# What's the maximum allowable amplitude modulation frequency for a given carrier frequency?

I'm currently studying wavelets and had an interesting thought experiment: If you were to calculate the wavelet transform of a signal using a wavelet of a fixed frequency, you would get time varying wavelet coefficient. Say this fixed frequency wavelet is 1000Hz. You essentially yield a signal that shows how a 1000Hz frequency component varies with time.

If you were to run a Fourier transform on this new signal, what is the maximum frequency content you could find in it?

My intuition says that there is some upper limit to this (i.e. you couldn't find 10kHz frequency content), but I'm curious if there is a way to prove this limit.

After thinking about it some more, it seems like what I'm asking is: what the maximum modulation frequency that can be encoder into a carrier frequency?