Pulse Code Modulation (PCM)

• PCM stands for Pulse Code Modulation, a method used to digitally represent sampled analog signals.
• It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications.
• A PCM stream has two fundamental properties that determine the fidelity of the original analog signal: the sampling rate and the bit depth.

PCM Stages

• Analogue signals are sampled at regular intervals.
• Sampling rate must be at least twice the highest frequency component in the analog signal to satisfy the Nyquist-Shannon sampling theorem, avoiding aliasing.
• Each sample is quantized, approximating the continuous range of amplitude values into a set of discrete levels.
• The number of quantization levels is determined by the bit depth.
• Quantized values are encoded into a digital format as a sequence of binary digits.
• These steps convert a continuous analog waveform into a discrete, digital representation suitable for processing, storage, and transmission in digital systems.

Sampling Rate

• Sampling rate specifies how many times per second the analog signal is sampled.
• Measured in Hertz (Hz).
• Higher sampling rates can represent higher frequencies in the analog signal.
• Common sampling rates include 44.1 kHz (used for CD audio), 48 kHz (used in professional audio), and 96 kHz or higher (used for high-resolution audio).
• According to the Nyquist-Shannon sampling theorem, the sampling rate must be at least twice the highest frequency component of the signal to avoid aliasing.
• Aliasing occurs when the sampling rate is too low, causing high-frequency components to be misrepresented as lower frequencies.

Bit Depth

• Bit depth determines the number of discrete levels used to represent the amplitude of the sampled signal.
• A higher bit depth provides a more accurate representation of the original signal.
• Common bit depths include 8 bits, 16 bits, 24 bits, and 32 bits.
• Each additional bit doubles the number of available levels.
• A 16-bit PCM signal has 2^16 (65,536) possible amplitude levels, while a 24-bit PCM signal has 2^24 (16,777,216) levels.
• Higher bit depths result in a greater dynamic range and lower quantization noise.
• Quantization noise is the error introduced by approximating the continuous amplitude values with discrete levels.
• Also known as quantization error, it is the difference between the original analog signal and the quantized digital signal.
• It is an unavoidable artifact of the quantization process, as continuous values are rounded to the nearest discrete level.
• The level of quantization noise is related to the bit depth; more bits mean finer steps.

PCM Advantages

• Simplicity: PCM is relatively simple to implement in both hardware and software.
• Robustness: PCM signals are robust to noise and distortion during transmission and storage.
• Standardization: PCM is a widely adopted standard, ensuring interoperability between different devices and systems.
• Flexibility: PCM can represent a wide range of audio signals, from low-quality voice recordings to high-resolution music.

PCM Disadvantages

• Bandwidth: PCM requires a relatively high bandwidth compared to other audio coding techniques.
• Storage: PCM data can consume a significant amount of storage space, especially at high sampling rates and bit depths.

PCM Applications

• Audio Recording and Editing: Used in digital audio workstations (DAWs) for recording, editing, and mastering audio.
• Telecommunications: Used in digital telephone systems for transmitting voice signals.
• Consumer Electronics: Used in CD players, DVD players, and other consumer audio devices.
• Digital Broadcasting: Used in digital radio and television broadcasting systems.
• Medical Imaging: Used in medical imaging devices such as MRI and CT scanners.

PCM Variants

• Linear PCM (LPCM): The most common type of PCM, where quantization levels are uniformly spaced.
• A-Law and μ-Law PCM: Non-linear PCM variants used primarily in telecommunications to improve the signal-to-noise ratio for voice signals.
• These algorithms compress the dynamic range of the audio signal, providing more quantization levels for quieter signals and fewer for louder signals.
• Differential PCM (DPCM): Encodes the difference between consecutive samples, rather than the absolute value of each sample.
• This can reduce the amount of data required to represent the signal, especially for signals with high sample-to-sample correlation.
• Delta Modulation: A simplified form of DPCM, where only a 1-bit quantizer is used to represent the difference between samples.
• Each bit indicates whether the signal has increased or decreased since the last sample.
• Adaptive Differential PCM (ADPCM): A variant of DPCM where the quantization step size is adaptively adjusted based on the characteristics of the signal.
• Can achieve better compression ratios than DPCM while maintaining good signal quality.