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For what type of signals group delay of a filter should be taken into account?

Here is an example showing the effect of group delay for different type of filters. And here are some conclusions from the site: Bessel: Has essentially zero overshoot. That was one of the design ...
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Difficulty understanding group delay concept

I’m having difficulty understanding the concept of group delay. The mathematical definition is not difficult, since it says it is the negative derivative of Bode plot’s phase curve wrt frequency. Most ...