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Aliasing and low-pass filtering question

Discussion in 'Electronic Basics' started by MRW, May 15, 2007.

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  1. MRW

    MRW Guest

    Hello,

    Can someone please para-phrase the following?

    "To avoid aliasing, an analog low-pass filter is placed at the input
    before the sampler. The low-pass filter determines the highest
    frequency of the FFT analyzer. Because the rate at which signals can
    be represented without error is one half the maximum sampling rate,
    signals are often cut off at a lower frequency to provide sampling
    rates greater than twice the maximum frequency components. Typically
    the cutoff of the low-pass filter is 2.5 times less than the maximum
    sampling rate of the analyzer. This determines the maximum frequency
    component."


    The part that I'm especially confused at is: "Because the rate at
    which signals can be represented without error is one half the maximum
    sampling rate, signals are often cut off at a lower frequency to
    provide sampling rates greater than twice the maximum frequency
    components"

    I cannot picture this properly.

    Thanks!
     
  2. Rich Grise

    Rich Grise Guest

    These guys explain it a lot better than I can:
    http://en.wikipedia.org/wiki/Aliasing

    Have Fun!
    Rich
     
  3. If you have say a 1KHz sample rate then you cannot sample any signal
    greater than half that (500Hz). If you do, input frequencies *higher*
    than 500Hz will appear as frequency artifacts *lower* than 500Hz. You
    will think you are looking at a real signal <500Hz when in fact you
    are just seeing an aliasing artifact caused by a signal >500Hz. This
    is why most analog to digital converters will have an anti-aliasing
    filter at around half the sample rate on the input.

    You might like to start here:
    http://en.wikipedia.org/wiki/Aliasing
    and some of the links might help explain it better, like this one:
    http://burtonmackenzie.blogspot.com/2006/07/i-cant-drive-55.html

    Dave.
     
  4. MRW

    MRW Guest

    Thanks! That seems clearer now.

    The text is actually in regards to a spectrum analyzer. For our
    project, I was assigned by my professor to find a spectrum analyzer
    that can work all the way up to 16GHz and get a quote. I didn't know
    these things were that expensive.

    Is it possible to still use a spectrum analyzer that works all the way
    up to 3GHz using an input signal of up to 16GHz? I was thinking of a
    mixer and vco to step down the frequency to something below 3GHz, but
    I'm not aware of any such modules for spectrum analyzers.
     
  5. John Fields

    John Fields Guest

    ---
    In some old western movies the spokes of wagon wheels would be going
    fast enough that in one frame one spoke would be caught vertical,
    while in the next frame the next spoke would be caught a little
    counter-clockwise from vertical, giving the appearance that the
    wagon wheels were rotating backwards.

    At higher speeds, the first spoke would be caught at vertical while
    the next spoke would be caught a little clockwise from vertical,
    giving the impression that the wheel was rotating much more slowly
    than it really was.
     
  6. Ben Jackson

    Ben Jackson Guest

    The "cut off" frequency of a filter is not a brick wall. Typically it's
    specified as the point with 3dB of loss. If your anti-aliasing filter
    has Fco = 1/2 FS, then there are a few issues:

    1. Your signal at 1/2 FS is at half the amplitude of the signal in the
    rest of your passband (3dB point), so if it's an important frequency it
    will be attenuated.

    2. No filter is a brick wall, so Fco + epsilon is near 3dB down, but it
    is aliasing back to Fco - epsilon, which it will be large enough to
    interfere with your signal of interest.

    3. (if you are really nit-picky) The phase response of your filter will
    probably also be changing around your cutoff frequency, which will matter
    if you care about the phase output of the FFT.

    What you really have to consider is how much you want to attenuate the
    aliases (stoppband attenuation of your filter), how much of your signal
    is important (your passband, but still beware of how passband is defined),
    and how wide the transition band is. You will want FS to be at least twice
    the start of your *stop*band, which is beyond the transition.

    If you look on google groups you can find a thread from a while back where
    I asked essentially the same question but about DAC reconstruction filters,
    where many of the same considerations apply.
     
  7. Bob Masta

    Bob Masta Guest

    Depending on what you are doing, you may very well be able to
    use signals that are higher than half the sample rate. This is
    called undersampling. It's typically used where you are only
    interested in a narrow band of frequencies, not the entire spectrum
    down to DC. You still get aliasing, but if you know for certain that
    the input signal is within a certain frequency range, you can
    interpret the aliased spectrum properly.

    The input signal bandwidth must be less than half the sample
    rate, so in your case less than 3/2 GHz or 1.5 GHz. Better if
    it is quite a bit less, to avoid confusion at the band edges.
    For example, if it only contains components between 15 and
    16 GHz, the bandwidth is only 1 GHz so that should work OK.
    Note that you will have to bypass the anti-alias filter on the 3 GHz
    analyzer.

    The aliased signal "folds over" the spectrum limits at the
    Nyquist frequency (half the sample rate) and at DC (zero Hz).
    A signal that is a little above Nyquist will be mirrored downward.
    For example, a 1.6 GHz signal will be mirrored about the 1.5 GHz
    Nyquist and appear at 1.4 GHz. As the input goes higher, the
    alias appears lower until it hits zero, where it "bounces back".
    So an input of 3 GHz will alias to 0, and 3.1 GHz will alias to
    0.1 GHz. This pattern repeats for higher inputs.

    I have some examples (at audio frequencies) in the
    discussion of aliasing at
    http://www.daqarta.com/dw_0haa.htm

    If you want to play around with aliasing to get a feel
    for how it works, you can use the Daqarta signal
    generator and the example at
    http://www.daqarta.com/dw_0hdd.htm

    (Note that the signal generator is free, even though
    Daqarta itself is $29. When the trial period expires,
    the signal generator and all the analysis features
    continue to work. You can use it this way for as
    long as you like.)

    Best regards,



    Bob Masta

    D A Q A R T A
    Data AcQuisition And Real-Time Analysis
    www.daqarta.com
    Scope, Spectrum, Spectrogram, Signal Generator
    Science with your sound card!
     
  8. Guest

    A 3GHz SpecA would not be useful with direct 16GHz signals. You can
    devise a mixer/VCO bit to bring down bands of interest narrower than 3
    GHz.
    To get accurate results you will also need to calibrate the setup.
    Some
    analyzers allow calibration of the external mixer. But perhaps it is
    better
    to spend more time measuring the device of interest, rather than the
    setup.
    Companies like Agilent make whole families of SpecA's that have 1GHz,
    2GHz, even 26GHz input range. Try Googling for "8563E rental".
     
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