MATLAB: 1)Amplitude modulation. 2) Negative amplitudes in the signal?

communication

      I studied about AM before 6 months, I believe. When I studied that I got some doubt. How do you say AM takes twice the bandwidth of the signal bandwidth. I tried everything to understand that but I couldn't. I have started using MATLAB about 2 or 3 ago and now I could understand many things. Now there is another doubt that I have.
Today I did this. 
1) I recorded my voice using wavrecord. It is in the variable y.
2) Then I plotted y.
      I later found that the variable 'y' has negative amplitudes too.
How do you get negative amplitudes?( I never knew that before!) 
Also I want to understand my first question,(i.e. AM has twice the BW of the signal BW) through simulation. If you write the code and post it, I would be much obliged.
Thanks in advance and I thank MATLAB for helping me understand the concepts.

Best Answer

The Fourier transform of any real-valued signal is conjugate symmetric, in other words, the Fourier transform at -f is the complex conjugate of the Fourier transform at +f. If you have a signal that is zero for all negative frequencies in the Fourier domain that means either you have a signal that is not real-valued, or you have a signal that is identically zero.
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