Pulse-density modulation

Pulse-density modulation, or PDM, is a form of modulation used to represent an analog signal with a binary signal. In a PDM signal, specific amplitude values are not encoded into codewords of pulses of different weight as they would be in pulse-code modulation (PCM); rather, the relative density of the pulses corresponds to the analog signal's amplitude. The output of a 1-bit DAC is the same as the PDM encoding of the signal. In a pulse-density modulation bitstream, a 1 corresponds to a pulse of positive polarity (+A), and a 0 corresponds to a pulse of negative polarity (−A). Mathematically, this can be represented as where x[n] is the bipolar bitstream (either −A or +A), and a[n] is the corresponding binary bitstream (either 0 or 1). A run consisting of all 1s would correspond to the maximum (positive) amplitude value, all 0s would correspond to the minimum (negative) amplitude value, and alternating 1s and 0s would correspond to a zero amplitude value. The continuous amplitude waveform is recovered by low-pass filtering the bipolar PDM bitstream. A single period of the trigonometric sine function, sampled 100 times and represented as a PDM bitstream, is: 0101011011110111111111111111111111011111101101101010100100100000010000000000000000000001000010010101 Two periods of a higher frequency sine wave would appear as: 0101101111111111111101101010010000000000000100010011011101111111111111011010100100000000000000100101 In pulse-density modulation, a high density of 1s occurs at the peaks of the sine wave, while a low density of 1s occurs at the troughs of the sine wave. Delta-sigma modulation A PDM bitstream is encoded from an analog signal through the process of a 1-bit delta-sigma modulation. This process uses a one-bit quantizer that produces either a 1 or 0 depending on the amplitude of the analog signal. A 1 or 0 corresponds to a signal that is all the way up or all the way down, respectively. Because in the real world, analog signals are rarely all the way in one direction, there is a quantization error, the difference between the 1 or 0 and the actual amplitude it represents.