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Quardrature Direct Fourier Transform

Discussion in 'Electronic Design' started by Luhan Monat, May 31, 2004.

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  1. Luhan Monat

    Luhan Monat Guest

    Hi,

    I've been using this method for tone decoding on several projects so far...

    http://members.cox.net/berniekm/qdft.html

    Since I am nearly 100% self educated in electronics and such, I have no
    idea if this idea is original. Anybody know anything about this?
     
  2. Jim Thompson

    Jim Thompson Guest

    Very interesting! Care to elaborate on your circuitry?

    ...Jim Thompson
     
  3. Activ8

    Activ8 Guest

    it's a PIC12F675. an 8 pin job. I guess you have to sample the hell
    out of the tones to find the peaks. First you'd have to filter out
    the high and low tones though.
     
  4. Your website says:
    " The resultant sums are then 'vector added' by taking the 'square
    root of the sum of the squares'."

    The DFT is defined with a complex output, which means that the real
    and imaginary parts are left as is; there is no square root operation
    in a DFT per se.

    You might want to use a sqrt to find the magnitude. However, if
    converting to dB, it's better to just sum the squares of the two parts
    then take 10.log(), rather than 20.log(sqrt()).


    As for your invention: this technique is well known. I posted a
    tutorial [about something that was essentially equivalent] to comp.dsp
    a few years ago.
    http://www.dspguru.com/comp.dsp/tricks/alg/cpxdown.htm

    Don't be discouraged though; this is an excellent idea, and you did
    well to think of it by yourself.

    Regards,
    Allan.
     
  5. Also, if comparing the magnitude against a threshold, it is much
    cheaper to compare the square of the magnitude against the square of
    the threshold, as this avoids a sqrt operation needed to find the
    magnitude.

    Also look at this family of cheap rectangular to magnitude
    approximations:
    http://www.dspguru.com/comp.dsp/tricks/alg/mag_est.htm

    Regards,
    Allan.
     
  6. Tim Wescott

    Tim Wescott Guest

    I designed a radio for my Master's thesis in 1990 that used this sort of
    gimmick to decode 400 baud MSK on a Motorola 6811 -- it worked very
    well, being only a dB or two below theoretically optimal performance.
     
  7. Luhan Monat

    Luhan Monat Guest

    Hi Jim,

    Circuitry - two 22k resistors from the A/D input to + and ground
    respectively, and a 0.1 uf cap from the source to the A/D input.
     
  8. Luhan Monat

    Luhan Monat Guest

    No, I just time the samples for the tartget frequency. You dont
    actually have to find the peak since the computations use both sine and
    cosine - just like regular old FFT.
     
  9. Luhan Monat

    Luhan Monat Guest

    Thanks, that answers my question.
     
  10. Joel Kolstad

    Joel Kolstad Guest

    I can't say I've seen it used before, but I think it's a clever idea --
    taking the usual 'correlation' approach and breaking it down to just 4
    samples per period! Have you compared the performance against other, say,
    DTMF decoders? I would suspect it's not quite as good, but given how
    parsimonious its CPU requirements are, I'd say it's still a big 'win!'

    I'd be particularly interested in comparing the performance to a straight
    'bandpass filter using coefficients of 0/+/-1' approach. This doesn't
    require the computation of I^2+Q^2 (which seems like it would be adequate
    for your needs, right? The square root, as others have pointed out, is
    rather slow to perform and is usually approximated anyway.), but needs
    (noticeably) more than 2 additions or subtractions per period.

    ---Joel Kolstad
     
  11. Fred Bloggs

    Fred Bloggs Guest

    Yes- you are about 22 years behind the curve- this type of processing is
    known as quadrature sampling with digital mixing:

    Considine,V. "Digital Complex Sampling" Electronics Letters, 19, 4 Aug 1983
    Rader, C.M., "A Simple Method for Sampling In-Phase and Quadrature
    Components", IEEE Transactions Aerospace and Electronics Systems, Vol.
    AES-20, No.6, November 1984
    Rice,D. and Wu, K.,"Quadrature Sampling with High Dynamic Range", IEEE
    Transactions Aerospace and Electronic Systems, Vol. AES-18, No.4, Nov 1982
    Pellon,L.E.,"A Double Nyquist Digital Product detector for Quadrature
    Sampling", IEEE Trans. Signal Processing, Vol.40,N0.7, July 1992
     
  12. Luhan Monat

    Luhan Monat Guest

    Wow, only 22 years! Looks like I'm catching up.
     
  13. maxfoo

    maxfoo Guest

    That should get you an honorary doctorate degree from the prestigious 'S.E.D.'
















    Remove "HeadFromButt", before replying by email.
     
  14. Bill Sloman

    Bill Sloman Guest

    The basic idea is definitely older - colour TV encodes the colour
    information as sine and cosine components of the colour carrier (which is
    something like 5MHz). The original systems used analog decoding in
    quadrature to demodulate two separate colour signals from the 5MHz carrier.
    IIRR RCA (America) and EMI (UK) patented identical systems at much the same
    time, one describing it as "sine and cosine" as the other as "quadrature".

    When the matter came to court, the lawyers couldn't be persuaded that the
    systems were identical .....
     
  15. Fred Bloggs

    Fred Bloggs Guest

    The idea here is not quadrature decoding per se but digital quadrature
    decoding using a single sampling channel. The impetus for this
    development was the shortfall in the analog circuitry available at the
    time for maintaining the quadrature in phase and amplitude across the
    requisite bandwidth at the required precision.
     
  16. Bill Sloman

    Bill Sloman Guest

    Seems odd. Quadrature sampling with high dynamic range isn't going to
    use a single stage flash A/D converter, and every other kind of fast
    A/D needs a sample and hold in front of it to sample the signal to be
    converted at the desired time and hold it stable through the various
    sorts of successive approximation steps.

    So how does digitisation get around the shortfall in the analog sample
    and hold that is doing the actual sampling?
     
  17. Joel Kolstad

    Joel Kolstad Guest

    (Yes, I know, talking to myself...)

    I took a look at the above mentioned approach, and the results are somewhat
    depressing... the 'slowest' case is the bandpass filter at 697Hz (for DTMF),
    and this ends up requiring 105 additions and 105 subtractions for every
    input if I spec things out such that I get 20dB suppression of 660Hz/710Hz.
    I have a suspicion that these numbers aren't particular better (and might
    actually be worse) than Luhan's method... although it's unclear to me just
    what the actual frequency response of his method turns out to be.

    ---Joel
     
  18. Luhan Monat

    Luhan Monat Guest

    Sample and hold functions are built into the PIC A/D circuitry.
     
  19. Fred Bloggs

    Fred Bloggs Guest

    I cannot speak for the 1982 era SH's- but they are no longer a
    limitation in modern times- with sampling apertures at under 100ps and
    much faster than the actual A/D pipelined conversion rate.
     
  20. Bill Sloman

    Bill Sloman Guest

    This is very common - we've had complaints here that the only way to
    get a really good sample-and-hold function these days is to buy a fast
    A/D converter.

    Burr-Brown used to sell 12- and 14-bit accurate sample and holds, with
    aperture times of the order of a few tens of nanoseconds, but they
    stopped selling them some years ago. I had copies of the data sheets
    in the late 1980's, but I can't find them in the Texas Instrument list
    of obsolete parts (Texas Instruments took over Burr-Brown a couple of
    years ago).
     
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