GPS-X Technical Reference

341 Tools Object
LOW-PASS FILTERING
The lowpass model can be used for analog or digital filtering, or a combination of both. The input
signal is fed to a first-order analog filter, a first-order digital filter, and a zero-order sample-andhold.
Any of these components may be used or bypassed. This is done by setting the filter type as
Analog, Digital, or Analog+Digital, and by setting sample and hold to either ON or OFF.
When the filter type is set to OFF, both filters are bypassed and the final output is either the
input signal or the sampled input signal, depending on the state of the sample and hold setting. A
signal flow diagram is shown in Figure 12-4. In this figure, the switches are set for a digital filter
with sampling.
First-order linear filters have one tuning parameter, the cutoff frequency ωc, which corresponds
to the corner frequency, i.e. the reciprocal of the filter time constant. The amplitude ratio of a
first-order system at the corner frequency is 1/√2, with corresponding phase lag φ=45 degrees’
With u(t) and y(t) representing the input and output of a first-order filter respectively, the filter
models are:
Analog:
Equation 12.8
Digital:
Equation 12.9
Figure 12-4 – Signal Flow Diagram for the lowpass Model
GPS-X Technical Reference