IIR to find minimum, maximum enveloppe of a signal

Hi all,

First of all, I'm a newbie in signal processing, so go easy :)

I have used an IIR filter to computer the local average of a signal,
and it works well. It essentially is what they call in finance a
moving average, i.e. the output at a sample point is a fraction of
itself and (1-fraction) of its predecessor. Results fit my
requirements, and the speed is absolutely tremendous.

Now, I would also like to find the enveloppe of the signal, i.e. the
local minimum and maximum. I'm trying to find a way to do that using
IIR filters (because of the speed), but I cannot for the life of me
find a way forward. Does anybody have ideas on that? Note that it does
not necessarily need to be a IIR filter, we can keep the conversation
more general at first. I suggested them because of the level of
performance they enabled, which is important to my project.

Thanks in advance,

A

On Wed, 24 Feb 2010 08:16:39 -0800 (PST)
vectorizor <vectorizor@googlemail.com> wrote:

> Hi all,
> 
> First of all, I'm a newbie in signal processing, so go easy :)
> 
> I have used an IIR filter to computer the local average of a signal,
> and it works well. It essentially is what they call in finance a
> moving average, i.e. the output at a sample point is a fraction of
> itself and (1-fraction) of its predecessor. Results fit my
> requirements, and the speed is absolutely tremendous.
> 
> Now, I would also like to find the enveloppe of the signal, i.e. the
> local minimum and maximum. I'm trying to find a way to do that using
> IIR filters (because of the speed), but I cannot for the life of me
> find a way forward. Does anybody have ideas on that? Note that it does
> not necessarily need to be a IIR filter, we can keep the conversation
> more general at first. I suggested them because of the level of
> performance they enabled, which is important to my project.
> 
> Thanks in advance,
> 
> A

An IIR filter is a fundamentally linear process.  Min/max is a
non-linear operation.  What you want is something that can detect a
peak, some sort of "peak detector".

-- 
Rob Gaddi, Highland Technology
Email address is currently out of order

vectorizor wrote:

> Hi all,
> 
> First of all, I'm a newbie in signal processing, so go easy :)
> 
> I have used an IIR filter to computer the local average of a signal,
> and it works well. It essentially is what they call in finance a
> moving average, i.e. the output at a sample point is a fraction of
> itself and (1-fraction) of its predecessor. Results fit my
> requirements, and the speed is absolutely tremendous.
> 
> Now, I would also like to find the enveloppe of the signal, i.e. the
> local minimum and maximum.

If you need to track local minimum/maximum within the time span T, you 
have to keep all history for the entire time span T. However, you may 
not have to do full search through T at every step.

> I'm trying to find a way to do that using
> IIR filters (because of the speed), but I cannot for the life of me
> find a way forward. Does anybody have ideas on that?

Are you asking how to know the future? Be sure, it is very-very-very 
difficult.


> Note that it does
> not necessarily need to be a IIR filter, we can keep the conversation
> more general at first. I suggested them because of the level of
> performance they enabled, which is important to my project.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

Vladimir Vassilevsky wrote:
> 
> 
> vectorizor wrote:
> 
>> Hi all,
>>
>> First of all, I'm a newbie in signal processing, so go easy :)
>>
>> I have used an IIR filter to computer the local average of a signal,
>> and it works well. It essentially is what they call in finance a
>> moving average, i.e. the output at a sample point is a fraction of
>> itself and (1-fraction) of its predecessor. Results fit my
>> requirements, and the speed is absolutely tremendous.
>>
>> Now, I would also like to find the enveloppe of the signal, i.e. the
>> local minimum and maximum.
> 
> If you need to track local minimum/maximum within the time span T, you 
> have to keep all history for the entire time span T. However, you may 
> not have to do full search through T at every step.

If you track min/max within blocks, you need to remember only two values 
within the time window: least-so-far and most-so-far. Any new value 
outside the range that they define replaces one of them. If you need a 
running min/max for the last n intervals, then it is as Vlad wrote.

>> I'm trying to find a way to do that using
>> IIR filters (because of the speed), but I cannot for the life of me
>> find a way forward. Does anybody have ideas on that?
> 
> Are you asking how to know the future? Be sure, it is very-very-very 
> difficult.

:-)

   ...

