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ADC without antialias filter? was: Anti-aliasing ADC samples

Discussion in 'Electronic Design' started by Marte Schwarz, May 9, 2006.

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  1. hello all,

    I have a little topic I couldn't understand completely (or as much I want to
    ;-)

    As a rule of thumb it is well known to use a filter to cut all frequencies
    above half the sample frequency. But I guess, there are cases that doesn't
    need this or where the signals would be more real without this filter than
    with such one. For example ECG-signals. A QRS complex has frequencies in the
    range of over 100 Hz. But these frequencies where not stationary so one
    criteria to construct alias is not present. But filtering these Signals to
    avoid frequencies over half the sampling rate may extend the QRS and in this
    case changes relevant parameters of the signal. In real world we often have
    nonstationary signals in which aliasing would not be created by having
    samplerates below the nyquist criteria. OK, we make errors having not enough
    sampling rate, sure, but depending on the goal of the signal analysis, may
    be it is sometimes better to take these errors and avoid others created from
    (analog) filters.

    Where is the error in this statement? Or is it correct? What do you think
    about?

    regards

    Marte
     
  2. Zak

    Zak Guest

    Wrong. They can still alias, and perhaps not give a tone but a wrong
    waveform.

    ---_--_--_----

    could become

    ------__------

    which is totally incorrect.
    I think you need to filter. If you are concerned about the waveform
    shape and do not want ringing: there are special filters for that. But
    expect that the rolloff is slower.


    Thomas
     
  3. Tim Wescott

    Tim Wescott Guest

    Well known, but generally misapplied.
    If the signal comes to you adequately bandlimited then you don't need to
    low-pass filter it. There are some signals where anti-alias filtering
    would degrade the signal -- specifically, a video signal is not
    optically anti-aliased. Instead you try to get the sharpest picture you
    can onto the detector, and avoid scenes that have a lot of high
    frequency content.
    I agree with that statement. If you're intentionally sampling below the
    frequency content of the parent signal then you _are_ going to degrade
    it, you should do so intelligently.

    --

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

    Posting from Google? See http://cfaj.freeshell.org/google/

    "Applied Control Theory for Embedded Systems" came out in April.
    See details at http://www.wescottdesign.com/actfes/actfes.html
     
  4. Pooh Bear

    Pooh Bear Guest

    I have indeed omitted an anti-aliasing filter when I'm confident of the
    bandwidth of the input signal.

    Graham
     
  5. Mac

    Mac Guest

    I don't fully understand your post. In particular, I don't know what QRS
    is, and I don't understand what you mean by stationary in this context.

    There are a few rules when it comes to sampling. The most strict case is
    when you can make no assumptions about the input signal bandwidth. Then
    you need to low- or band-pass filter it very well prior to sampling.

    Another interesting case would be where you know that the majority of the
    signal of interest is below Nyquist, and there is little signal or noise
    above Nyquist. In this case, you could omit the filter based on this
    a priori knowledge.

    I see frequent references to under-sampling in literature about ADC's for
    communications applications. In particular, you might see an 80 MHz ADC
    with an analog input bandwidth of 200 MHz or something. Why would you feed
    such a high BW signal into an 80 MHz ADC?

    Well, what is going on there is that they band-pass the input signal
    until it has less than 40 MHz of bandwidth, and then they under-sample it.
    So it is aliased, but that is OK because you know exactly which alias
    region it inhabits (because of the BPF), so you can account for it later.

    For example, I was thinking that it would be kind of cool to build a
    direct sampling FM radio. You could have an antenna, then a LNA and AGC
    circuit followed by an 88-108 MHz bandpass followed by an ADC. If you ran
    the ADC at, say, 80 MHz, you could pick up the entire FM band. Sure, it
    would be aliased, but since you know the frequency content is between 88
    and 108, you don't care, and you can demodulate it digitally in spite of
    that.

    Another example would be if you have some kind of parametric model of what
    you think you are sampling. Then you can just adjust the parameters until
    they fit with the samples. By making these kind of assumptions, your
    reconstructed signal could conceivably have detail not present in the raw
    samples. But there are a lot of assumptions built-in to the process, so it
    is important that they be understood and verified.

    HTH

    --Mac
     
  6. Steve Burke

    Steve Burke Guest

    Marte:

    I disagree with some of your points. I start by pointing out some sampling
    issues and then I'll comment on your main point regarding filters.

