optimal filters

What is an optimal filter?

--tobin

Tobin Fricke wrote:
> What is an optimal filter?

A filter that is the best possible for its intended purpose, sometimes 
factoring in cost. What is an optimal motor vehicle?

If you specify the purpose, you can have a more satisfying answer.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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Tobin Fricke wrote:

> What is an optimal filter?

Well, it's this filter, see, and it's, like, optimal.  :-)

There are many different things that can be thought of as an optimal
filter.

In some areas, designing an FIR filter using a minimax criterion (e.g.
using the Parks-McClellan / Remez exchange algorithm) is called an
optimal filter.

In other areas, a Kalman filter is described as an optimal filter
because it minimizes the least squared error on the estimate of the
state of the system under investigation.

Do you have any specific thing in mind?  More background information
would probably generate a better answer.

Ciao,

Peter K.

Tobin Fricke wrote:

> What is an optimal filter?
> 
> --tobin

What Jerry and Peter said, but also:

Usually when you encounter the word "optimal" or "optimum" in the 
theoretical engineering literature it means there is a system (like a 
filter) that best meets some defined performance criteria.  Usually the 
performance criteria are chosen to make the design of the optimal system 
possible, if not easy.

So you'll see Kalman fiters which are optimal for (more or less) linear 
systems with additive Gaussian noise and some error-squared cost 
function, or the Parks-McClellan algorithm mentioned.  What you _won't_ 
see, in general, are system models, noise models, or cost functions 
drawn from reality, because designing for an optimal system in such a 
case is darn near impossible.

You will also find that in practice such "optimal" systems are not often 
implemented unless they address a problem that is either broad (such as 
PSK demodulators) or highly mission critical (such as Kalman filters in 
inertial nav systems), and even there you will find that the problem 
definition has been massaged so that it is approximated by one of the 
known optimal-system solutions.

Why is this?  Because managers often want to optimize for time to 
market, or the man-hours to design the system, and they're willing to 
live with lower performance and/or higher materials cost if they can 
keep down the number of hours spent by the costliest of engineers to 
make the "optimal" solution work.

-- 
-------------------------------------------
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Tobin Fricke wrote:
> What is an optimal filter?
> 
> --tobin
If your taking a class or reading a paper in statistical estimation or 
detection it is "optimal" with respect to some statistical criteria, 
like least squares, maximum likelihood, or trying to maximize the signal 
to noise ratio.  The second chapter of volume 1 of Van Trees's, 
Detection, Estimation, and Modulation Theory, develops a number of 
optimal processors.  The terms, processor and filter are somewhat 
interchangeable.  One thing to note about optimal filters is that they 
are not necessarily something that can be actually constructed.  Some 
people use the terms optimal and adaptive, interchangeably but this is 
not usually true.  Adaptive filters often approximate optimal filters.

Tim wrote:

>Why is this?  Because managers often want to optimize for time to
>market, or the man-hours to design the system, and they're willing to
>live with lower performance and/or higher materials cost if they can
>keep down the number of hours spent by the costliest of engineers to
>make the "optimal" solution work.

Very true words. In contradiction to Jerry, my definition of
engineering (I guess managing as well - actually, the two are very
related) is to solve a given problem optimally. The criterion for
optimality (in my work) is usually a weighted and project dependent mix
of
- project specificiation tolerance,
- development time,
- software availability, extendability and re-usability,
- code quality and efficiency,
- hardware availability,
- usable man power and skill.

I guess the larger the projects and teams become, the more such terms
have to be accounted for (I'm thinking about administrative issues
etc.). If you come to think about how difficult such high dimensional
optimization problems become (where some of the parameters might not be
readily quantifiable), the amount and range of mismanagement comes as
no surprise.

Regards,
Andor

Andor wrote:

> I guess the larger the projects and teams become, the more such terms
> have to be accounted for (I'm thinking about administrative issues
> etc.). If you come to think about how difficult such high dimensional
> optimization problems become (where some of the parameters might not be
> readily quantifiable), the amount and range of mismanagement comes as
> no surprise.

