Johnny was a Chemist’s Son,
but Johnny is No More.
What Johnny thought was H2O,
was H2SO4!
Seeing this sum and knowing the carrier frequency, one might wonder: can’t we make do with just one term of the sum α + β, and ignore α - β ? Indeed, if one applies a filter to cut the frequencies less than the carrier from the transmitted signal, one can save half the bandwidth and still recover the signal. This trick is known as the Upper Side Band, and it used for the actual digital radio transmissions.