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Say we have a sampled signal for which the inputs can be out of range. For instance, say a sampled sensor has a range of 0 to 1, and is presented with a time-varying stimulus where a peak occurs with max amplitude 1.2. In the data we would see a saturated or clipped peak.

What are some of the approaches to making estimates about the peak value?

How good of an estimate can be made by interpolating the value of the peak from the slope on either side of the clipping? This becomes difficult because if analysis relies on the dataset being at a specific sample rate, interpolation will result in upsampling, unless interpolation is done and the new signal is downsampled with an offset so that the peak becomes a data point. I'm sure this isn't an ideal approach.

What about calculations in the frequency domain?

Has anyone ever been presented with this problem?

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Depends on the amount of clipping and what other information about the signal you have. It's pretty easy to detect clipping (wave form constant at +xmax or -xmax). Once a region has been found you can try to replace the clipped region with an interpolation from the non-clipped regions around this. The best interpolation scheme will depend on what else you know about the signal. You can try polynomial expansions, Taylor series, Frequency domain interpolation, etc.

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