PDM representation by pulse density
Pulse Density Modulation (PDM) represents an analog signal with a one-bit digital stream. In the unipolar 0/1 mapping used here, information is carried by pulse density. PAM assigns the signal value to pulse amplitude, while PWM assigns it to pulse duration. In the one-bit stream described here, the clock fixes the pulse period and levels: PWM changes the high-state duration in each period, while PDM changes the number and spacing of '1' bits in an observation window. The clock fixes the time scale, and the observation interval determines how density is estimated: an isolated bit has no amplitude value on its own.
For a binary stream observed over a finite window, the fraction of '1' bits tracks the normalized input level. A higher fraction represents a higher value, while a lower fraction represents a lower value. In PDM:
- A higher amplitude in the original analog signal corresponds to a higher density of '1' bits in the digital stream.
- A lower amplitude corresponds to a lower density of '1' bits (or a higher density of '0' bits).
PDM stream for a sinusoidal input
The relationship between the analog signal and the PDM bitstream is shown for a sinusoidal input. The diagram pairs the analog sine wave with the PDM stream generated from it.
The diagram illustrates three relationships:
- At the peakof the sine wave (highest positive amplitude), the PDM stream contains a high concentration of '1's.
- In the troughof the sine wave (most negative amplitude), the stream is dominated by '0's.
- With a symmetric one-bit mapping, where the sine wave crosses the zero point, the density of '1's and '0's is roughly equal. The average of the PDM stream over a suitable time window corresponds to the analog amplitude in that window.
Generating a PDM stream with Sigma-Delta () modulation
A one-bit Sigma-Delta () modulator can produce a PDM stream directly. Many digital MEMS microphones expose this high-rate stream before a decimation filter converts it to a lower-rate audio representation. The decimation filter sets the output sample rate and limits the retained signal band.
A Sigma-Delta modulator uses a feedback loop that compares the analog input with an estimate derived from its output and emits a '1' or '0' at an oversampling clock. The resulting one-bit stream can serve as a PDM signal. The "Sigma" part refers to accumulation or integration of the error, while "Delta" refers to the difference operation in the feedback loop. The 1-bit that generates the output bit.
PDM reconstruction with a low-pass filter
Recovering the original analog signal from a high-frequency PDM stream requires a .
The filter attenuates the rapid clock-rate transitions and preserves their average over the selected bandwidth. Under the mapping described above, local density of '1's corresponds to the original signal's amplitude, so this filtering process reconstructs the band-limited analog waveform.
PDM applications
PDM is used in high-rate digital audio interfaces and in systems that apply digital filtering to a one-bit stream.
- Digital audio: The Super Audio CD (SACD) format uses Direct Stream Digital (DSD), a one-bit, high-rate sigma-delta representation whose information is carried by pulse density. Noise shaping shifts quantization noise toward frequencies above the audio band, where reconstruction filtering attenuates it.
- Digital MEMS microphones: Many digital microphones based on micro-electromechanical systems contain a built-in Sigma-Delta modulator and output PDM directly. A digital stream can reduce sensitivity to analog interference along the board connection, while the receiver still needs clock and data integrity.