[GPS_Standard] Converting sample frequency to MHZ

[Dave Platt]

On 07/13/2015 02:12 PM, Dimitri.p wrote:
> Montrol will display and log the Current frequency in hex, but what 'd
> like to do is have mental fun with the actual frequency in MHz. I
> converted the hex to decimal but have trouble with the "decimal sample
> frequency".
> How can I convert the sample frequency of 26631 to MHz?

Well, you'll have to work back (mathematically) from the meaning of
this field.

It turns out (due to "the nature of the beast") that there's no
completely unambiguous mapping of "this value to a frequency",
since the value being shown is the result of a modulus operation.
However, as long as your oscillator is reasonably close to the
correct speed, there's a mapping that you can count on fairly
well.

The value that you see here (call it X) is equal to:

  ((the frequency measured in Hz) * 16) modulo 65536

So, if your frequency is dead-on (10,000,000.00 Hz), the
value you see will be 160,000,000 mod 65536, or 26624.

To a reasonable first approximation, you can figure that
every value of 1 different between the value you see, and
26624, means that your oscillator is off by 1/16 cycle
out of 10 million, or 1/16 Hz.

26631 is 7 greater than 26624, so your oscillator is running
about 7/16 Hz fast, or at around 10000000.4375 Hz.

Hence, the frequency you would want to display ("purely for
entertainment purposes) would be

	10000000 + (X - 26624) / 16

It isn't really meaningful to write out that many digits of
precision on the basis of just one sampling period, though...
precision does not imply accuracy (as a high school teacher
of mine would have pointed out, when he took off points on the
test for anybody who provided an answer to more degrees of precision
than were present in the numbers given as inputs on the problem).