Signal strength at some fixed frequency

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...

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

Compute the correlation with a 440 Hz sine wave.

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.

Thanks-- Dave

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.

D.S.

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

gm

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

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 included.

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

-Dave

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 ?

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 :)

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

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.

-Ed

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

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...

-Dave

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.

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.

-Dave

takes

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

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?

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).