So one technique in signal processing and comm. technology is to extract the analytic signal of a real-valued signal. And particularly they often extract the magnitude of the analytic signal in order to get the envelope of the signal.
However, several sources claim that this method works well only for band-limited signals. Why is this?
Given that the concept of analytic function should apply to all signals, then why does it work only for band-limited signals?
Ref.
A function that is not band limited may not be smooth enough to be possible to make complex analytic. The Hilbert transform tries to find the imaginary part of a function so that the Cauchy Riemann equations are fulfilled - in other words : "extend" it to become complex analytic. But not all real valued functions are so nicely behaving so that is possible to do.