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Entry  Thu Sep 17 19:58:06 2015, gautam, Summary, Computer Scripts / Programs, Frequency counting algorithm 
    Reply  Mon Sep 21 18:31:06 2015, gautam, Summary, Computer Scripts / Programs, Frequency counting algorithm 6x
       Reply  Mon Sep 21 23:18:55 2015, ericq, Summary, Computer Scripts / Programs, Frequency counting algorithm 
          Reply  Tue Sep 22 02:11:17 2015, rana, Summary, Computer Scripts / Programs, Frequency counting algorithm 
Message ID: 11628     Entry time: Mon Sep 21 18:31:06 2015     In reply to: 11615     Reply to this: 11629
Author: gautam 
Type: Summary 
Category: Computer Scripts / Programs 
Subject: Frequency counting algorithm 

I have been working on setting up a frequency counting module that can give us a readout of the beat frequency, divided by a factor of 2^14 using the Wenzel frequency dividers as described here. This is a summary of what I have thus far.

The algorithm, and simulink model

The basic idea is to pass the digitized signal through a Schmitt trigger (existing RCG module), which provides some noise immunity, and should in theory output a clean square wave with the same frequency as the input. The output of the Schmitt trigger module is either 0 (for input < lower threshold value) and 1 (for input greater than the high threshold value). By differencing this between successive samples, we can detect a "zero-crossing", and by measuring the time interval between successive zero crossings, we can take the reciprocal to get the frequency. The last bit of this operation (i.e. measuring the interval) is done using a piece of custom C code. Initially, I was trying to use the part "GPS" from CDS_PARTS to get the current GPS time and hence measure intervals between successive zero-crossings, but this didn't work out because the output of GPS is in seconds, and that doesn't give me the required precision to count frequency. I tried implementing some more precision timing using the clock_gettime() function, which is capable of giving nanosecond precision, but this didn't work for me. So I am now using a more crude way of measuring the interval, by using a counter variable that is incremented each time a zero-crossing is NOT detected, and then converting this to time using the FE_RATE macro (=16384). In any case, the ADC sampling rate limits the resolution of frequency counting using zero-crossing detection (more on this later). Attachment 1 shows the SIMULINK block diagram for this entire procedure.

Testing the model

I implemented all of this on c1tst, and followed the steps listed here to get the model up and running. I then used one of the DB37 breakout boards to send a signal to the ADC using the DS345 function generator. Attachment 2 shows some diagnostic plots - input signal was a 2.5Vpp (chosen to match the output from the Wenzel dividers) square wave at 2kHz:

  • Bottom left: digitized version of the input signal - I used this to set the upper and lower thresholds on the Schmitt trigger at +1000 counts and -1000 counts respectively.
  • Top left: Schmitt trigger output (red trace) and the difference between successive samples of the Schmitt trigger output (blue trace - this variable is used to detect a zero crossing)
  • Top right: Counter variable used to measure intervals between successive zero crossings, and hence, the frequency. The frequency output is held until the next zero crossing is detected, at which time counter is reset
  • Bottom right: frequency output in Hz.

The right column pointed me to the limitations of frequency counting using this method - even though the input frequency was constant (2kHz), the counter variable, and hence the frequency readout, was neither accurate nor precise. But this was to be expected given the limitations imposed by ADC sampling? We only get information of the state of the input signal once within each sampling interval, and hence, we cannot know if a zero crossing has occurred until the next sampling interval. Moreover, we can only count frequency in discrete steps. In attachments 3 and 4, I've plotted these discrete frequencies which can be measured - the error bars indicate the error in the frequency readout if the counter variable is 1 more or less than the "true" value - this can (and does) happen if the high and low times of the Schmitt trigger are not equal over time (see top left plot in Attachment 2, its not very obvious, but all the "low" times are not equal, and so, the interval between detected zero crossings is not equal). This becomes a problem for small values of the counter variable, i.e. at high input frequencies. I was having a look at the elogs Aidan wrote some years ago for a different digital frequency counting approach, and I guess the conclusion there was similar - for high input frequencies, the error is large. 

I further did two frequency sweeps using the DS345, to see if I could recover this in the frequency readout. Attachments 5 and 6 show the results of these sweeps. For low frequencies, i.e. 100-500 Hz, the jitter in the readout is small (though this will be multiplied by a factor of 2^14), but by the time the input frequency gets up to 2kHz, the jitter in the readout is pretty bad (and gets worse for even higher frequencies.

Bottom line

Some refinements can be made to the algorithm, perhaps by introducing some averaging (i.e. not reading out frequency for every pair of zero crossings, but every 5) which may improve the jitter in the readout, but I would think that the current approach is not very useful above 2kHz (corresponding to ~30MHz of pre-divider frequency), because of the limitations shown in attachments 3 and 4. 

Attachment 1: Simulink_model.pdf  81 kB  | Show | Hide all | Show all
Attachment 2: diagnostic_plots.pdf  9 kB  | Hide | Hide all | Show all
diagnostic_plots.pdf
Attachment 3: Error_high_frequency.pdf  43 kB  | Hide | Hide all | Show all
Error_high_frequency.pdf
Attachment 4: Error_low_frequency.pdf  47 kB  | Show | Hide all | Show all
Attachment 5: Frequency_sweep_100_500_Hz.pdf  8 kB  | Hide | Hide all | Show all
Frequency_sweep_100_500_Hz.pdf
Attachment 6: Frequency_sweep_100_2000_Hz.pdf  9 kB  | Show | Hide all | Show all
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