michael brown wrote:
>This may sound like a dumb question, but I have not run across a good
>"plain
>English" description of low-pass [...]
A time-varying signal can be represented as a function of time, f(t).
The same function can be represented in "frequency space" via a linear
transformation called the Fourier transform as F(w), which tells you
how much sinusoidal component the original function has at each
frequency w (read as omega). If you know much linear algebra, you can
think of f(t) and F(w) as being vectors related through a change of
basis, though of course we are talking here about an infinite-
dimensional function space rather than the (possibly) more familiar
finte-dimensional euclidean vector space. A low-pass filter is very easy
to define in frequency space: it lets through the low-frequency
components but blocks the high-frequency components. Mathematically,
you Fourier transform the original function, multiply by the filter
function (as represented in frequency space), then invert the Fourier
transform to get the filtered time-varying signal.
Hm, this isn't really "plain English" is it? Try again.
A low-pass filter lets the slowly-varying part of a signal through,
but blocks the quickly-varying part. Like, if you had a 1kHz wiggle
superimposed on 60Hz mains voltage, then after filtering with an
appropriate low-pass filter, you would recover the 60Hz part with the
1kHz wiggle blocked out. A simple low pass filter is a resistor
followed by a capacitor to ground:
(Please excuse my hideous ASCII "graphics"). The capacitor serves to
shunt any high-frequency component of Vin to ground (a capacitor has
low impedance to high-frequency, high impedance to low-frequency). It
is easy to show that the 3dB point of this filter is at 1/(2 pi R C).
In frequency space, this simple filter falls off at higher frequencies
rather gently: it is not a very precise low-pass filter. For better
filtering you can use active filters.
Was this in the least bit useful? I hope so.
Michael V
Thank you for reading my "little" posting.
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> michael brown wrote:
> >This may sound like a dumb question, but I have not run across a good
> >"plain
> >English" description of low-pass [...]
>
> A time-varying signal can be represented as a function of time, f(t).
> The same function can be represented in "frequency space" via a linear
<SNIP>
>
> Hm, this isn't really "plain English" is it? Try again.
Not to me, it pretty much reads like the rest of the "explanations" I've
seen. ;-)
> A low-pass filter lets the slowly-varying part of a signal through,......
<SNIP>
DSP's are good.
> Was this in the least bit useful? I hope so.
Thanks for the reply. It reinforces what I already understand about
filtering electrical or electro-magnetic "waves". I am looking for the
definition as it applies to EE and sampled data. Also I hear/see the term
"integrate" and am not completely clear as to what this means in the context
of EE and data samples. I hear these terms being used frequently, but I've
never taken any EE type classes, so I'm not sure what it means. Never took
a calculus class either.
michael brown wrote:
>[In reply to my [MV's] evidently less-than-useful reply to his
> question about low-pass filtering]
>
>Thanks for the reply. It reinforces what I already understand about
>filtering electrical or electro-magnetic "waves". I am looking for the
>definition as it applies to EE and sampled data.
One simple approach to digital low-pass filtering is just to do a
windowed average. That is, if you have a sequence of measurements
(samples) of a signal, then you average together every N of them
(like every pair, or every 10, or every 10000, as appropriate). In
this way, you average out the high-frequency "wiggles" and get just
the lower-frequency variations in the signal. By "average" I mean
exactly what you think I mean: add them up and divide by the number N.
>Also I hear/see the term
>"integrate" and am not completely clear as to what this means in the
>context
>of EE and data samples.
"Integrate" in the case of discrete samples just means "add 'em up".
Same as the averaging technique I mentioned above.
Michael V (still trying to be helpful...)
Thank you for reading my little posting.
_________________________________________________________________
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> Thanks for the reply. It reinforces what I already understand about
> filtering electrical or electro-magnetic "waves". I am looking for the
> definition as it applies to EE and sampled data. Also I hear/see the term
> "integrate" and am not completely clear as to what this means in the
context
> of EE and data samples. I hear these terms being used frequently, but
I've
> never taken any EE type classes, so I'm not sure what it means. Never
took
> a calculus class either.
There are many ways to describe a low pass filter, let's see if I can
make it without the math...
Imagine a wide water tube that is connected to a swimming poll by a
narrow tube. The water level on the wide tube will follow the poll level but
will be much less "wavy" than the pool. That is a low pass filter for water
level, the wide tube does the function of the capacitor and the narrow tube
is the resistor.
On the algorithm side... If you take 8 samples of a signal and average
them to decide what the 9'nth sample will be and keep doing that with the
last 8 samples all the time you have a low pass filter also, you will
minimize the effect of fast varying signals in your sample window. Finite
impulse response filters, very used in DSP's, are almost impossible to
describe without the math :-( Imagine that a low pass filter is always
something that "smooths" the signals.
