Post by thread:[EE]: What is low pass filtering

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: Vin o----^v^v^v---*-----o Vout (Resistor) | --- --- (Capacitor) | GND o-------------*-----o GND (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. _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

See below > 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 (unedumacated foole) -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

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. _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

Hi, > 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. Hope this helps... best regards, Alexandre Guimaraes -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

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 {Original Message removed}

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" ================================================================ -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

Hi Lawrence, 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 ---------------------------------------------------- Sign Up for NetZero Platinum Today Only $9.95 per month! http://my.netzero.net/s/signup?r=platinum&refcd=PT97 -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

> 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. ******************************************************************** Olin Lathrop, embedded systems consultant in Littleton Massachusetts (978) 742-9014, .....olinKILLspam@spam@embedinc.com, http://www.embedinc.com -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

> 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 > Michael V (still trying to be helpful...) You were, thanks. ;-) michael brown (not a linguist) -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

> 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 michael brown -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email listservKILLspammitvma.mit.edu with SET PICList DIGEST in the body

> > >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. ******************************************************************** Olin Lathrop, embedded systems consultant in Littleton Massachusetts (978) 742-9014, .....olinKILLspam.....embedinc.com, http://www.embedinc.com -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email EraseMElistservspam_OUTTakeThisOuTmitvma.mit.edu with SET PICList DIGEST in the body

> > 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 -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email @spam@listservKILLspammitvma.mit.edu with SET PICList DIGEST in the body

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 [...] > If you can put up with a long download, have a look at http://www.hallikainen.org/cuesta/et113/RcLPF.pdf where an RC low pass filter is analyzed. http://www.hallikainen.org/cuesta/et113/RcHpfBreakFreq.pdf shows a Bode plot approximation for a high pass filter. The same approach works for a low pass filter. Harold FCC Rules Online at http://hallikainen.com/FccRules Lighting control for theatre and television at http://www.dovesystems.com ________________________________________________________________ GET INTERNET ACCESS FROM JUNO! Juno offers FREE or PREMIUM Internet access for less! Join Juno today! For your FREE software, visit: dl.http://www.juno.com/get/web/. -- http://www.piclist.com#nomail Going offline? Don't AutoReply us! email RemoveMElistservTakeThisOuTmitvma.mit.edu with SET PICList DIGEST in the body