Methods and systems for amplitude modulation in a parametric speaker system are provided that perform truncated double sideband (TDSB) frequency modulation of audio signal in which most of the processing is performed in the frequency domain, thus permitting use of fast processing techniques for amplitude modulation (AM) and filtering and reducing computation cost over time domain processing. A maximum envelope value of the time domain audio signal may be to the carrier signal in the frequency domain that avoids emitting the carrier signal when the input signal level is low or mute. The application of the envelope value may be smoothed to reduce discontinuity at input block boundaries.