Smoothing math
Smoothing problem.
For a tachometer I am building, I would like to experiment with mathematical
smoothing.
The tach monitors the rps of an underwater impeller on a model sailboat. It is
a Hall switch circuit, and works nicely.
But the numbers come fast and the trend jumps around a bit. With a VOM display,
the inertia inherent in the galvanometer movement tends to smooth out the trend.
But for the finished product I want to use an
LCD. No inertia.
Stock market data is often smoothed out with a simple moving average. But since
the stamp cannot divide faithfully, I was wondering if an exponential smoothing
function might work better.
I know these exponential smoothing functions exist, but can't remember how they
look or how they work. Or if they require division.
Thank you for any insights on how to smooth the stream of numbers coming in from
the impeller.
Michael
For a tachometer I am building, I would like to experiment with mathematical
smoothing.
The tach monitors the rps of an underwater impeller on a model sailboat. It is
a Hall switch circuit, and works nicely.
But the numbers come fast and the trend jumps around a bit. With a VOM display,
the inertia inherent in the galvanometer movement tends to smooth out the trend.
But for the finished product I want to use an
LCD. No inertia.
Stock market data is often smoothed out with a simple moving average. But since
the stamp cannot divide faithfully, I was wondering if an exponential smoothing
function might work better.
I know these exponential smoothing functions exist, but can't remember how they
look or how they work. Or if they require division.
Thank you for any insights on how to smooth the stream of numbers coming in from
the impeller.
Michael
Comments
in the Stamp. Otherwise, check out a PAK-I, a PAK-II, or a PAK-IX (A/D
built into the PAK-IX).
Suppose your data ranges from 0 to 100. You can use a word and scale
everything up by say, 10.
So your data stream is 90,88,92,89...
You do this:
V1=90*10
V1=V1+(88*10)
V1=V1+(92*10)
V1=V1+(89*10)
' now V1= 3590 which is really 359.0
V1=V1/4 ' 4
' now V1=897
V1=V1+5 ' round off V1=902
V1=V1/10
' V1=90, very close to the correct 89.75
Now to do a moving average, you'd deduct 900 from the total before
adding the next sample (*10 of course). That means you have to remember
4 samples.
You can do the same trick with other scales. For example, rounding to a
bit level is easy with the shift instructions or by bit manipulation.
Consider this:
Sample=90
V1=Sample<<4 ' * 16
Sample=88
V1=V1+(Sample<<4)
Sample=92
V1=V1+(Sample<<4)
Sample=89
V1=V1+(Sample<<4)
' Now V1=5744
V1=V1/4 ' V1=1436
' Now we want to round to the bit level so
V1=V1+8 ' 16/2
V1=V1>>4 ' V1=90
You can also "keep" the decimal point if you prefer. Consider this
quasi-code:
V1=90*100
V1=V1+(88*100)
V1=V1+(92*100)
V1=V1+(89*100)
' now V1= 35900 which is really 359.00
V1=V1/4 ' 4
' now V1=8975
V1=V1+5 ' round off V1=8980
V1=V1/10
Debug dec v1/10, ".", dec v1 // 10
That will print out 89.8 which is awfuly close to 89.75. Also, you could
skip the +5/10 steps and do something like:
Ipart = V1/100
Fpart = v1//100
Debug dec Ipart, ".", dec2 Fpart (I think that works)
In other words, if the Fpart is 9, you want .09 not .9!
Of course, this only works because the maximum number is 100 and
100*4*100=40000 which is <65535. If your maximum number was 200, you
might overflow the 16-bit variable. Then you'd need to scale smaller or
use fewer samples (200*3*100=60000).
I'm sure Tracy can explain it better...
Good luck!
Al Williams
AWC
* Floating point math for the Stamp, PIC, SX, or any microcontroller
http://www.al-williams.com/awce/pak1.htm
>
Original Message
> From: Michael Gianturco [noparse]/noparse]mailto:[url=http://forums.parallaxinc.com/group/basicstamps/post?postID=n8_74gD1k74ynj8S_GYE94fjKIH5LDd71fr1c7Svv1oJo-iofGDQLv2LEWRWwcHuxqY5fX4-yxva6ps]michcg@m...[/url
> Sent: Monday, March 25, 2002 8:06 AM
> To: basicstamps@yahoogroups.com
> Subject: [noparse][[/noparse]basicstamps] Smoothing math
>
>
> Smoothing problem.
>
> For a tachometer I am building, I would like to experiment
> with mathematical smoothing.
>
> The tach monitors the rps of an underwater impeller on a
> model sailboat. It is a Hall switch circuit, and works nicely.
>
> But the numbers come fast and the trend jumps around a bit.
> With a VOM display, the inertia inherent in the galvanometer
> movement tends to smooth out the trend. But for the
> finished product I want to use an
> LCD. No inertia.
>
> Stock market data is often smoothed out with a simple moving
> average. But since the stamp cannot divide faithfully, I was
> wondering if an exponential smoothing function might work better.
>
> I know these exponential smoothing functions exist, but
> can't remember how they look or how they work. Or if they
> require division.
>
> Thank you for any insights on how to smooth the stream of
> numbers coming in from the impeller.
