This is not possible, if you only have the given information.
The signal could be the sea-level at a specific location. If you signal is the height of the tide, the high-frequency waves are the noise, with a specific distribution. But if you want to measure the height of waves, the regular low-frequency tides are the noise. The pure signal alone does not allow to identify what you consider as noise.
You have to define, what is the noise and what is the wanted signal. Unfortunately in most real cases you have to assume the nature of the noise, e.g. the amplitude and frequency distribution, at first to be able to distinguish it from the usable signal. This means, that having a signal does not allow to determine the type of the noise without further knowledge or assumptions.