    I agree with Tim that poor Mr. Nyquist is often misunderstood. Nyquist's
    rate has to do with re-constructing a band-limited signal from a sampled
    data set. If your intent is to extract signal features without
    reconstructing the actual waveform, then you can take all sorts of liberties
    with the sample rate, provided you do no violence to the mathematical
    properties of the sampled data you want to extract/preserve. A common
    application of this is in sampling a radio receiver IF, say for an AM radio
    station. The carrier is typically converted to 455 kHz but the actual audio
    modulation of that carrier is only about 15 kHz wide. So the sample rate
    must be greater than 30 kHz to recover the modulation without introducing
    alias products. It doesn't have to be greater than 910 kHz, because we are
    not trying to recover the carrier after we digitize. This is often called
    "undersampling", but in reality it is still oversampling the bandwidth of
    interest. Its undersampling the carrier, because we don't really need it.

    The second thing to understand is that alias products are always present in
    any sampled data set, no matter if its filtered before digitizing or not.
    This is a natural result of the sampling theorem, (when you look at the
    entire frequency band, not just the band from 0 to half the sample rate).
    What actually has to be avoided is the condition where the alias products
    intermix with (or overlap) the desired non-alias products, because then you
    don't know which ones you can ignore when you do the digital processing.

    If you sample a 45 Hz tone at 100 Hz sample rate, you get a tone at 45 Hz in
    the digital domain, and you will also have a tone at (100-45 = ) 55 Hz. You
    also have an infinite number of tones at the repeating locations of 145,
    155, 245, 255, etc. but I'm going to ignore them for this discussion. As
    long as we reject everything above 50 Hz, we can see exactly what we
    digitized : 45 Hz. But suppose we digitized 55 Hz at the same 100 Hz rate.
    We'd have a tone at 55 Hz, and another at 100-55 = 45 Hz. (and 145, 155....)
    Now if we process the lower 0 - 50 Hz band, we are going to think we had 45
    Hz coming in when we actually did not. Here the alias product showed up in
    the desired signal band.

    I apologize if you understand all this already, but I wanted to set up a
    numerical case to disagree with some of your assertions, because numbers
    help make things clearer. I've already spoken to your statement that:I assume you mean that because the pulse is transient, its not stationary in
    the mathematical sense. That doesn't really matter here - the fact that we
    sample it at all means that we have to concern ourselves with alias issues.
    The duration of the alias energy is exactly as long as the duration of the
    digitized signal whether it's transient or continuous, and its always there.

    Your primary concern seems to be in these statements:

    First, if the QRS signal changes in any relevant way due to the filter, then
    either there is really higher frequency energy than you think there is, or
    the filter is not as good as it needs to be. Building a good anti-alias
    filter can be difficult or impossible, if the design tries to use a sampling
    rate that's very close to the minimum (2x). The biggest reason for raising
    the sample rate above 2x is to relax the analog filter specs. Its usually
    much easier to process more data digitally than to build a sharper analog
    filter. In my example, if the highest component to preserve is 45 Hz, then
    the analog filter has to pass 45 Hz with no loss or phase perturbations, and
    reject everything above 50 Hz. That is a 50/45 = 1.1 to 1 shape factor. It
    is almost impossible to build a low pass filter that steep, and even harder
    to keep it stable over temperature and time.

    But if my digital processing can reject everything above 45 Hz in the
    digital spectrum, then I don't really have to worry about a 51 Hz analog
    signal causing a problem. Its digital alias will show up at 49 Hz and the
    digital processing will reject it. But if an analog signal arrives at 55 Hz,
    its going to create an alias at 45 and my digital processing won't be able
    to reject that. The digital filtering does allow the cutoff for the analog
    filter to be extended from 50 to 55 Hz though. This changes the shape factor
    to 55/45 = 1.2 to 1. Still hard to build, but better than before. Moving
    the sample rate up to 120 Hz will buy big improvement. An input at 75 Hz
    will alias to 45 Hz when sampled at 120 Hz. Now the filter shape decreased
    to 75/45 = 1.6 to 1. Here we get to practical shape for an analog filter.
    The farther I'm willing to raise that sample frequency, the easier to ensure
    clean digitizing with no alias issues and no in-band distortion from the
    filter.

    My advice is to not get hung up on squeezing your signal into the minimum
    number of samples per second. Make your life easier by giving margin for
    your filters. ADC's without filters mean you can never be certain that the
    digital data stream really represents what appeared at the analog input.
    Noise, static electricity pops, ground loops, etc are all facts of life and
    analog filters are a necessity for signal integrity.

    I agree with Tim that if the filtering is done elsewhere, you don't need to
    do it twice. But it must be done. Avoiding filters because they seem to
    degrade the signal indicates you are actually interested in more of the
    signal than you designed for.

    A great book on this topic is Richard Lyons "Understanding Digital Signal
    Processing". His graphical illustrations of many of these principles are
    very unique and bring a lot of clarity without a pile of obscure math.

