Why do we say that a good time response means a bad frequency response?

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    $\begingroup$ Hi! Can you please try to explain the terms "good" and "bad"? Tell us a few things about what kind of answer you're looking for or give an example of "good" and "bad" time and frequency response, respectively. $\endgroup$ – GKH Mar 8 '20 at 18:18
  • $\begingroup$ Hi! Welcome here. What does "good" and "bad" mean to you? My bet is that whoever said that meant "concentrated" or something for "good", but that's not inherently a given. However, even assuming that, this is overly broad. You've ever heard of the Heisenberg-Gabor limit? (same thing exists under many names) $\endgroup$ – Marcus Müller Mar 8 '20 at 18:20
  • $\begingroup$ For example, a moving average digital filter is said to be a good smoother (time domain) but a bad low pass filter (frequency domain). The way I see it by smoothering the signal I have already achieved a low pass filtering. $\endgroup$ – Manzillo Mar 8 '20 at 22:34

These terms refer to the general duality properties of these two domains. It should be obvious that higher frequency components mean faster changes in time and lower rise/fall times. In most natural systems, some of these fundamental properties oppose each other: Shorter rise time means more overshoot and higher settling times and vice versa; lower overshoot means a higher settling time as well as a higher damping factor resulting in a higher rise time. In general, achieving better frequency domain properties (in the sense of time domain duals) means worsening other time domain properties. Apart from that, in specific applications such as digital transmission, cleaner pulses (lower rise/fall time) means broader spectrum and frequency content, which is undesirable in the sense of bandwidth efficiency. But again there is no unique answer to what you have asked. Each application must consider its own tradeoffs.


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