Hence Carnegie-Mellon's introduction of CMM and CMMI.

http://www.sei.cmu.edu/cmmi/adoption/cmmi-start.html

It's not perfect, but it gives a much better set of management handles
on an otherwise unmanageable process.

Ciao,

Peter K.

Andor wrote:

>Tim wrote:
>
>  
>
>>Why is this?  Because managers often want to optimize for time to
>>market, or the man-hours to design the system, and they're willing to
>>live with lower performance and/or higher materials cost if they can
>>keep down the number of hours spent by the costliest of engineers to
>>make the "optimal" solution work.
>>    
>>
>
>Very true words. In contradiction to Jerry, my definition of
>engineering (I guess managing as well - actually, the two are very
>related) is to solve a given problem optimally. The criterion for
>optimality (in my work) is usually a weighted and project dependent mix
>of
>- project specificiation tolerance,
>- development time,
>- software availability, extendability and re-usability,
>- code quality and efficiency,
>- hardware availability,
>- usable man power and skill.
>
>I guess the larger the projects and teams become, the more such terms
>have to be accounted for (I'm thinking about administrative issues
>etc.). If you come to think about how difficult such high dimensional
>optimization problems become (where some of the parameters might not be
>readily quantifiable), the amount and range of mismanagement comes as
>no surprise.
>
>Regards,
>Andor
>  
>
Companies aren't in business to make products. They are in business to 
make money. The optimal solution is the one which maximises profit. 
Never loose sight of that, or nothing in engineering makes any sense.

A dirty troublesome half baked solution which hits a market window where 
people will pay a good price for a dirty troublesome half baked solution 
might be optimal..... provided the troublesome part doesn't bite too 
badly with costly recalls.

Regards,
Steve

Am Mon, 6 Jun 2005 13:00:05 -0700 schrieb Tobin Fricke:

> What is an optimal filter?
> 
> --tobin

Perhaps you mean "matched filter". In German literature, "Optimalfilter" is
the same as "matched filter".
Siegbert

Steve Underwood wrote:
> Andor wrote:
...
> >I guess the larger the projects and teams become, the more such terms
> >have to be accounted for (I'm thinking about administrative issues
> >etc.). If you come to think about how difficult such high dimensional
> >optimization problems become (where some of the parameters might not be
> >readily quantifiable), the amount and range of mismanagement comes as
> >no surprise.
...
> Companies aren't in business to make products. They are in business to
> make money. The optimal solution is the one which maximises profit.
> Never loose sight of that, or nothing in engineering makes any sense.

Just the type of thinking that migh boost a short term profit with
absolutely no thought to long term considerations (you just missed a
whole set of parameters in the optimization problem :-). A company that
sells a product where every shortcut was made to save money in the
production and every marketing register pulled to increase the margin
in sale might make more short term money in sales of that product. What
about the customers? After a second look, they'll know what they bought
and are likely to buy from another company the next time.

No, I think a company has to make products which adhere to its standard
/ philosophy of production. This is the task of the "engineers" (in a
wide sense of the word, anybody responsible in the core of the
company). It is the task of the markting that potential customers are
aware of the product and its values. Together they will make money, if
both make a good job. Company's that work the other way around aren't
places where I want to work (or make products which I want to buy, for
that matter). You'll always loose in the long run.


> A dirty troublesome half baked solution which hits a market window where
> people will pay a good price for a dirty troublesome half baked solution
> might be optimal..... provided the troublesome part doesn't bite too
> badly with costly recalls.

This of course works well if you have no competition. In an
economically healthy environment, this philosophy won't make for a
lasting company.

>
> Regards,
> Steve

Steve, I wonder: I know from some past posts of yours that are at least
a seasoned engineer. What kind of business are you in? Don't answer if
you don't want to.

Regards,
Andor