Definition and Basic Principles of PDM

Mathematical Representation of PDM

Pulse Density Modulation (PDM) encodes an analog signal into a single-bit digital stream where the instantaneous signal amplitude is represented by the density of pulses over time. Unlike Pulse Width Modulation (PWM), which varies pulse duration at a fixed frequency, PDM maintains fixed pulse widths while modulating their occurrence rate. The output is a high-frequency binary sequence where the average value over a given time window corresponds to the input signal amplitude.

Here, y(t) is the PDM output, δ(t) is the Dirac delta function, T_s is the sampling interval, and ε_n represents quantization noise. The sgn function ensures binary output (1 or 0).

Delta-Sigma Modulation Core

PDM is fundamentally a 1-bit form of delta-sigma modulation. The process involves:

• Oversampling: Input signals are sampled at frequencies far exceeding the Nyquist rate (typically 64× or 128× the target bandwidth).
• Noise shaping: A feedback loop pushes quantization noise to higher frequencies, improving in-band signal-to-noise ratio (SNR).

where N is the number of bits and L is the modulator order.

Practical Implementation

Modern PDM systems leverage switched-capacitor circuits or digital FIR decimation filters to reconstruct the original signal. Key components include:

• A comparator for 1-bit quantization
• An integrator in the feedback path
• A clocked flip-flop to generate fixed-width pulses

Advantages Over PCM

PDM’s single-bit nature provides inherent advantages in:

• Clock jitter immunity: Pulse timing variations affect all pulses equally, canceling out in the averaged output.
• Simplified DAC design: Requires only a low-pass filter for reconstruction.
• High linearity: Avoids multi-bit DAC nonlinearities.

1.2 Comparison with Pulse Width Modulation (PWM)

Fundamental Differences in Modulation Techniques

Pulse Width Modulation (PWM) encodes analog signals by varying the duty cycle of a fixed-frequency square wave, where the pulse width is proportional to the instantaneous amplitude of the input signal. The output is characterized by:

where D(t) is the duty cycle, t_on is the active pulse duration, and T is the period of the carrier wave. In contrast, Pulse Density Modulation (PDM) uses a fixed pulse width but varies the density of pulses in time, with the number of pulses per unit time proportional to the signal amplitude. Mathematically, PDM can be expressed as:

where ρ(t) is the pulse density, N_p(t) is the number of pulses in a sampling interval, and T_s is the sampling period.

Spectral Characteristics and Noise Performance

PWM generates harmonic distortion at multiples of its carrier frequency, requiring steep analog filters for reconstruction. The baseband signal-to-noise ratio (SNR) for PWM is given by:

where A is the signal amplitude, B is the bandwidth, and N₀ is the noise spectral density. PDM, however, shapes quantization noise through oversampling and noise shaping, pushing noise energy to higher frequencies. Its SNR improves with oversampling ratio (OSR):

Implementation and Hardware Considerations

• PWM requires precise timing control and analog filtering, making it susceptible to clock jitter and electromagnetic interference (EMI) from high-frequency switching.
• PDM simplifies hardware by using 1-bit sigma-delta modulation, enabling direct interfacing with digital systems (e.g., MEMS microphones) without anti-aliasing filters.

Applications in Audio Systems

PWM dominates in power amplification (Class-D amplifiers) due to its efficient switching characteristics. PDM is preferred in high-resolution audio acquisition systems, where its noise shaping allows 24-bit resolution with 1-bit converters. Modern digital microphones (e.g., STMPE811) use PDM to achieve >100 dB dynamic range at sampling rates up to 4 MHz.

1.3 Mathematical Representation of PDM Signals

Pulse Density Modulation (PDM) is a time-encoded signal representation where the instantaneous amplitude of an analog signal is mapped to the density of pulses in a binary bitstream. Unlike Pulse Width Modulation (PWM), which varies pulse duration, PDM maintains fixed-width pulses while modulating their occurrence frequency.

Time-Domain Representation

A PDM signal s(t) can be modeled as a train of Dirac delta functions, weighted by the binary pulse density:

where b[n] ∈ {0,1} represents the binary pulse at the n-th sample instant, and T_s is the sampling period. The pulse density D(t) over a moving window of N samples relates to the input signal x(t) as:

assuming x(t) is normalized to the range [−1, 1]. The approximation error arises from quantization noise, which we will analyze in the frequency domain.

