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I have been told that the fourier transform of a function tells us the minimum components required to support that function and that a real pulse may have extra frequencies, but not too few frequencies.

I don't understand why fourier transform only gives the min possible frequencies. Actually, I haven't seen the math. So I'd be glad some kind person could please give an intuition for what actually goes in a fourier transform in relation to what I have been told.

Just one other quick question:

A fourier transform can contain negative amplitude terms. What is that supposed to mean in a physical sense? It can also contain -ve frequency components. Is that physical?