# [ntp:questions] Kernel PLL, microkernel and the simulator.

David L. Mills mills at udel.edu
Wed Jul 23 17:30:00 UTC 2008

```David,

You quote the sampling theorem, which is a little more powerful than
Nyquist. However, you are correct in that the NTP filter is not
brick-wall. To compensate for that, the minimum sampling rate is at
least twice the Nyquist rate. Having said all that, the proof is in the
very many simulation runs with the actual code, which confirms the
expected risetime and overshoot.

Dave

David Woolley wrote:
> blu wrote:
>
>>
>> Okay, so how is the bandwidth equal to the inverse TC, and is that the
>> TC as in 3 or as in 2^3=7? I don't understand the meaning of the term
>
>
> The time constant as linear time, i.e. 8.
>
>> bandwidth in this context. And when you say that it works even if you
>
>
> ntpd implements a phase locked loop in software.  Phase locked loops
> measure a phase error, low pass filter that measurement, and feed it
> back as a frequency correction.  The bandwidth is that of the low pass
> filter and it is a fairly fundamental consequence of definition of
> frequency that it is inversely proportional to the length of the
> (significant part of the the) impulse response, i.e. the time constant.
>
>> only use every seventh sample, is that even if the sample is seven
>> poll intervals old every time?
>
>
> Where the reason is actually slightly flawed is that Nyquist says that
> you can accurately reproduce a signal which is hard band limited, but
> that assumes you know the sampling points.  In any case, the error
> signal is not limited to the bandwidth and the low pass filter is far
> from a brick wall filter, meaning there will be aliasing effects, which
> will cause a sensitivity on sample rate if you only sample at only twice
> the filter nose bandwidth.
>
> I'm not 100% sure, but I don't think that the ntpd processing
> compensates fully for the positions of the samples.

```