In a typical single-sideband transmitter, what is the purpose of the filter that follows the balanced modulator?

A balanced modulator takes an audio signal and an RF carrier and produces a double-sideband suppressed-carrier (DSB-SC) signal. While it successfully suppresses the carrier, both the upper and lower sidebands still remain in the output. To generate a true single-sideband (SSB) signal, one of these sidebands must be eliminated. The filter immediately following the balanced modulator is a highly selective bandpass filter designed specifically to pass the desired sideband and block or remove the unwanted sideband. Common distractors suggest the filter suppresses the RF carrier, but that is incorrect because the balanced modulator has already accomplished that task. The filter's sole job is to strip away the extra sideband before the signal is amplified and transmitted.