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?