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I have a bandwidth-unlimited periodic signal. All I know about this signal is its finite peak amplitude. I pass this signal through a known and simple low-pass filter (gain = 1 within the pass band; say 2nd-order Butterworth or Bessel type filter). I am interested to estimate the maximum change rate of the resulting signal (that is, absolute maximum / minimum of the derivation of the resulting signal) for the worst case.

1. Does the ‘worst case’ (that is the case where the resulting signal changes most rapidly) happens if (and only if?) the original signal has peak-to-peak discontinuities? For example, when the original signal is a square-wave signal.

2. What is a good estimation for the maximum change rate of the resulting signal?

 

At the moment I naively estimate the maximum change rate by finding the maximal A * Gn * wn; for an index ‘n’. Where:
- A is the amplitude of the original input signal;
- Gn is the filter gain at frequency wn;
- wn is the frequency (rad/s) of the n-th component of the signal (think Fourier series).

In practice, for wn I use a frequency near the cut-off frequency of the filter, and Gn as 1. However I cannot even say if this estimation method is any good.... I have no much taste for overly complex estimators, but can you still propose something better?

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