Pulse Code Modulation

Pulse Code Modulation (PCM)

Introduction to Digital Communication

Before diving into PCM, it's essential to understand why we need to convert analog signals to digital ones. Analog signals are continuous in both time and amplitude. While they are a direct representation of real-world phenomena (like sound waves), they are highly susceptible to noise and interference during transmission. Noise accumulates over long distances and can distort the signal, making it difficult to recover the original information.

Digital signals, on the other hand, are discrete. They are represented by a finite set of values, typically binary digits (0s and 1s). The main advantage of a digital signal is its resilience to noise. As long as the noise level is not so high that it changes a '1' to a '0' or vice versa, the original signal can be perfectly reconstructed at the receiver. This robustness makes digital communication far more reliable for long-distance and high-quality transmission

1.0Modulation

Modulation is the process of altering one or more properties of a periodic waveform known as a carrier signal with respect to the modulation signal, which contains information to be transmitted. Modulation is performed by the device known as a modulator, and this technique is mainly used to overcome the interference of the signal. Modulation techniques typically aid in long-distance communication.

Modulation is of two types:

Analog Modulation
Digital Modulation

In analog modulation, a continuously varying sine wave is considered a carrier wave. This wave modulates the data signal. In amplitude modulation, three parameters can be altered, they are: frequency, amplitude and phase.

Types of analog modulation are:

Amplitude modulation (AM)
Frequency modulation (FM)
Phase modulation (PM).

What is Pulse Code Modulation?

Pulse Code Modulation (PCM) is the most widely used method for converting an analog signal into a digital stream of binary digits. It's not a single process but a series of three distinct steps that systematically transform a continuous waveform into a series of pulses that represent a code. The output of a PCM system is a sequence of binary codes, or "pulses," which can be easily transmitted and stored.

The three primary stages of the PCM process are:

Sampling
Quantization
Encoding

The Three Stages of PCM

Sampling

Sampling is the process of measuring the amplitude of the analog signal at uniform intervals of time. According to the Nyquist-Shannon sampling theorem, to avoid aliasing and accurately reconstruct the original signal, the sampling rate must be at least twice the highest frequency present in the analog signal.

Nyquist–Shannon sampling theorem:If a continuous signal x(t) contains no frequencies higher than

$f_{m a x}$ hertz, then it can be completely determined by its samples taken at a rate

$f_{s} \geq 2 f_{m a x}$

$f_{s} =$ sampling frequency (samples per second)

$f_{m a x}$ =highest frequency present in the signal

This minimum sampling rate $f_{s} = 2 f_{m a x}$ is called the Nyquist rate, and

$f_{N} = \frac{f _{s}}{2}$ is called the Nyquist frequency.

Quantization

Quantization involves mapping the sampled amplitude values to a finite set of discrete levels. This process introduces quantization error, which is the difference between the actual sampled value and the quantized value.

Encoding

Encoding is the process of converting the quantized values into a binary format. Each quantized level is assigned a unique binary code, and the sequence of these binary codes represents the original analog signal in digital form

2.0Block Diagram of PCM

The PCM system can be represented by the following block diagram:

$[A na l o g S i g na l] \to [L o wP a ss F i lt er] \to [S am pl er] \to [Q u an t i zer] \to [E n co d er] \to [PCMS i g na l]$

At the receiver end, the process is reversed:

$[PCMS i g na l] \to [Deco d er] \to [R eco n s t r u c t i o n F i lt er] \to [A na l o g S i g na l]$

3.0Types of PCM

Linear PCM (LPCM)

In Linear PCM, the quantization levels are uniformly spaced. This type of PCM is widely used in audio applications, including CDs and DVDs, due to its simplicity and high fidelity.

Differential PCM (DPCM)

Differential PCM encodes the difference between successive samples rather than the absolute value of each sample. This reduces the amount of data required for transmission and is particularly useful in applications with limited bandwidth.

Adaptive Differential PCM (ADPCM)

Adaptive Differential PCM is an enhancement of DPCM that adjusts the quantization step size based on the signal's characteristics. This adaptation improves compression efficiency and is commonly used in speech coding applications.

The PCM System: Transmitter and Receiver

A complete PCM communication system consists of a transmitter that performs the three PCM stages and a receiver that performs the reverse process.

The PCM Transmitter

The transmitter takes the analog input signal and processes it through the following blocks:

Low-Pass Filter (LPF): This filter removes any high-frequency components above fm to prevent aliasing.
Sampler: Samples the LPF output at a rate of fs≥2fm.
Quantizer: Rounds off the amplitude of each sample to the nearest quantization level.
Encoder: Converts the quantized sample values into a binary code stream.

The output of the transmitter is a digital signal ready for transmission through a channel (e.g., optical fiber, satellite link, etc.).

The PCM Receiver

The receiver performs the inverse operations to recover the original analog signal:

Decoder: Converts the binary code stream back into a series of quantized amplitude levels.
Reconstruction Filter (Low-Pass Filter): This filter smoothens the discrete-time signal by removing the high-frequency components introduced by sampling, reconstructing a continuous-time signal. The result is an analog signal that closely approximates the original one.

The receiver's LPF is crucial for eliminating the unwanted replicas of the original signal's spectrum that are created during the sampling process.

Advantages of PCM

PCM's dominance in modern communication is due to several key advantages:

Robustness to Noise: The digital nature of the signal makes it highly resistant to noise and interference.
Signal Regeneration: Digital repeaters can be used to perfectly regenerate the signal at regular intervals, eliminating noise accumulation and allowing for very long-distance transmission without degradation.
Signal Security: Digital signals are easier to encrypt and secure, making them ideal for confidential communication.
Compatibility with Digital Networks: PCM signals can be easily multiplexed (combined with other signals) and transmitted over a single channel, allowing for efficient use of network resources.
Flexible Format: Digital data can be stored, processed, and manipulated easily using computers.

Bandwidth of a PCM Signal

The bandwidth required to transmit a PCM signal is a key consideration. The bit rate (R_b) of the PCM signal is given by:

$R_{b} = n \times f_{s}$

where n is the number of bits per sample and fs is the sampling frequency.

The bandwidth of a digital signal is approximately half of the bit rate.

$B W \approx \frac{1}{2} R_{b} = \frac{1}{2} n f_{s}$

Since $f_{s} \geq 2 f_{m}$ ,the minimum bandwidth required for a PCM signal is:

$B W_{m i n} = n \times f_{m}$

This shows that the bandwidth of a PCM signal is directly proportional to the number of bits per sample (n) and the maximum frequency of the message signal ( $f_{m}$ ).

4.0Why PCM Is Essential in Modern Communication

PCM provides high noise immunity and supports signal regeneration without quality loss over long distances.
It enables multiplexing of various data types—voice, text, video—over a single medium, offering flexibility and compatibility with digital processing systems.
With precise digital representation, PCM allows secure storage, easy encryption, and integration with digital switching systems.