A low pass filter will allow low frequencies through without much loss, will
tend to block high frequencies, and at some magic frequency determined by
the values of the components will attenuate the signal by about half.
Frequencies above this are attentuated more, below this are attenuated less.
A classic low pass filter (there are dozens of different types) is simply:
Vin--------R--------OUT
|
C
|
GND
This is useful in PICs to take a high frequency signal, say a PWM output,
and turn it into a smooth nearly DC signal, say for an input to a
comparator.
Calculus is handy for figgering out how this stuff really works, but it is
possible to understand it in a practical way without it. I was building
stuff with low pass filters long before I ever studied calculus.
OK, what about sampled data? An old fella named Nyquist said that you need
to sample your data at least twice the highest frequency present in the
signal for it to make any sense. Another fella named Lile said that Nyquist
was an optimist. A low pass filter is often used in front of a data
acquisition system of any kind to limit high frequencies. If the high
frequency cutoff of your filter is 10KHZ, you need to sample at least 20KHZ
(per Nyquist) and realistically even faster (per Pessimistic Mr. Lile) to
get good useful data without aliasing and other problems.
Next you are going to ask how to calculate the cutoff frequency of such a
filter. I'll bet there are some good cookbook methods that don't involve
any calculus. I, being lazy, just chuck parts into BSpice and let it figger
the answer for me. Anybody want to weigh in?
At 10:18 AM 2/28/02 -0600, Michael wrote:
> > michael brown wrote:
> > >This may sound like a dumb question, but I have not run across a good
> > >"plain
> > >English" description of low-pass [...]
> >
> > A time-varying signal can be represented as a function of time, f(t).
> > The same function can be represented in "frequency space" via a linear
><SNIP>
> >
> > Hm, this isn't really "plain English" is it? Try again.
>
>Not to me, it pretty much reads like the rest of the "explanations" I've
>seen. ;-)
A low-pass filter is simply a moving-average in a sampled data system.
An analog system is continuous, so you have to visualize an infinite number
of infinitesimal pieces going into the moving-average. In this case, the
moving-average is called an "integral" and the process of adding up the
infinite number of pieces is called "integration".
================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS e-mail: spam_OUTralTakeThisOuTlcfltd.com
Least Cost Formulations, Ltd. URL: http://lcfltd.com/
824 Timberlake Drive Tel: 757-467-0954
Virginia Beach, VA 23464-3239 Fax: 757-467-2947
"Vere scire est per causas scire"
================================================================
Very good explanation and I'm glad to see that you have introduced Lile's
Law ;-)
One little correction, though: to be able to recover the information from a
signal, it is NOT necessary to sample at a rate which is more than twice
the maximum frequency content. It is only necessary to sample at a rate
which is more than twice the bandwidth. So, for example, if you have a
signal at 10MHz which is amplitude modulated by a 10kHz signal, the
spectrum looks like a narrow band (20kHz wide) way up at 10MHz and nothing
else. The signal bandwidth in this case is actually 10kHz (half the width
of the band of freqs that you see) and you need only sample at 20kHz (or
preferably a little higher to prevent problems, as you say). You DO,
though, need an ADC which has a very small sample aperture (i.e., it's
sample and hold just looks at a very small region in time to grab each sample).
This makes it easier to do things like software radio where you do
demodulation and IF filtering in DSP. Your IF may be at RF frequencies, but
you need only sample according to the bandwidth.
Sean
At 10:44 AM 2/28/02 -0600, Lawrence Lile wrote: {Quote hidden}
>Let's try plainer plain Inglitsch:
>
>A low pass filter will allow low frequencies through without much loss, will
>tend to block high frequencies, and at some magic frequency determined by
>the values of the components will attenuate the signal by about half.
>Frequencies above this are attentuated more, below this are attenuated less.
>
>
>A classic low pass filter (there are dozens of different types) is simply:
>
>Vin--------R--------OUT
> |
> C
> |
> GND
>
>This is useful in PICs to take a high frequency signal, say a PWM output,
>and turn it into a smooth nearly DC signal, say for an input to a
>comparator.
>
>Calculus is handy for figgering out how this stuff really works, but it is
>possible to understand it in a practical way without it. I was building
>stuff with low pass filters long before I ever studied calculus.
