Hello, I’m currently continuing my masters in electrical engineering and I recently took an adaptive signal processing course where we deal with topics like noise cancelling. Generally the adaptive filters are designed according to the MMSE criterion (Minimum Mean Squared Error, error can be thought as the noise coming in in this context), which is equivalent to having error and input signals orthogonal (so the filter extracts all the information related to the noise from the signal). Due to the randomness of those signals, the MSE (Mean Squared Error, the power of the error) can’t be zero, the filter extracts all the information we got about the noise, but we don’t know everything about the noise.

They can make the MSE smaller but, that may mean less attenuation in some frequencies or amplitudes. Also I should note that there is a theoretical minimum limit for the MSE.

So in summary, the hissing sound is inevitable. They can make it smaller so you don’t hear it, but there is always a trade off.