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Signal strength at some fixed frequency

Discussion in 'Embedded' started by David Ashley, Oct 18, 2006.

  1. David Ashley

    David Ashley Guest

    Can someone point me to a simple algorithm to compute
    the signal strength at some frequency? Say I've got 1024
    samples, 16 bit signed values, at 44100 hz, and I want
    to know how much of 440 hz is present in the signal.

    David Ashley, Oct 18, 2006
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  2. David Ashley

    Tim Wescott Guest

    You can do it by correlation -- multiply your signal by sine and cosine
    waves at 440Hz, add the results, then find the RMS of those two numbers.

    Or you can do it using the Goertzel algorithm -- it's a favorite of CS
    types, it does the job, but it has lots of subtle details to it that
    most cookbook solutions overlook. OTOH, there are cookbook solutions
    out there...


    Tim Wescott
    Wescott Design Services

    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
    Tim Wescott, Oct 18, 2006
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  3. With such small number of samples, you just get the amount of signal
    in the neighbourhood of 440 Hz, perhaps sufficient for some "real time
    analyzer" but definitively not for instrument tuning.

    Paul Keinanen, Oct 18, 2006
  4. David Ashley

    Bill Davy Guest

    Compute the correlation with a 440 Hz sine wave.
    Bill Davy, Oct 18, 2006
  5. David Ashley

    David Ashley Guest

    I tried Goertzel and the results look promising. I want to use
    integer math but the Goertzel sample code I got from
    Wikipedia uses doubles, and the numbers balloon up. One
    tunable was the number of samples used in the calculation.

    David Ashley, Oct 18, 2006
  6. It may not be that simple. You will see truncation and leakage effect.
    Then you start to think about the window, then you need more than one
    spectrum line to calculate the overall rms.

    If he wants to achieve an estimation with high accuracy, I have not
    seen a simple answer yet.

    DigitalSignal, Oct 18, 2006
  7. David Ashley

    GMM50 Guest

    Tim Wescott has the right idea. It's also called synchronous
    demodulation. It simple and works quite well.

    GMM50, Oct 18, 2006
  8. David Ashley

    rivas.ed Guest

    I recall an article in Circuit Cellar where they implemented the
    Goertzel on an 8 bit micro without using floating point math. Since the
    number of frequencies they were looking for was limited (as in your
    case) they "pre-calculated" some of the operations needed to compute
    the magnitude that you're looking for. They also did some
    approximations to simplify the math. Search circuit cellars website. It
    may work for your needs.

    -Ed Rivas
    rivas.ed, Oct 19, 2006
  9. David Ashley

    David Ashley Guest

    I did find a code snippet on CC related to a design contest, I think
    it was a complete phone answering machine. It used
    Goertzel for the tone recognition, probably for data entry.
    There was a small function referred to but it wasn't complete.
    It was obviously integer math but seemed iffy. One section
    showed ">>15" and another ">> AMP_BITS". But the code
    to set up the coefficients and the definition of AMP_BITS wasn't

    I figured I'd just play around with it when I next get a chance.

    David Ashley, Oct 19, 2006
  10. David Ashley

    Ico Guest

    Which makes me wonder: does anybody have recomendations on an allround
    DSP cookbook for embedded programmers, especially the
    non-mathematicians? I'm thinking of something describing the dirty
    details of sampling theory (Tim Wescott's "what Nyquist didn't say"!),
    introduction to FIR/IIR filters and other alternatives, with practical
    guidlines on implemententation, also on smaller CPU's without FPU
    hardware, and 'tricks' from the more experienced in the field. The
    'hackers delight' version about digital signal processing ?
    Ico, Oct 19, 2006
  11. David Ashley

    Arlet Guest

    I found "Digital Signal Processing - A Practical Approach", by
    Ifeachor and Jervis fairly easy to digest. It does have math, but also
    code examples, so if you can't follow the math, you can at least copy
    the code :)
    Arlet, Oct 19, 2006
  12. David Ashley

    linnix Guest

    Here is one form of Goertzel, doesn't seem to hard to integerize it.

    float goertzel(float *x, int N, float frequency, int samplerate) {
    float Skn, Skn1, Skn2;
    Skn = Skn1 = Skn2 = 0;

    for (int i=0; i<N; i++) {
    Skn2 = Skn1;
    Skn1 = Skn;
    Skn = 2*cos(2*PI*frequency/samplerate)*Skn1 - Skn2 + x;

    float WNk = exp(-2*PI*frequency/samplerate); // this one ignores
    complex stuff
    return (Skn - WNk*Skn1);
    linnix, Oct 19, 2006
  13. David Ashley

    rivas.ed Guest

    In the snippet below, Pi = 3.14, freq = 440, samplerate = 44100. You
    can calculate cos of this number and use it as a constant. I think this
    was the goal of the article I read. Not sure if it was the same one as
    you are referring to, I don't think it was though.

    Did some searching and I don't think they have the particular article
    I'm referring to available on the web. The issue is 182 (Digital
    Decoding Simplified: Sequential Exact-Frequency Goertzel Algorithm, by
    Eric Kiser, p. 22)

    good luck, post up if you get something working.

    rivas.ed, Oct 19, 2006
  14. David Ashley

    linnix Guest

    I just ran the test program on an 50MHz ARM Cortex (LM3S811). It takes
    about 10K bytes of code including floating points and complete in
    approx 20msec. It is certainly doable with a decent micro. I would
    not spent too much time trying to convert it to integer.

    Test case:

    R=8000Hz F=941Hz N=200
    linnix, Oct 19, 2006
  15. David Ashley

    David Ashley Guest

    Well it's a bit more complicated, I need to determine signal presence of
    almost 100 different frequencies, all at the same time, not just one.
    So I think integer arithmetic is in order...

    David Ashley, Oct 20, 2006
  16. David Ashley

    linnix Guest

    More like 40mesc.
    Within what time frame? What Sampling rates and processing bins? For
    example, the 50MHz ARM can process a 10Khz signals in 3 to 4 seconds.
    Of course, you can hook-up 100 of them to get results in 40 msec
    If you really need it.
    linnix, Oct 20, 2006
  17. David Ashley

    David Ashley Guest

    Actually now that I think about it I can probably get by with
    looking at just 24 frequencies at a time. But I need to know
    about 10 times per second whether each frequency is present
    in the signal.

    David Ashley, Oct 20, 2006
  18. For touch-tone you want 8 frequencies, updated in real time. For 200 samples
    you've got 25 ms for all eight.

    That is abysmal, 0.040 sec * 50 MHz / 200 data points = 10000 cycles per
    data point! The algorithm requires an add, a subract and a multiply per
    sample. Even for software FP thats aweful.
    If you have to go to integer, which I think you must in this case, then even
    a 32.32 fix-point solution would work well on a ARM. A 16.16 fix-point might
    be quicker but you'd need to analyse the rounding errors. 100
    cycles/sample/freq, absolute tops.

    The problem I see is that if you have 100 frequencies and that is much
    smaller then the FFT then you much be using lots of samples.

    Peter Dickerson, Oct 20, 2006
  19. David Ashley

    linnix Guest

    Yes, you are right. This is not optimized. I will take the cos() out
    of the loop and redo it for 24 frequencies, as required by the OP.
    Anyone want to post a integer version?
    linnix, Oct 20, 2006
  20. David Ashley

    linnix Guest

    It would need approx. 120MHz for floating points and 80MHz for
    integers. Can you sample a subset and do the rest if necessary. For
    DTMF, you only need to decode 8 for first harmonics and another 8 for
    second harmonics (to confirm pure tones).
    linnix, Oct 20, 2006
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