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The advantage of pulse frequency modulation is better immunity to noise interference than PAM.
The different names for the modulation method are the result of pulse frequency modulation by different electronic implementations, which all produce similar transmitted waveforms.
Delta-sigma modulation converts the analog voltage into a pulse frequency and is alternatively known as Pulse Density modulation or Pulse Frequency modulation.
These amplifiers use pulse width modulation, pulse density modulation (sometimes referred to as pulse frequency modulation) or a more advanced form of modulation such as Delta-sigma modulation (for example, in the Analog Devices AD1990 class-D audio power amplifier).