Frequency-Domain Analysis

Applying the Fourier transform to the PDM signal yields both the baseband audio spectrum and high-frequency quantization noise. The power spectral density (PSD) of s(t) decomposes into:

where X(f) is the desired audio spectrum and E(f) is the shaped quantization noise. For a first-order sigma-delta modulator, the noise transfer function (NTF) shapes E(f) as:

Here, Δ is the quantization step size (Δ = 2 for binary PDM), and f_s is the sampling frequency. The sin² term demonstrates high-pass noise shaping, pushing quantization noise away from the audio band.

Modulator Implementation

A first-order sigma-delta modulator generates PDM through the difference equation:

where u[n] is the integrator state and x[n] is the sampled input. This recursive structure creates the noise-shaping property essential for high-resolution audio encoding.

Signal-to-Noise Ratio (SNR)

The theoretical SNR for a PDM system with oversampling ratio OSR = f_s/(2f_B) (where f_B is the signal bandwidth) follows:

For binary PDM (L = 1 bit), this simplifies to 9.1 dB per doubling of OSR. Practical implementations often use higher-order modulators to achieve steeper noise shaping.

2.1 Advantages of PDM for Audio Signal Processing

High Noise Immunity and Robustness

Pulse Density Modulation (PDM) encodes analog audio signals into a single-bit digital stream, where the signal's amplitude is represented by the density of pulses. This approach inherently rejects common-mode noise due to its differential signaling nature. The quantization noise is shaped by oversampling and pushed into higher frequencies, allowing easy filtering with a low-pass decimation filter. Mathematically, the noise shaping function for a first-order delta-sigma modulator is:

where N(f) is the shaped noise, f_s is the sampling frequency, and Q_e(f) is the quantization error. The high-frequency noise can be attenuated effectively, improving the signal-to-noise ratio (SNR) in the audio band.

Simplified Analog-to-Digital Conversion

PDM eliminates the need for multi-bit analog-to-digital converters (ADCs), reducing circuit complexity. A single comparator and a feedback loop (delta-sigma architecture) suffice, making PDM ideal for integrated MEMS microphones and digital audio interfaces. The oversampling ratio (OSR) directly impacts resolution:

where N is the effective number of bits. For example, a 1-bit PDM stream with OSR=64 achieves ~12-bit resolution after decimation.

Low Latency and High Bandwidth

PDM’s single-bit nature allows high-speed serial transmission without parallel data alignment issues. This is critical for real-time audio processing in applications like beamforming and active noise cancellation. Modern inter-IC sound (I2S) interfaces support PDM at clock rates up to 3.072 MHz, enabling multi-channel audio with minimal delay.

Power Efficiency

Since PDM avoids linear amplifiers and multi-bit DACs, power consumption is significantly lower than pulse-code modulation (PCM). The switching activity scales with signal amplitude, reducing dynamic power in quiet passages. This efficiency makes PDM dominant in portable devices, where a typical MEMS microphone consumes <200 µA.

Compatibility with Digital Systems

PDM interfaces natively with digital signal processors (DSPs) and field-programmable gate arrays (FPGAs), bypassing analog signal conditioning. Decimation filters (e.g., Cascaded Integrator-Comb filters) can be implemented efficiently in hardware, leveraging parallel processing. The direct digital output also minimizes electromagnetic interference (EMI) from analog traces.

Applications in Modern Audio Systems

• MEMS Microphones: PDM’s simplicity enables tiny, low-cost digital microphones with high SNR (>65 dB).
• Digital Hearing Aids: The power efficiency and noise resilience are critical for battery-operated devices.
• Automotive Audio: PDM’s EMI robustness suits noisy environments like infotainment systems.

2.2 Common Use Cases in Digital Audio Systems

Pulse Density Modulation (PDM) is widely employed in digital audio systems due to its high signal-to-noise ratio (SNR), simplicity in hardware implementation, and compatibility with oversampling techniques. Below are key applications where PDM excels.

Microphone Interfaces

PDM is the dominant modulation scheme in digital microphones, particularly MEMS-based designs. Its single-bit output simplifies analog-to-digital conversion while maintaining high dynamic range. The PDM bitstream is typically generated at sampling rates between 1–3.2 MHz, leveraging noise shaping to push quantization noise beyond the audio band. A first-order sigma-delta modulator (ΔΣ) is commonly used, described by:

where x[n] is the input signal, y[n] the output bitstream, and e[n] the quantization error. The differential term e[n]−e[n−1] shapes the noise toward higher frequencies.

