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AM is not known as simply double sideband. It is ONLY if BOTH sidebands and a full carrier are used. Some older radios did indeed use a carrier and only one sideband, usually USB, for transmitting AM. Since both sidebands are mirror images of each other only one is needed as long as the carrier is present.



In some cases, it may be desirable to maintain some degree of compatibility with simple AM receivers, while still reducing the signal's bandwidth. This can be accomplished by transmitting single-sideband with a normal or slightly reduced carrier. This mode is called compatible (or full carrier) SSB or Amplitude Modulation Equivalent (AME). In typical AME systems, harmonic distortion can reach 25% and intermodulation distortion can be much higher than normal, but minimizing distortion in receivers with envelope detectors is generally considered less important than allowing them to produce intelligible audio.



https://en.wikipedia.org/wiki/Single-sideband_modulation#Full.2C_reduced.2C_and_suppressed_carrier_SSB