Symmetry in ASK

The spectrum of an ASK signal can easily be determined if the spectrum of the baseband data symbol stream is known, by viewing the ASK modulation process as a mixing or multiplication of the baseband symbol stream with the carrier component.
If we consider for the moment a single frequency component, cos wmt, from within the baseband spectrum, and perform the mathematical multiplication with the carrier, cos wct, the modulated signal becomes:

cos wmt x cos wct = 0.5 cos (wc – wm)t + 0.5 cos (wc + wm)t

The modulated spectrum for this sample component becomes two identical components spaced symmetrically either side of the carrier frequency.