>
> Michael
>
>
>
>
> To UNSUBSCRIBE, just send mail to:
> basicstamps-unsubscribe@yahoogroups.com
> from the same email address that you subscribed. Text in the
> Subject and Body of the message will be ignored.
>
>
> Your use of Yahoo! Groups is subject to
> http://docs.yahoo.com/info/terms/
>
simple technique a long time ago that I've used in these situations. You can
create a simple digital filter by adding a fraction of the current reading to
a fraction of the previous reading. Like this:
GOSUB Get_Tach ' put current valu into thisReading
thisReading = (thisReading */ $00B3) + (lastReading */ $004D)
lastReading = thisReading
You can change the response by changing the percentages (swayed toward
current reading make it fast, toward last reading makes it slow).
In the equation above, 70% of the current reading is added to 30% of the
previous reading. If you've never used the */ (star-slash) operator, it
works like this: it mutliplies by a fractional value expressed in 1/256. To
find the parameter, multiply your fractional value by 256.
0.70 * 256 = 179.2 --> $00B3
0.30 * 256 = 76.8 --> $004D
A great place to learn about Stamp math is Dr. Tracy Allen's web site:
http://www.emesystems.com/BS2index.htm
-- Jon Williams
-- Applications Engineer, Parallax
In a message dated 3/25/02 8:04:17 AM Central Standard Time,
michcg@m... writes:
> Smoothing problem.
>
> For a tachometer I am building, I would like to experiment with
> mathematical smoothing.
>
> The tach monitors the rps of an underwater impeller on a model sailboat.
> It is a Hall switch circuit, and works nicely.
>
> But the numbers come fast and the trend jumps around a bit. With a VOM
> display, the inertia inherent in the galvanometer movement tends to smooth
> out the trend. But for the finished product I want to use an
> LCD. No inertia.
>
> Stock market data is often smoothed out with a simple moving average. But
> since the stamp cannot divide faithfully, I was wondering if an exponential
> smoothing function might work better.
>
> I know these exponential smoothing functions exist, but can't remember how
> they look or how they work. Or if they require division.
>
> Thank you for any insights on how to smooth the stream of numbers coming in
> from the impeller.
>
[noparse][[/noparse]Non-text portions of this message have been removed]
>
>For a tachometer I am building, I would like to experiment with
>mathematical smoothing.
>... But since the stamp cannot divide faithfully, I was wondering
>if an exponential smoothing function might work better.
>
> I know these exponential smoothing functions exist, but can't
>remember how they look or how they work. Or if they require division.
>
>Thank you for any insights on how to smooth the stream of numbers
>coming in from the impeller.
>
>Michael
I have an example of exponential smoothing posted at
http://www.emesystems.com/BS2math5.htm
It is important to scale up your raw numbers by a factor of at least
10 or 16 (the more the better) before they are input to the filter.
Otherwise strange numerical problems result from the roundoff
errors. For example, without the up-scaling, there will be
hysteresis--the filter will "stick" at low values.
I recently posted a double precision version that works even with
word size variables. I needed that to filter the output of an
altimeter.
Another effective algorithm is the median filter. It is good as the
first stage filter on data that occasionally has extreme outliers due
to shot noise. Outliers have a relatively large effect on the
smoothing and windowed average filters, but they completely fall out
of the median filter. That is why it is such a good pre-filter. It
is a table based, that is, you have to store several samples in
memory and discard the oldest when you add the newest. It is kind of
cumbersome on the Stamp. But the URL has a tutorial on how to do it.
-- regards,
Tracy Allen
electronically monitored ecosystems
mailto:tracy@e...
http://www.emesystems.com
governor is used on old and worn engines there is a lot of elctrical noise
and the readings are all over the place. I solved it with the following
method:
Each sample consists of six readings. If a reading varies by more than say
15% from the average of the last sample I substitute the last sample average
plus/minus 15%.
If there are large sudden variations in the engine speed there is a lag
between the output to the lcd and the actual reading.
I tried many other methods but in my application this worked best
espescially with a fast sampling rate
Regards
Peter Hofman
Original Message
From: "Michael Gianturco" <michcg@m...>
To: <basicstamps@yahoogroups.com>
Sent: Tuesday, March 26, 2002 1:06 AM
Subject: [noparse][[/noparse]basicstamps] Smoothing math
> Smoothing problem.
>
> For a tachometer I am building, I would like to experiment with
mathematical smoothing.
>
> The tach monitors the rps of an underwater impeller on a model sailboat.
It is a Hall switch circuit, and works nicely.
>
> But the numbers come fast and the trend jumps around a bit. With a VOM
display, the inertia inherent in the galvanometer movement tends to smooth
out the trend. But for the finished product I want to use an
> LCD. No inertia.
>
> Stock market data is often smoothed out with a simple moving average. But
since the stamp cannot divide faithfully, I was wondering if an exponential
smoothing function might work better.
>
> I know these exponential smoothing functions exist, but can't remember
how they look or how they work. Or if they require division.
>
> Thank you for any insights on how to smooth the stream of numbers coming
in from the impeller.
>
> Michael
>
>
>
>
> To UNSUBSCRIBE, just send mail to:
> basicstamps-unsubscribe@yahoogroups.com
> from the same email address that you subscribed. Text in the Subject and
Body of the message will be ignored.
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>
Best, Michael