COMMAND RANGING & TELEMETRY UNIT CORTEX
CRT QUANTUM USER'S MANUAL
Ref. DTU 100042
Is.Rev. 5.17
Date: Dec.
03, 2021Sept. 30, 2021
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It cannot be duplicated or distributed without expressed written consent.
3.3.4.3. Interpolation Process
In some cases, when the sampling rate and the generation rate are asynchronous, a linear interpolation is
applied to provide the accumulated phases at the required sampling frequency.
Such an interpolation generates an error. Let’s call
the interpolated phase,
the phase error, T the
10-ms period and the time between 0 and T when the phase is interpolated.
The Taylor expression of the phase at is :
where D(t) is the input Doppler and R2(t) the rest such that (Lagrange overestimation):
So
For instance, a Doppler rate of 1000 Hz/s with a second-order Doppler variation of 10 Hz.s
-2
gives a phase error
lower than (0.0125 + 3.33x10
-6
) cycle.
In most cases, user would not use cranky values for the sampling rate. Thus, no interpolation would be applied,
because accumulated phase is generated synchronously with the sampling rate dates.
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