What is Pulse Code Modulation (PCM)?

Pulse Code Modulation, or PCM, is the most fundamental and widely used method for converting analog signals into a digital format. It is the bedrock of modern digital telephony and the basis for countless digital audio applications, from music CDs to voice transmission over the internet.

The primary goal of PCM is to take a continuous analog signal, such as a voice from a telephone, and transform it into a binary stream-a sequence of 0s and 1s-that can be processed, stored, and transmitted by digital systems.

The Three Steps of the PCM Process

The conversion from analog to digital via PCM is a three-stage process. The signal must first be sampled, then quantized, and finally coded.

1. 1. Sampling: Capturing the Signal in Time

   The first step is sampling, which converts a signal that is continuous in time into a signal that is discrete in time. The process works on a pre-processed signal that has already been passed through Pulse Amplitude Modulation (PAM).

   • The PAM Signal: The input to the PCM process is a PAM signal, which is a sequence of pulses. While discrete in time (captured at specific moments), the amplitude (height) of each pulse can still have any continuous value.
   • The Rule: The rate at which the signal is sampled is governed by the Nyquist-Shannon Sampling Theorem. Mathematically: $f_s \ge 2 \cdot f_{max}$
   • Voice Sampling: For voice telephony, the relevant frequency range is considered to be up to about 3400 Hz. To satisfy the theorem, a sampling frequency of 8000 Hz (8 kHz) was standardized. This means the analog voice signal is measured 8,000 times per second.
2. 2. Quantization: Discretizing the Amplitude

   After sampling, each pulse in the PAM signal can have an infinite number of possible heights. Quantization converts this continuous range of amplitudes into a finite, discrete set of levels. This is done by rounding the amplitude of each sample to the nearest available level. In telephony PCM, 256 discrete levels are used.

3. 3. Coding: Assigning Binary Codes

   The final step is to assign a unique binary code (a string of 0s and 1s) to each of the discrete amplitude levels. Since there are 256 levels, we need 8 bits to represent them all, because $2^8 = 256$. Each sample is thus converted into an 8-bit binary word.

The PCM 32/30 (E1) Frame Structure

To transmit multiple 64 kbps voice channels over a single line, they are combined using Time Division Multiplexing (TDM) into a structure called a frame. The European standard is known as E1.

E1 Frame Characteristics

• Frame Duration: The sampling rate of 8 kHz dictates the frame rate. Each frame must be sent every $1 / 8000$ seconds, which is 125 microseconds (µs).
• Time Slots: Each 125 µs frame is divided into 32 equal Time Slots, numbered 0 to 31.
• Bits per Slot: Each time slot carries one 8-bit sample from a channel.
• Total Bit Rate: The total speed of the E1 stream is calculated as:
  $8000 \text{ frames/s} \times 32 \text{ slots/frame} \times 8 \text{ bits/slot} = 2,048,000 \text{ bps} = 2.048 \text{ Mbps}$

Allocation of Time Slots

The 32 slots are not all used for voice data:

• Time Slot 0 (TS0): Reserved for synchronization purposes. It carries a special pattern, the Frame Alignment Signal (FAS), so the receiver knows where each frame begins. It alternates patterns in odd and even frames.
• Time Slots 1-15 and 17-31: These 30 slots are used to carry the actual user data (e.g., the 8-bit samples from 30 different voice calls).
• Time Slot 16 (TS16): Reserved for signaling information, which is the control data needed to set up, manage, and tear down the calls carried in the other 30 channels.