>
>
>OK, what about sampled data? An old fella named Nyquist said that you need
>to sample your data at least twice the highest frequency present in the
>signal for it to make any sense. Another fella named Lile said that Nyquist
>was an optimist. A low pass filter is often used in front of a data
>acquisition system of any kind to limit high frequencies. If the high
>frequency cutoff of your filter is 10KHZ, you need to sample at least 20KHZ
>(per Nyquist) and realistically even faster (per Pessimistic Mr. Lile) to
>get good useful data without aliasing and other problems.
>
>Next you are going to ask how to calculate the cutoff frequency of such a
>filter. I'll bet there are some good cookbook methods that don't involve
>any calculus. I, being lazy, just chuck parts into BSpice and let it figger
>the answer for me. Anybody want to weigh in?
>
>--Lawrence Lile
> It reinforces what I already understand about
> filtering electrical or electro-magnetic "waves". I am looking for the
> definition as it applies to EE and sampled data.
Inside a computer a simple low pass filter working on successive samples is:
Filt <-- Filt + (New - Filt)*FFrac
Where FILT is the filter that is being updated, and NEW is the new sample
being accumulated into the filter. FFRAC is the filter fraction, a value
from 0 to 1 for a normal low pass filter. It governs how "heavy" the
filtering is. A value of 0 is infinitely heavy, which means the filter
output never changes at all. A value of 1 causes the input signal to be
passed thru without any filtering. Do an example on paper to see how this
works. I often cascade two of these things, called "poles", to make a "two
pole" digital filter.
> michael brown wrote:
> >[In reply to my [MV's] evidently less-than-useful reply to his
> > question about low-pass filtering]
> >
> >Thanks for the reply. It reinforces what I already understand about
> >filtering electrical or electro-magnetic "waves". I am looking for the
> >definition as it applies to EE and sampled data.
>
> One simple approach to digital low-pass filtering is just to do a
> windowed average. That is, if you have a sequence of measurements
> (samples) of a signal, then you average together every N of them
> (like every pair, or every 10, or every 10000, as appropriate). In
> this way, you average out the high-frequency "wiggles" and get just
> the lower-frequency variations in the signal. By "average" I mean
> exactly what you think I mean: add them up and divide by the number N.
So basically, it means to use quality sampling instead of quantity sampling.
Just pick an arbitrary pattern (that hopefully doesn't synchronize or beat
with your samples) and smart-sample® your way to success. ;-)
> >Also I hear/see the term
> >"integrate" and am not completely clear as to what this means in the
> >context
> >of EE and data samples.
>
> "Integrate" in the case of discrete samples just means "add 'em up".
> Same as the averaging technique I mentioned above.
That's simple enough for my pea-brain. ;-) Why don't they just say that???
I'd learn this stuff faster if it wasn't for the language barrier. ;-D
> Inside a computer a simple low pass filter working on successive samples
is:
>
> Filt <-- Filt + (New - Filt)*FFrac
>
> Where FILT is the filter that is being updated, and NEW is the new sample
> being accumulated into the filter. FFRAC is the filter fraction, a value
> from 0 to 1 for a normal low pass filter. It governs how "heavy" the
> filtering is. A value of 0 is infinitely heavy, which means the filter
> output never changes at all. A value of 1 causes the input signal to be
> passed thru without any filtering. Do an example on paper to see how this
> works. I often cascade two of these things, called "poles", to make a
"two
> pole" digital filter.
Woohoo, way to go Olin. This is the best description yet, and it even
includes a formula. ;-D
> > >Also I hear/see the term
> > >"integrate" and am not completely clear as to what this means in the
> > >context
> > >of EE and data samples.
> >
> > "Integrate" in the case of discrete samples just means "add 'em up".
> > Same as the averaging technique I mentioned above.
>
> That's simple enough for my pea-brain. ;-) Why don't they just say
that???
Because there's a lot more to it than that in many cases. You can only wing
it so far. You need to go learn some math if you really want to use this
stuff for more than a one-off hobby project.
> > A low-pass filter is simply a moving-average in a sampled data system.
>
> Ding! Ding! Ding! The perfect "plain english" description. I get it now.
Not so fast. That's only one way to achieve a low pass filter. In
techno-speak that's called a box filter, which is usually not what you want
to implement in a PIC. For most ordinary situations, there are better
methods that are actually easier to implement.
********************************************************************
Olin Lathrop, embedded systems consultant in Littleton Massachusetts
(978) 742-9014, olinspam_OUTembedinc.com,http://www.embedinc.com
On Thu, 28 Feb 2002 08:01:15 -0800 Michael Vinson <KILLspammjvinsonKILLspamHOTMAIL.COM>
writes:
> michael brown wrote:
> >This may sound like a dumb question, but I have not run across a
> good
> >"plain
> >English" description of low-pass [...]
>
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