Pulse Code Modulation (PCM) Study Guide

Introduction to PCM

Pulse Code Modulation (PCM) is a digital representation of an analog signal where the magnitude of the signal is sampled regularly at uniform intervals, then quantized to a series of symbols in a digital (usually binary) code.

Figure 1.  Block diagram of a basic PCM system

 

 

Key Concept: PCM is the standard form of digital audio in computers, compact discs, digital telephony, and other digital audio applications.

PCM was invented in 1937 by Alec Reeves at the International Telephone and Telegraph. The technology to implement it practically wasn't available until the development of semiconductor components which started in 1948. The first successful commercial PCM telecommunication system was developed at Bell Labs and put into operation in 1962. This system, known as T1, utilized 24 digital channels and was a significant advancement in telecommunications, enabling greater capacity through digitization and time-division multiplexing.

The PCM Transmiter

PCM transmitter involves four main steps:

  1. Low-pass filter limits signal  bandwidth, preventing aliasing during sampling.
  2. Sampling: Converting a continuous-time signal into a discrete-time signal
  3. Quantization: Converting a continuous-amplitude signal into a discrete-amplitude signal
  4. Encoding: Representing each quantized sample by a binary code

1. Sampling

Low Pass Filter  eliminates the high frequency components present in the input analog signal which is greater than the highest frequency of the message signal, to avoid aliasing of the message signal.

Sampling converts a continuous-time signal into a discrete-time signal by measuring the signal's amplitude at regular time intervals.

Nyquist Theorem

The sampling theorem states that a signal can be exactly reconstructed if the sampling frequency is greater than twice the highest frequency component in the signal.

fs > 2 × fmax

Where:

Example: For audio signals with a maximum frequency of 20 kHz, the sampling rate should be at least 40 kHz. CD-quality audio uses 44.1 kHz.

2. Quantization

Quantization converts the continuous-amplitude samples into discrete amplitude values.

Quantization Levels

The number of possible amplitude values is determined by the number of bits used:

Number of levels = 2n

Where n = number of bits per sample

Bits per sample Quantization levels Application
8-bit 256 Telephone quality
16-bit 65,536 CD audio
24-bit 16,777,216 Professional audio

Quantization Error

The difference between the actual analog value and the quantized digital value is called quantization error or quantization noise.

Signal-to-Quantization-Noise Ratio (SQNR) = 6.02n + 1.76 dB

3. Encoding

Each quantized sample is converted to a binary code. The most common encoding method is linear PCM where the quantization levels are uniformly spaced.

Binary Representation

For a 3-bit system (8 levels):

Quantization Level Binary Code
0 000
1 001
2 010
... ...
7 111

PCM REGENERATIVE REPEATER

A PCM regenerative repeater reconstructs and retransmits digital signals. It compensates for signal degradation caused by the transmission medium, ensuring reliable data transmission over longer distances. These repeaters perform equalization, timing recovery, and decision-making to regenerate the original signal. 
A PCM repeater essentially performs three key operations:
1. Reshaping: It reconstructs the distorted pulses, restoring their original shape. 
2. Retiming: It corrects the timing of the pulses, ensuring they are aligned with the original clock signal. To regenerate the signal accurately, the repeater needs a timing signal. This timing signal is typically extracted from the received PCM pulses themselves.  
3. Amplification: It increases the signal strength to compensate for signal loss. 

Modern PCM repeaters can be implemented as single integrated circuits (ICs), which offer advantages in terms of performance, power consumption, and reliability.

PCM RECEIVER

The PCM receiver consists of three main parts:

1. Regenerator: A regenerative repeater is placed at the receiving end also so as to have an exact PCM transmitted signal. Here, also the regenerator works in a similar manner as that when employed in the transmission path. It eliminates the channel induced noise and reshapes the pulse.

2. DAC and Sampler: Digital to analog converter performs the conversion of digital signal again into its analog form by making use of the sampler. As the actual message signal was analog thus at the receiver end there is a necessity to again convert it into its original form.

3. LPF: The sampler generates analog signal but that is not the original message signal. Thus, the output of the sampler is fed to the LPF having cutoff frequency fm. This is sometimes termed as the reconstruction filter that produces the original message signal.

Advantages of PCM

Disadvantages of PCM

Applications of PCM

PCM Variations

Differential PCM (DPCM)

Encodes the difference between the current sample and a predicted value from previous samples.

Adaptive DPCM (ADPCM)

Varies the size of the quantization step to allow better reproduction of signals with varying amplitude.

Bit Rate Calculation

The bit rate of a PCM system is calculated as:

Bit rate = Sampling rate × Number of bits per sample × Number of channels

Example: CD-quality audio has:

Bit rate = 44,100 × 16 × 2 = 1,411,200 bits/sec (1.411 Mbps)

Self-Assessment Quiz

1. What is the minimum sampling rate required for a signal with maximum frequency of 15 kHz?

Answer: According to Nyquist theorem, it should be greater than 30 kHz (2 × 15 kHz).

2. How many quantization levels are there in a 12-bit PCM system?

Answer: 212 = 4,096 levels.

3. Calculate the SQNR for a 16-bit PCM system.

Answer: 6.02 × 16 + 1.76 = 98.08 dB.

4. What is the bit rate of a mono PCM system with 8 kHz sampling rate and 8 bits per sample?

Answer: 8,000 × 8 × 1 = 64,000 bits/sec (64 kbps).

5. Name two advantages of PCM over analog transmission.

Answer: Any two from: noise immunity, regeneration capability, flexibility, security, easier storage.