Digital-to-Analog Conversion (DAC)

High-end audio DACs often employ PDM internally before reconstruction filtering. The multibit DAC architecture converts the PDM stream into an analog signal through:

• Switched-capacitor networks that average the pulse density
• Current-steering circuits for low-distortion conversion

The output current I_out of a typical PDM DAC is proportional to the duty cycle:

where N_high is the number of '1's in a given window and N_total the total pulses.

Class-D Amplifiers

PDM is fundamental to Class-D audio amplifiers, where the input signal modulates the switching frequency of power MOSFETs. The amplifier’s efficiency (η) approaches 90% due to minimized resistive losses:

P_sw (switching losses) and P_cond (conduction losses) are reduced by operating the output stage in saturation. Modern implementations use closed-loop feedback to linearize the PDM-to-analog conversion.

Noise Shaping and Oversampling

PDM’s inherent noise shaping makes it ideal for oversampled systems. The SNR improvement (ΔSNR) for an N-th order modulator with oversampling ratio (OSR) follows:

For example, a second-order modulator with OSR=64 achieves ~105 dB SNR in the 20 kHz audio band. This principle is exploited in DSD (Direct Stream Digital) audio formats, where PDM operates at 2.8 MHz or 5.6 MHz sampling rates.

Embedded Audio Processing

Low-power microcontrollers leverage PDM for real-time audio due to minimal computational overhead. Decimation filters (e.g., CIC filters) downsample the PDM stream to PCM at manageable rates. The filter’s frequency response H(z) for a K-stage CIC is:

where R is the decimation ratio. This allows 16/24-bit PCM output from a 1-bit PDM input with efficient integer arithmetic.

2.3 PDM vs. PCM in Audio Quality and Bandwidth

Quantization Noise and Dynamic Range

Pulse Code Modulation (PCM) quantizes audio signals into discrete amplitude levels at fixed intervals, introducing quantization noise that scales with bit depth. For an N-bit PCM system, the signal-to-noise ratio (SNR) is given by:

In contrast, Pulse Density Modulation (PDM) trades amplitude resolution for temporal density, shaping quantization noise away from the baseband via oversampling. The noise transfer function (NTF) of a first-order PDM modulator is:

This high-pass characteristic pushes noise to higher frequencies, which can be filtered out, resulting in a dynamic range advantage at lower bit depths.

Bandwidth Efficiency and Oversampling

PDM achieves higher bandwidth efficiency by operating at ultra-high sample rates (typically 64× or 128× the Nyquist rate) with 1-bit resolution. The oversampling ratio (OSR) directly impacts the achievable SNR:

where L is the effective number of bits. For example, a 1-bit PDM stream at OSR=64 can achieve ~12-bit equivalent resolution in the audio band.

Practical Trade-offs in Audio Systems

• PCM Advantages: Lower computational complexity for decoding, native compatibility with DSP algorithms, and straightforward digital filtering.
• PDM Advantages: Reduced sensitivity to clock jitter, inherent anti-aliasing from noise shaping, and simplified analog front-end design (e.g., direct microphone interfacing).

Modern high-resolution audio codecs often combine both: using PDM for analog-to-digital conversion (ADC) followed by decimation to PCM for processing, leveraging the strengths of each method.

Real-World Performance Metrics

In measured implementations, 24-bit/192 kHz PCM typically achieves ~144 dB dynamic range, while 1-bit/3.072 MHz PDM (OSR=64) reaches ~120 dB. However, PDM's noise floor rises at higher frequencies due to its NTF, making it less ideal for ultrasonic applications unless higher-order modulators are employed.

where Δ is the quantization step, f_s the sample rate, and n the modulator order.

3.1 PDM Modulators and Demodulators

Modulator Architecture

A Pulse Density Modulation (PDM) modulator converts an analog signal into a single-bit digital stream where the average pulse density represents the signal amplitude. The core component is a 1-bit sigma-delta (ΣΔ) modulator, which consists of an integrator, a quantizer, and a feedback loop. The feedback ensures noise shaping, pushing quantization noise to higher frequencies.

Here, x[n] is the input sample, y[n] is the output bitstream, and a_k are feedback coefficients. The oversampling ratio (OSR) determines the modulator's noise-shaping efficiency, given by:

where f_s is the sampling frequency and f_B is the signal bandwidth.

Demodulation Techniques

PDM demodulation involves reconstructing the analog signal from the 1-bit stream. A low-pass filter (LPF) is the simplest demodulator, averaging the pulse density over a window. For higher precision, a decimating FIR filter followed by a sinc³ filter is common. The signal-to-noise ratio (SNR) of the demodulated output depends on the filter's stopband attenuation and the modulator's order.