    Steve
     
  7. Ban

    Ban Guest

    Marte,
    first of all: analog filters work with known parameters. Whatever change
    they induce is linear and can be compensated for during the digital
    processing if needed.
    Aliasing on the other hand is not a linear phenomenon. When the signal is
    digitized you cannot differ between the folded back alias and the original
    signal, because the frequency is no more related to the signal frequency.
    Additionally there are timing errors, because the remaining analog filters
    will delay the aliasing signal much less than the original.
    An example:
    The probes pick up the heart muscle signal plus some mains-, motor-
    cellphone- radiation. Later the doctor wants to see the heart signal with a
    resolution of 10cm/beat and is used to a resolution of 1mm. this means a
    signal range of 2Hz*100=200Hz, so if you digitize with 1000Hz and 12bit,
    your analog filter has to attenuate all signals above 800Hz by at least
    74dB. a 700Hz disturbance will fold back to 300 hz and can be filtered out
    digitally, but not one at 900Hz, that folds back to 100Hz. So your analog
    filter has to be quite steep and complicated.
    Much better is to oversample and use a simple analog filter. So with 12800Hz
    sample rate you just need a 3rd order filter, easy to implement and no
    adjustment needed.
    The most important thing is to shield the analog processing to eliminate the
    induced undesired crap, then the filter might even be just a first order
    lowpass.
     
  8. Hi all,
    This is the one case that I don't want to take in account. Just let's take
    the heart-signal as it is. For those who don't know I try to simplify it:

    _____ _____ _____
    | | | | | |
    | | | | | |
    | | | | | |
    _________| |________________| |________________________| |_________

    t1 t2 t3 t4 t5 t6

    Look @ this: Really we have (nearly) infinite frequencies in this signal. So
    we have to decide whether we have to filter or not.
    I pointed, that as long as the distances t3-t1, t5-t3... are not equal (in
    case of ECG varying randomly from 0.3 to 1 s) I do not get aliasing
    frequencies if i use a sampling rate from lets say 100 Sps. Well, it is
    obvious, that the time-resolution won't be more than 10 ms but I can't see,
    where in this example would be any chance for alias errors.
    Right, but there you have stationary signals in contrast to the upper
    situation, where the higher frequencies exists only a very short time and
    because of the nonstationarity there is no chance to create alias effects.
    but guess, if you have 8 channels with 24 Bit resolution @ 12800 Sps that
    creates a dataflow that needs too much µC-power for a small, and portable
    system.

    Marte
     
  9. Rich Grise

    Rich Grise Guest

    The QRS wave is a sample of an EKG (electrocardiogram) waveform, that has
    segments known as P, Q, R, S, and T. "QRS" is the "important" part". The
    waveform can tell a lot about the health of the heart, but I can't imagine
    anything anywhere near 100 Hz being meaningful - the fundamental is about
    1 Hz, after all. ;-)

    I once worked with a unit that did that very thing, but I was on the
    software side, so just got a data stream - I have no idea if they used
    antialiasing filters, but since it was an FM RF link, it was probably
    pretty low. Just for perspective, if you listen to the FM, it goes
    wuooooooWEEEoowuoooooWEEoowuoooooWEEoowuooo....., then that goes to an
    F/V converter and gets ADC'd.

    Cheers!
    Rich

    Cheers!
    Rich
     
  10. Ban

    Ban Guest

    Have you ever seen an ECG? What you have drawn has only timing information
    and a lot of redundancy. You better take a logic analyzer for that kind of
    signal.
    And you should study again the sampling theorem. It actually doesn't talk
    about aliasing, but that any waveform can be perfectly reconstructed, if the
    highest frequency is below half the sampling frequency. If your heartbeats
    are equal or not is irrelevant.
    Don't mix Shannon and Fourier.
    Of course there is aliasing. Lets zoom into the rising edge. There is a
    +/-10ms uncertainty when it happened, so only a 50Hz signal can be exactly
    reconstructed. And what happens when you sample in the moment it rises?
    There is a random step, which is the higher frequencies folding back into
    your signal.
    You seem to know too little about digital processing. And if you have a
    24bit A/D, it must be a Delta/Sigma converter, which will work completely
    different than you thought. BTW these converters do a similar data reduction
    that I was proposing. And they *are* small.
     
  11. GregS

    GregS Guest

    We are looking at heart surface being fluoresced by heart signals, looking at it with a phodiode
    camera and the bandwidth needs to be high, but I figure most of the signal is below
    100 Hz. The bandwith of the system is several hundred Hz. There is some other stuff
    apparently as they wish to get a 10 kHz bandwidth.