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

vectorizor wrote:
> Hi all,
> 
> First of all, I'm a newbie in signal processing, so go easy :)
> 
> I have used an IIR filter to computer the local average of a signal,
> and it works well. It essentially is what they call in finance a
> moving average, i.e. the output at a sample point is a fraction of
> itself and (1-fraction) of its predecessor. Results fit my
> requirements, and the speed is absolutely tremendous.
> 
> Now, I would also like to find the enveloppe of the signal, i.e. the
> local minimum and maximum. I'm trying to find a way to do that using
> IIR filters (because of the speed), but I cannot for the life of me
> find a way forward. Does anybody have ideas on that? Note that it does
> not necessarily need to be a IIR filter, we can keep the conversation
> more general at first. I suggested them because of the level of
> performance they enabled, which is important to my project.
> 
> Thanks in advance,
> 
> A

What everyone has said so far:

* the moniker "IIR" implies a linear recursive filter, and
   the min/max operation is quite nonlinear

* To do a running min/max you need to keep a full history
   (and I'd like Vladimir to give us a reference to the
    "don't have to do full search at each step")

* To do a block/block min/max you just need to keep
   'max so far' and 'min so far' -- I do this often, it's
   very handy.  If you need finer resolution than the whole
   span of data you're tracking, you can do multiple
   blocks.

And:

You can implement a _non_-linear recursive filter, that forces its
output to the signal maximum (or minimum) whenever

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

Tim Wescott wrote:


> * To do a running min/max you need to keep a full history
>   (and I'd like Vladimir to give us a reference to the
>    "don't have to do full search at each step")

Let's say you need a running min/max through the past N samples. You 
only have to do full search through N when the known min or max is 
dropped out of scope of N, i.e. lost in the past. Otherwise you compare 
the new sample to the current values of min and max - that's just one 
operation.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

Tim Wescott wrote:

   ...

> You can implement a _non_-linear recursive filter, that forces its
> output to the signal maximum (or minimum) whenever

Whenever what?

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

vectorizor wrote:
> Hi all,
> 
> First of all, I'm a newbie in signal processing, so go easy :)
> 
> I have used an IIR filter to computer the local average of a signal,
> and it works well. It essentially is what they call in finance a
> moving average, i.e. the output at a sample point is a fraction of
> itself and (1-fraction) of its predecessor. Results fit my
> requirements, and the speed is absolutely tremendous.
> 
> Now, I would also like to find the enveloppe of the signal, i.e. the
> local minimum and maximum. I'm trying to find a way to do that using
> IIR filters (because of the speed), but I cannot for the life of me
> find a way forward. Does anybody have ideas on that? Note that it does
> not necessarily need to be a IIR filter, we can keep the conversation
> more general at first. I suggested them because of the level of
> performance they enabled, which is important to my project.
> 
> Thanks in advance,
> 
> A

What everyone has said so far:

* the moniker "IIR" implies a linear recursive filter, and
   the min/max operation is quite nonlinear

* To do a running min/max you need to keep a full history
   (and I'd like Vladimir to give us a reference to the
    "don't have to do full search at each step")

* To do a block/block min/max you just need to keep
   'max so far' and 'min so far' -- I do this often, it's
   very handy.  If you need finer resolution than the whole
   span of data you're tracking, you can do multiple
   blocks.

And:

You can implement a _non_-linear recursive filter, that forces its
output to the signal value if the signal value exceeds it's state, but
otherwise implements a first order low-pass (which is DSP for the
Economist's 'moving average' filter).  For signals which hit their
maxima often this works pretty well, but if you're looking for an
infrequent but guaranteed maximum this will often be wrong.

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

Jerry Avins wrote:
> Tim Wescott wrote:
> 
>   ...
> 
>> You can implement a _non_-linear recursive filter, that forces its
>> output to the signal maximum (or minimum) whenever
> 
> Whenever what?
> 
> Jerry

Uhh, whenever Thunderbird hiccups and deletes part of a message?

(I resent)

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

Tim wrote:
>vectorizor wrote:
>> Now, I would also like to find the enveloppe of the signal, i.e. the
>> local minimum and maximum. I'm trying to find a way to do that using
>> IIR filters (because of the speed), but I cannot for the life of me
>> find a way forward. Does anybody have ideas on that? Note that it does
>> not necessarily need to be a IIR filter, we can keep the conversation
>> more general at first. I suggested them because of the level of
>> performance they enabled, which is important to my project.
>
>
>You can implement a _non_-linear recursive filter, that forces its
>output to the signal value if the signal value exceeds it's state, but
>otherwise implements a first order low-pass (which is DSP for the
>Economist's 'moving average' filter).  For signals which hit their
>maxima often this works pretty well, but if you're looking for an
>infrequent but guaranteed maximum this will often be wrong.


Essentially an idealized diode envelope detector, right?  It'd be
interesting to know what additional tricks can be played digitally, though
I imagine it's pretty dependent on prior knowledge about the signal.