Here, N is the number of bits (1 for PDM), and L is the modulator order.

Practical Implementations

In audio applications, PDM modulators are often integrated into MEMS microphones and digital amplifiers. For example, the ADMP521 MEMS microphone uses a 5th-order ΣΔ modulator with an OSR of 64. Demodulation is typically handled by dedicated hardware (e.g., STM32's DFSDM peripheral) or software-based decimation filters.

Key Design Trade-offs

• Modulator order vs. stability: Higher-order modulators improve SNR but risk instability without careful coefficient design.
• OSR vs. power: Increasing OSR reduces in-band noise but raises clocking power.
• Filter complexity vs. latency: Steeper filters improve SNR but introduce group delay.

Noise Shaping and Quantization Error

The modulator's noise transfer function (NTF) shapes quantization error away from the signal band. For an Lth-order modulator, the NTF is:

This high-pass characteristic suppresses noise in the audio band (0–20 kHz) while allowing higher-frequency noise to be filtered out during demodulation.

3.2 Noise Shaping Techniques in PDM

Noise shaping is a critical technique in Pulse Density Modulation (PDM) that redistributes quantization noise away from the signal band, improving the signal-to-noise ratio (SNR) in the frequency range of interest. By leveraging feedback loops and filter design, noise shaping pushes quantization noise to higher frequencies where it can be more easily filtered out.

First-Order Noise Shaping

The simplest form of noise shaping employs a first-order delta-sigma modulator, which uses a single integrator in the feedback loop. The quantization noise E(z) is high-pass filtered, while the input signal X(z) remains unaffected. The output Y(z) can be expressed as:

Here, the term (1 - z^-1) represents the first-order high-pass noise transfer function (NTF). The magnitude of the NTF increases with frequency, effectively attenuating noise in the baseband while amplifying it at higher frequencies.

Higher-Order Noise Shaping

Higher-order modulators (e.g., second-order or third-order) use multiple integrators to further suppress in-band noise. The NTF for an N-th order modulator is given by:

This results in a steeper noise attenuation slope of 20N dB/decade in the baseband. However, higher-order modulators introduce stability challenges due to increased loop gain and phase delay, necessitating careful design of the loop filter coefficients.

Stability Considerations

Higher-order noise shaping requires stability analysis to prevent limit cycles or chaotic behavior. The Lee criterion provides a rule of thumb for stability:

Exceeding this limit risks instability, leading to tonal artifacts or increased noise modulation. Techniques such as zero optimization or multi-stage noise shaping (MASH) are often employed to mitigate these effects.

Practical Implementation

In audio applications, a common approach is the 5th-order single-loop modulator, which balances noise suppression and stability. The loop filter typically consists of cascaded integrators with distributed feedback:

Optimal coefficients a₁...a₅ are derived using simulations or optimization algorithms to minimize in-band noise while maintaining stability.

Real-World Applications

Noise shaping is widely used in digital-to-analog converters (DACs) and microphones employing PDM. For example, MEMS microphones often integrate a 3rd-order modulator with a 64× oversampling ratio, achieving an SNR > 100 dB in the 20 Hz–20 kHz band. The shaped noise is then removed by a decimation filter.

3.3 Filtering Requirements for PDM Signals

Pulse Density Modulation (PDM) signals inherently contain high-frequency quantization noise due to their 1-bit encoding nature. Effective filtering is critical to reconstruct the original analog signal while suppressing out-of-band noise. The two primary filtering stages involved are:

• Anti-aliasing filtering before PDM conversion.
• Reconstruction filtering after PDM demodulation.

Noise Shaping and Spectral Characteristics

PDM relies on noise shaping, where quantization noise is pushed to higher frequencies. The power spectral density (PSD) of a first-order sigma-delta modulator is given by:

where Δ is the quantization step size and f_s is the sampling frequency. The sin² term demonstrates high-pass noise shaping.

Reconstruction Filter Design

The reconstruction filter must meet stringent requirements:

• Passband flatness within ±0.1 dB up to the Nyquist frequency (f_N = f_s/2).
• Stopband attenuation ≥60 dB beyond the transition band.
• Group delay variation minimized to preserve phase linearity.

A typical filter response resembles a brick-wall low-pass characteristic. For audio applications, a 4th- to 8th-order Butterworth or elliptic filter is common. The cutoff frequency f_c is selected as:

Implementation Trade-offs

Analog vs. digital filtering presents key trade-offs:

Practical Considerations

In MEMS microphones and Class-D amplifiers, switched-capacitor filters are often employed due to their:

• Precision matching (0.1% capacitor ratios).
• Programmable cutoff via clock frequency.
• Integration compatibility with CMOS processes.

