Signal distortion under non-linear channel
I think this will help you: Think about how the &quot;frequency&quot; is given by the zero crossings of the waveform, and then ask if the transfer function you show (and for that matter even if it did have sharp corners and clipping), would that have any effect possibly on the zero-crossings? Can we determine the frequency completely and accurately from the zero crossings for a real waveform?
Also consider this: All noise can be decomposed into AM and PM components, meaning Amplitude modulation and Phase Modulation. (Frequency Modulation and Phase Modulation are similar: If you have FM then you have PM since they are related by an integral-- a change in phase over time is Frequency). So if you have a signal that has AM and FM components, and you hard limit it, you remove all the AM components and you would only be left with FM. Here is the thing to think about then: What if you have a FM signal and hard limit it (which is the sharp corners and clipping you mention)-- it would remove AM if it existed, but how would it effect the FM?
For more mathematical thoroughness, explore how ANY pattern that repeats in time over period T can exist in frequency only at frequency n/T for n as the set of all integers. Would the transfer function from x to y that you show possibly change T for any given waveform that repeats over T?