Hi all,

I had been searching the 'net for simple digital frequency
discriminator
algorithms (fm detection, eg for SSTV etc) but have not really found
any
suitable info. In the mean time though, I figured out what I think is a
simple solution to this problem and tried it, using my computer's sound
system to digitize a sinewave signal from my FT847 rig (tuned to a MW
BC
station in CW mode and using the narrowest filters).

The results were mixed, with an accuracy of about 1% in many readings
but with a small portion of them having large errors 50%. The errors
seemed to be spaced at 1/4 of an audio cycle and near peaks and zero's.
But before I speculate on possible causes, I would like to take the
liberty to describe this algorithm so that experienced DSP boffins
might
first judge the viability and/or correctnes of it.

In a stream of digitized samples of a sine wave, the value s of a
sample
is given by s = V * sin(F) where V is the peak amplitude and F the
phase
of the sine wave at the moment the sample was taken. If we take three
consecutive samples, s0, s1, s2, we can form the following set of
simultaneous equations (by expanding sin(F+dF) & sin(F-dF)).

1. s0 = V*sin(F-dF) = V*{sin(F)*cos(dF)-cos(F)*sin(dF)}
2. s1 = V*sin(F)
3. s2 = V*sin(F+df) = V*{sin(F)*cos(dF)+cos(F)*sin(dF)}

where dF is the phase difference between successive samples.

By adding 1. and 3. we have:

4. s0+s2 = V*2*sin(F)*cos(dF)

By substituting sin(F) from 2. we have:

5. s0+s2 = V*2*(s1/V)*cos(dF)

So finally solving 5. for dF we have:

6. dF = arc cos{(s0+s2)/(2*s1)}

The frequency f of the sampled signal can then be estimated by:

7. f = (df/2pi)*S or f = S*arc cos{(s0+s2)/(2*s1)}/2pi (2pi=2*pi)

I tried this formula by feeding it with calculated samples and it
worked
fine. In practice, the expected problems I had were division by zero
when s1 = 0 and failure of the acos() C function when (s0+s2)/2s1 1.
But there were inaccuracies in he results as I mentioned near the peaks
and zeros since it seems errors in sampling by the dsp distorted the
relationship between consecutive samples.

I am using Linux and an AC97 type on-board sound system and I already
know there are some bugs in the ALSA (the Linux sound systems project)
drivers. This is especially obvious when sampling at a non-native DSP
rate (other than 48 Khz / 16-bit linear) where the sound driver has to
resample the output.

I would be greatful for any input on the "legitimacy" of the above
derived formula and/or its weak points, so that I can furher study the
output of the DSP for possible errors (not very easy ;-)).

My apologies for a longish and/or possibly boring article!

73's de "Nick" 5B4AZ http://5b4az.mattsnetwork.co.uk/

neok wrote:
Hi all,

I had been searching the 'net for simple digital frequency
discriminator

Very sorry guys, posted to wrong group :-(