When emitted an AM signal has two symmetric sidebands. A mirror placed at the carrier frequency would produce a mirror image of one sideband that is identical to the other sideband. That is seldomly seen on the spectrum display - when arriving at my antenna the signal is distorted by multi path propagation.

It is obvious from the graphs below that the audio quality of the signal extracted from shortwave AM signals can be greatly improved by signal processing. The multi path propagation acts like a filter that is inserted in the path between the transmitter and the receiver. There is enough information to extract both the amplitude and the phase response of this filter so one can add a digital filter with the inverse response that will restore the transmitted signal at all frequencies where S/N is still good enough.

The audio signal is best recovered as the S/N weighted average of the two signals recovered indepently from the two sidebands. Since S/N varies with frequency the sidebands have to be split into narrow enough sub bands so S/N is constant within each sub band.