Sideband frequencies in radio are produced when a carrier frequency is:

Sideband frequencies in radio communication are generated during the modulation process of a carrier frequency. When a carrier wave is modulated, it means that the amplitude, frequency, or phase of the wave is varied in accordance with the information signal (such as audio or video data) that is being transmitted.

Through modulation, new frequencies are created that are positioned around the original carrier frequency. These new frequencies are referred to as sidebands: the upper sideband (USB) and the lower sideband (LSB). The carrier frequency remains at its original value, but the modulation process produces frequencies that are offset from this carrier frequency. In amplitude modulation (AM) for instance, the sidebands contain the actual information signal, which is not present in the carrier wave alone.

While amplification, demodulation, or filtering might play roles in the overall process of transmission and reception in radio systems, they do not fundamentally create sideband frequencies. Amplification increases signal strength without altering frequency content. Demodulation is the process of extracting the information from the modulated signal, and filtering involves removing unwanted frequencies or noise from a signal. Therefore, the act of modulation is what directly results in the formation of sideband frequencies around a carrier wave.