The filter's quality factor Q must be carefully controlled to avoid peaking. For a 20 kHz audio bandwidth with f_s = 2.8 MHz:

Higher-order filters cascade multiple biquad stages, with each stage's transfer function given by:

4.1 Clock Jitter and Its Impact on PDM

Clock jitter, defined as the short-term deviation of a clock signal from its ideal periodicity, introduces non-linear distortions in Pulse Density Modulation (PDM) systems. In PDM-based audio, where signal fidelity depends on precise timing, even sub-nanosecond jitter can degrade performance. The impact manifests as increased noise and harmonic distortion, particularly in high-frequency signal components.

Mathematical Modeling of Jitter-Induced Noise

The relationship between clock jitter Δt and signal-to-noise ratio (SNR) in a PDM system can be derived from the sampling uncertainty principle. For a sinusoidal input signal x(t) = A sin(2πft), the voltage error ΔV due to timing jitter is:

The root-mean-square (RMS) jitter-induced noise voltage V_n,jitter becomes:

where σ_j is the standard deviation of the jitter distribution. The SNR due to jitter alone follows:

Practical Implications in Audio Systems

In 1-bit sigma-delta converters operating at 3.072 MHz (typical for CD-quality audio reconstruction), a jitter of 50 ps RMS limits the theoretical SNR to:

This matches the dynamic range of 16-bit PCM, demonstrating why low-jitter clocks are critical. The spectral effects appear as:

• Wideband noise floor elevation proportional to f²
• Spurious tones when jitter correlates with signal content
• Intermodulation distortion in multi-tone signals

Jitter Mitigation Techniques

Modern PDM interfaces employ several countermeasures:

• Phase-locked loops (PLLs) with voltage-controlled oscillators (VCOs) achieving <1 ps RMS jitter
• Differential clock distribution to reduce power supply-induced modulation
• Jitter attenuators using digital filtering in clock cleaner ICs

Experimental data from MEMS microphones shows that reducing clock jitter from 100 ps to 10 ps improves THD+N by 14 dB at 1 kHz. The improvement follows the 20 dB/decade slope predicted by theory.

Measurement Methodology

Characterizing jitter in PDM systems requires:

• Phase noise analyzers for spectral decomposition of clock imperfections
• Jitter histograms from high-speed oscilloscopes (≥10 GS/s)
• Coherent sampling techniques to separate random and deterministic jitter

The Allan variance provides a time-domain measure of clock stability, particularly useful for identifying long-term drift components that affect PDM decimation filters.

4.2 Power Consumption and Efficiency

Switching Losses in PDM Systems

The power efficiency of a Pulse Density Modulation (PDM) system is primarily governed by switching losses in the output stage. Unlike Pulse-Width Modulation (PWM), where switching frequency is fixed, PDM's variable pulse density leads to dynamic power dissipation. The average power loss P_loss in a Class-D amplifier implementing PDM can be expressed as:

where f_sw is the effective switching frequency, E_on and E_off are the turn-on and turn-off energy losses per transition, Q_g is the total gate charge, and V_dr is the gate drive voltage.

Thermal Considerations

In high-density PDM audio applications, such as digital microphones or MEMS speakers, thermal management becomes critical. The power dissipated as heat P_diss in the output MOSFETs follows:

where I_RMS is the root-mean-square current through the switching element and R_DS(on) is the on-resistance of the MOSFET. For a 1-bit ΣΔ modulator operating at 3.3V with a 64× oversampling ratio, typical efficiency ranges between 85-92%, significantly higher than equivalent PWM implementations.

Comparative Analysis with PCM and PWM

When benchmarked against Pulse-Code Modulation (PCM) and PWM, PDM exhibits distinct power characteristics:

• Idle Power: PDM consumes minimal power during silence (near-zero bit density), whereas PCM systems maintain constant power due to clocking requirements.
• Dynamic Range Scaling: Power consumption in PDM scales linearly with signal amplitude, unlike PWM's fixed-frequency losses.
• EMI Tradeoffs: While PDM's randomized switching reduces electromagnetic interference, the spectral dispersion increases high-frequency losses in parasitic capacitances.

