> this is just an integrator.
>>
>> Hardy
>
>ok it's a matched filter. How do you implement this - say in analogue?
>I imagine just a leaky integrator?
>
>Hardy

An integrator, specifically an integrate-and-dump filter, is the
matched filter for receiving a rectangular pulse.    Is this what
you're asking about?

If so, such an integrator is not that hard to build with analog
components.


Eric Jacobsen
Anchor Hill Communications
www.anchorhill.com