oyvdahl
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Low order, flat response IIR filters (Bessel, Butterworth) have the smallest group delay for a given cut-off frequency. Obviously, the group delay depends also on the cut-off frequency (tg ~ 1/fc).
Your signal has essentially just a sinusoidal component of 1 Hz frequency.What I am trying to do is to measure the position of a pendulum using a radar and visualize this position on my computer. I want the visualization to look as "real-time" as possible.
Yes, for a given form of a low-pass filter.zorro: Are you saying that if I increase my cut-off frequency, the group-delay becomes smaller?
Hi oyvdahl,
Your signal has essentially just a sinusoidal component of 1 Hz frequency.
In that case, you are interested in phase delay rather than in group delay.
I suggest you to use a second-order passband filter (simple resonator) centered at the pendulum frequency (1 Hz). At the resonant frequency, the phase delay is 0 (input and output are exactly in phase).
Interestingly, tuning the frequency of the resonator (Fo) you can adjust the phase delay: the delay is positive if the signal frequency is higher than Fo, and negative at frequencies below Fo. (Note: that does not mean that the filter "predicts future", because that works in that way only for sinusoids.) The amplitude gain is maximum at Fo.
In that way, it is possible to compensate delays in other parts of the system (sampling, processing, etc.) adjusting Fo of the filter.
The Q of the filter should not be very high. Otherwise, it would be too selective.
Yes, for a given form of a low-pass filter.
Best regards
Z
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