Optimization Techniques

Several methods improve PDM power efficiency:

• Adaptive Biasing: Dynamically adjusting the gate drive voltage V_dr based on signal amplitude reduces switching losses by up to 22%.
• Zero-Voltage Switching (ZVS): Resonant topologies can eliminate capacitive discharge losses during transitions.
• Process Technology: Using GaN FETs instead of silicon MOSFETs cuts R_DS(on) by 3-5× while reducing gate charge requirements.

where η_peak is the peak efficiency, Z_load is the speaker impedance, and C_oss is the MOSFET output capacitance. Modern PDM audio ICs like the MAX98357 achieve >90% efficiency at 1W output into 8Ω loads.

4.3 Design Trade-offs in PDM Systems

Noise Shaping vs. Quantization Error

Pulse Density Modulation (PDM) relies on noise shaping to push quantization error out of the audio band. The noise transfer function (NTF) of a first-order sigma-delta modulator is given by:

Higher-order modulators (e.g., 2nd or 3rd order) further suppress in-band noise but introduce stability challenges. The signal-to-noise ratio (SNR) improves by approximately 6 dB per octave for each additional order, but nonlinearities in the feedback loop can lead to limit cycles or instability. Practical implementations often use multi-stage noise shaping (MASH) architectures to mitigate this.

Oversampling Ratio (OSR) and Bandwidth

The oversampling ratio, defined as:

where \( f_s \) is the sampling frequency and \( f_{\text{audio}} \) is the audio bandwidth, directly impacts design complexity. A higher OSR reduces in-band noise but demands faster clock speeds and higher power consumption. For example, a 64× OSR at 48 kHz audio requires a 6.144 MHz clock, which strains low-power embedded systems.

Decimation Filter Trade-offs

PDM-to-PCM conversion requires a decimation filter to suppress high-frequency noise. A sinc filter (e.g., \(\text{sinc}^3\)) is commonly used, but its group delay and computational cost scale with filter order. A 5th-order FIR filter may achieve >120 dB stopband attenuation but requires ~100× more multiply-accumulate (MAC) operations than a 3rd-order design. This trade-off is critical for real-time audio processing on resource-constrained DSPs.

Clock Jitter Sensitivity

PDM’s 1-bit encoding is robust against amplitude noise but highly sensitive to clock jitter. The timing error \( \Delta t \) translates to voltage error \( \Delta V \) as:

For a 3.3 V system with a 6.144 MHz clock, just 100 ps of jitter introduces ~2 mV of noise. This necessitates low-jitter oscillators (e.g., MEMS or crystal-based) in high-fidelity applications, increasing BOM cost.

Power Consumption vs. Resolution

The figure of merit (FoM) for PDM ADCs combines resolution and power:

A 16-bit ENOB design at 20 kHz bandwidth typically consumes 1–10 mW in modern CMOS processes. Aggressive noise shaping can improve ENOB but raises dynamic power due to higher switching activity in the modulator. For battery-powered devices, this trade-off often favors adaptive OSR schemes that adjust resolution dynamically.

Implementation Case Study: MEMS Microphones

Commercial MEMS microphones (e.g., Knowles SPU0410LR5H-QB) exemplify these trade-offs:

• 64 dB SNR achieved via 4th-order noise shaping
• 2.6 mA current draw at 3.3 V (8.6 mW)
• ±1% clock tolerance to balance jitter immunity and cost

These specs reflect optimizations for consumer audio, where moderate SNR and low power outweigh ultra-high resolution.