    A chart of collected data of signals propagating the heart surface. I could not find the movie
    I was looking for.
    http://ajpheart.physiology.org/content/vol280/issue4/images/large/h40410665005.jpeg



    greg
     
  12. Hi Rich,
    The range of heartbeats is about 50 to 180 bpm, that's true. But ig you want
    to create a QRS which usualy looks like a triangle you need a frequency
    range up to 200 Hz. IMHO IEC and AAMI says about 100 Hz is needed for
    diagnostic ECG.
    That is not the point I mean.

    Marte
     
  13. Hi Ban,
    Guess, I say a lot of EGCs. As I wrote: It is simplified and while I didn't
    want to "draw" real looking ECG signals, the drawn signal is very good to
    explain what I want to know.
    In face of the postulation I did i can not see the relevance of real
    amplitude or something else. The question is the same with such a signal:

    _____
    _____ | |
    | | | | _____
    | | | | | |
    _________| |________________| |________________________| |_________
    t1 t2 t3 t4 t5 t6

    I know, this is not a ECG signal but is very pretty to explain, why I think,
    a filter derates my signal more than it would help.
    I this special case ther is no sampling point in the moment of rising
    possible (infinity small). That would mean, I only get a jitter of 10 ms and
    gan reconstruct the Signal as is. I gan not see any mirroring frequencies
    created by aliasing.
    The AD we uses at the moment (AD1254) gives us 4 ksps when multiplexing the
    channels. I get the sample values like with every other AD, isn't it?
    Clock frequency is not the same than sample rate here.
    Yes, and now what do you want to say me with this?

    Marte
     
  14. Rich Grise

    Rich Grise Guest

    OK, so find a filter design with a 300 Hz cutoff, that's flat in the
    passband. Or am I missing something?
    Yeah, but was it cute? ;-)

    Cheers!
    Rich
     
  15. Hi Rich,

    Yes, may be I want to sample with 100 Sps. There are really higher
    frequencies
    in the ECG signal as well as in the exsample signal above.
    Normally we have to built an antialias filter with cutoff under 50 Hz. The
    obvious effect then is, that the signal without filter is much more like the
    original signal (sampled with >1 kSps) than the (correct) filtered signal.
    Theory says the filter should be there to reduce unwanted / unreal signals
    that are produced via aliasing. Fact is, we do not see such unwanted signal
    parts but we realise degraded quality with filters.

    Marte
     
  16. Ban

    Ban Guest

    I didn't find that one on AD, but the 7718. These converters work completely
    different. They integrate the incoming analog signals and are open as long
    as the channel is active. Which means you get an ugly step instead of your
    square edge and anyway you want that step only on rising or falling edges,
    not when the signal is almost constant. You are describing a sampling
    converter, using much more current and having much less resolution.
    You can pretty easily downsample with a small FIR filter, but if you do not
    know that, I would recommend to read your script about A/D converters again.
    Then it would be better to simulate the whole project with Matlab. Record
    some real probe signal with a digital scope and use that wav file for your
    simulation. You can also simulate analog filters with CoolEdit and the
    digital part with Matlab DSP toolbox and filter toolbox. When this works you
    should only start with the hardware. This is also tricky as the converter is
    extremely delicate and has to be protected from blowout. We can give you
    some hand there, but we cannot do the understanding for you.
     
  17. Rich Grise

    Rich Grise Guest

    That's probably because in an EKG signal there probably aren't very many
    harmonics above 50 Hz to _do_ any aliasing. :) As long as you can follow
    the slew rate, you should be fine as is.

    Good Luck!
    Rich
     
  18. Hi,
    Thank you, but as long as I have the feeling that you didn't understand the
    topic here I won't miss your help :)

    Have a nice weekend

    Marte
     
  19. Ban

    Ban Guest

    Marte, the part is called ADS1254, that's why I didn't find it.

    Please read about Sigma/Delta converters. You will see that you are just
    dreaming what you wrote. And I'm sure your professor will ask you as well.
    So you should be a little more humble if someone points out your
    misunderstanding. This is not only true for the principle of operation, but
    also about the sampling theorem. This is one of the fundamentals for any
    engineer, which you will be asked about. And I can see you know deep down
    that your understanding is missing: "I get the sample values like with every
    other AD, isn't it?"
    No, it is integrating and *not* sampling. And maybe you know that this is
    equivalent to a lowpass filter. So the whole question is bogus, you are
    already filtering with this converter and maybe you do not need an
    additional analog filter, if you choose the right parameters, and you will
    loose many details and you won't get any square edges, they are also not
    needed anyway.
    But I think Karlsruhe is not a bad place to study, so you seem to be still
    in the beginning. Talk with some tutor about the project, is it for the
    "Studienarbeit?"
    And why don't you ask the question in de.sci.electronics, where you
    participate with some arrogant answers:I'm sure Mawin will put you right.
     
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