5.1 Key Research Papers on PDM

• PDF AN3998.book - STMicroelectronics — 1 Introduction This application note presents the algorithms and architecture of an optimized software implementation for PDM signal decoding and audio signal reconstruction when connecting an ST MP45DT02 MEMS microphone with an STM32 microcontroller. It can directly take the Pulse Density Modulated (PDM) data output from the microphone and convert it to 16-bit pulse-code modulation (PCM) format.
• Direct Digital Pulse Width Modulation for Class D Amplifiers — Two common pulse modulation techniques are pulse width modulation (PWM) and pulse density modulation (PDM) (see figure below). PWM generates pulses with widths proportional to the input amplitude while PDM generates pulses with fixed width but where the density of the pulse train relates to the amplitude.
• PDF Pulse Modulation - Electrical & Computer Engineering — Pulse Duration Modulation The width of the pulse re ects the sampled signal amplitude. the position of the leading edge, trailing edge or both may be modi ed to re ect the changing duration of the pulse also known as: pulse width modulation or pulse length modulation
• pdm与pwm (我只用pdm 希望你看了后也只用pdm，抛弃pwm)v-CSDN博客 — PDM是脉冲密度调制 (pulse density modulation)，PWM是脉冲宽度调制 (pulse width modulation)， 与PWM类似 ,PDM也是通过改变高电平与低电平时间的比值得到不同的输出电压 ,芯片外 围只需使用简单的 RC 滤波器. 但从输出波形看,PWM波形的周期是固定的 ,改变的是占 空比 ,也就是高电平的宽度;而PDM的脉冲的宽度是固定 ...
• The Class D Audio Power Amplifier: A Review - MDPI — The Class D amplifier is categorized as four ordinary models based on several varying modulation programs, which are pulse-width modulation (PWM), pulse-density modulation (PDM), Δ-Σ modulation, and self-oscillating [18].
• PDF Interfacing PDM digital microphones using STM32 MCUs and MPUs ... — This document targets digital MEMS microphones having a pulse-density modulated (PDM) output and describe how to connect them in mono and stereo configurations to STM32 MCUs and MPUs by using the SPI/I2S, SAI and DFSDM peripherals.
• PDF i.MXRT600 PDM MEMS Microphone Audio Path Optimal Settings — The Pulse-Density Modulation (PDM) is a data format used at the output of MEMS digital microphones (for example, Knowles SPH0641LM4H-1). Such microphones are used in mobile devices, because they output digital data, are immune to interferences, allow for flexible topology and board layout, and they have low noise level and cost.
• (PDF) Design Exploration and Performance Strategies towards Power ... — A power-efficient reconfigurable acoustic beamforming architecture, which embeds not only a time-domain Delay-and-Sum beamformer but also all the operations to demodulate the Pulse Density Modulation (PDM) signals from the microphones, is proposed and analysed in Section 5.
• Class-D Audio Amplifier using Sigma-Delta (ΣΔ) Modulator — In this article we design a low-power class-D audio amplifier circuit where the analog signal is encoded into pulse density modulation (PDM) using a first-order sigma-delta (ΣΔ) modulator. The designed circuit is built using Orcad-PSpice and results are analyzed with Matlab.
• STMCU中文官网 — This document targets digi tal MEMS microp hones having a pulse-density modulated (PDM) output and describe how to conn ect them in mono and stereo configurations to STM32

5.2 Recommended Books and Articles

• PDF PULSE CODE MODULATION STANDARDS - trmc.osd.mil — 5.1 General This chapter defines continuous variable slope delta (CVSD) modulation as the standard for digitizing audio and addresses the method of inserting CVSD encoded audio into a PCM stream. Additional information and recommendations are provided in Appendix F, Continuous Variable Slope Delta Modulation.
• PDF Interfacing PDM digital microphones using STM32 MCUs and MPUs ... — This document targets digital MEMS microphones having a pulse-density modulated (PDM) output and describe how to connect them in mono and stereo configurations to STM32 MCUs and MPUs by using the SPI/I2S, SAI and DFSDM peripherals.
• PDF AN3998.book - STMicroelectronics — 1 Introduction This application note presents the algorithms and architecture of an optimized software implementation for PDM signal decoding and audio signal reconstruction when connecting an ST MP45DT02 MEMS microphone with an STM32 microcontroller. It can directly take the Pulse Density Modulated (PDM) data output from the microphone and convert it to 16-bit pulse-code modulation (PCM) format.
• PDF Getting Started with the SAMA5D2 Audio Subsystem — For a more detailed description of the individual components of the DSP engine, refer to "Digital Signal Processing (Digital Filter)", in Section "Pulse Density Modulation Interface Controller (PDMIC)" of the SAMA5D2 device datasheet.
• PDF Pulse Modulation - Electrical & Computer Engineering — S. Haykin and M. Moher, Introduction to Analog & Digital Communications, 2nd ed., John Wiley & Sons, Inc., 2007. ISBN-13 978--471-43222-7.
• PDF i.MXRT600 PDM MEMS Microphone Audio Path Optimal Settings — The Pulse-Density Modulation (PDM) is a data format used at the output of MEMS digital microphones (for example, Knowles SPH0641LM4H-1). Such microphones are used in mobile devices, because they output digital data, are immune to interferences, allow for flexible topology and board layout, and they have low noise level and cost.
• Class-D Audio Amplifier using Sigma-Delta (ΣΔ) Modulator — In this article we design a low-power class-D audio amplifier circuit where the analog signal is encoded into pulse density modulation (PDM) using a first-order sigma-delta (ΣΔ) modulator. The designed circuit is built using Orcad-PSpice and results are analyzed with Matlab.
• Class-D Audio Amplifier using Sigma-Delta (ΣΔ) Modulator — PDF | On Sep 9, 2022, Nour El Imane Bellili and others published Class-D Audio Amplifier using Sigma-Delta (ΣΔ) Modulator | Find, read and cite all the research you need on ResearchGate
• STMCU中文官网 — This document targets digi tal MEMS microp hones having a pulse-density modulated (PDM) output and describe how to conn ect them in mono and stereo configurations to STM32
• USB Audio Design Guide - Digi-Key Electronics — The xCORE Microphone Array board features 7 MEMS microphones with PDM (Pulse Density Modulation) output. Figure 2 shows the microphone arrangement on the board.

5.3 Online Resources and Tutorials

• PDF A R w and Comp rison of Pulse Width Modulatio PWM) Met eprin For Analog ... — AN AUDIO ENGINEERING SOCIETY PREPRINT. A Review and Comparison of Pulse Width Modulation (PWM) methods ... The pulse modulator can be based on pulse width modulation (PWM) or pulse density modulation (PDM). Since PDM is a quantizing pulse modulation scheme, the HF spectrum has a stochastic nature. Some reports have been given
• PDF Getting Started with the SAMA5D2 Audio Subsystem - Microchip Technology — 3. Pulse Density Modulation Interface Controller (PDMIC) The PDMIC peripheral is a mono PDM decoder module that decodes an incoming PDM sample stream. The PDMIC module takes either the system clock (MCK) or the generic clock (e.g., Audio PLL PMC output) as its clock source. It then generates the PDM clock in the PDMIC_CLK pin to be fed to the
• PDF Chapter 5 Pulse Modulation: Transition from Analog to Digital — Professor Deepa Kundur (University of Toronto)Pulse Modulation22 / 61 5.2 Pulse Modulation Ithe variation of aregularly spacedconstant amplitudepulse stream to superimpose information contained in a message signal. t T T s Note: T < T s A IThree types: 1.pulse amplitude modulation (PAM) 2.pulse duration modulation (PDM) 3.pulse position ...
• 5.3 Pulse Width Modulation - Avionics II - NSCC — Another technique to encode the input is pulse width modulation, or PWM. Instead of altering the number of pulses in a given period of time, we keep the frequency constant and adjust the width of the pulses. If the input amplitude is high, the width of the corresponding pulse will be wide and if the amplitude is low, the pulse width will be narrow.
• Class-D Audio Amplifier using Sigma-Delta (ΣΔ) Modulator — This modulation is likewise known as PDM "pulse density modulation", in which the density of pulses determines the digital signal strength and frequency due to the integration functions of the analog to digital converter. [10] The principle of PDM is, a clock signal with high frequency is applied to sample and hold the
• PDF AN5027 Application note - STMicroelectronics — audio capability with a rich connectivity, including serial and enhanced voice-acquisition interfaces allowing the user to easily build solution for microphone-based applications. This document targets digital MEMS microp hones having a pulse-density modulated (PDM) output and describe how to connect them in mono and stereo configurations to STM32
• PDF Interfacing PDM digital microphones using STM32 32-bit Arm® Cortex® MCUs — PDM MODULATOR converts the buffered analog signal into a serial pulse density modulated signal. The clock input (CLK) is used to control the PDM modulator. The clock frequency range for ST digital microphones is from 1 MHz to 3.25 MHz. This frequency will define the sampling rate at which the amplifier' s analog output signal is sampled to ...
• PDF Channels, modulation, and demodulation - MIT OpenCourseWare — CHANNELS, MODULATION, AND DEMODULATION of binary PAM where the basic pulse shape p(t) is a sinc function. Comparing (6.1) with (6.3), we see that PAM is a special case of digital modulation in which the underlying set of functions φ 1(t),φ 2(t),... , is replaced by functions that are T-spaced time shifts of a basic function p(t).
• Class-D Audio Amplifier using Sigma-Delta (ΣΔ) Modulator - ResearchGate — Most favorable modulation topologies are pulse-width modulation (PWM) or pulse-density modulation (PDM). The output stage could be performed using half-bridge or full-bridge topologies.
• Direct Digital Pulse Width Modulation for Class D Amplifiers - DiVA — counter to keep the pulse high for a number of clock cycles and low for the rest of the sample period. This solution would require a very high clock frequency for high quality audio (e.g. 48 kHz, 16 bits audio require a clock of 3.2 GHz) and is unreasonable for a low-power circuit.