1. Pulse Code Modulation
Lecture 5

2. Why a Particular Encoding Technique
Digital data, digital signal
Equipment less complex and expensive than digital-to-analog modulation equipment
Analog data, digital signal
Permits use of modern digital transmission and switching equipment

3. Why a Particular Encoding Technique
Digital data, analog signal
Some transmission media will only propagate analog signals
E.g., optical fiber and unguided media
Analog data, analog signal
Analog data in electrical form can be transmitted easily and cheaply
Done with voice transmission over voice-grade lines

4. Criteria For Signal Encoding
What determines how successful a receiver will be in interpreting an incoming signal?
Signal-to-noise ratio
Data rate
Bandwidth
An increase in data rate increases bit error rate
An increase in SNR decreases bit error rate
An increase in bandwidth allows an increase in data rate

5. Factors Used to Compare Encoding Schemes
Signal spectrum
With lack of high-frequency components, less bandwidth required
With no dc component, ac coupling via transformer possible
Transfer function of a channel is worse near band edges
Clocking
Ease of determining beginning and end of each bit positionSignal interference and noise immunity
Performance in the presence of noise
Cost and complexity
The higher the signal rate to achieve a given data rate, the greater the cost

6. Reasons for Analog Modulation
Modulation of digital signals
When only analog transmission facilities are available, digital to analog conversion required
Modulation of analog signals
A higher frequency may be needed for effective transmission
Modulation permits frequency division multiplexing

7. Basic Encoding Techniques
Analog data to analog signal
Amplitude modulation (AM)
Angle modulation
Frequency modulation (FM)
Phase modulation (PM)

8. Spectrum of AM signal

9. Amplitude Modulation Transmitted power
Pt = total transmitted power in s(t)
Pc = transmitted power in carrier

10. Single Sideband (SSB) Variant of AM is single sideband (SSB)
Sends only one sideband
Eliminates other sideband and carrier
Advantages
Only half the bandwidth is required
Less power is required
Disadvantages
Suppressed carrier can’t be used for synchronization purposes

11. Pulse Modulation
Analogue modulated systems are quite widely used, because of their simplicity.
An alternative to analogue modulated systems is Pulsed systems.
This system is based on digital signals or pulses.
The basis of such a system is the use of a digital carrier signal, which is modulated by an analogue signal.
There are various ways in which this can be achieved, giving rise different systems.

12. Sampling of signals
An analogue signal is transmitted continuously in its entire form.
This need not be done provided certain conditions are satisfied.
Samples of the analogue signal may be transmitted at given intervals of time.
The original signal may then be recovered at the receiving end from the transmitted samples.
This technique is known as sampling and it underlies pulsed systems.

13. Consider a train of signals, with a repetition frequency f and period T where

14. If the pulse train were amplitude modulated by the analogue signal, the result will be pulses whose amplitudes are samples of the analogue signal at time intervals T.

15. If the amplitude modulated pulse train is then analysed, its spectrum will consist of Fourier components,
At each of this there will be a set of sum and difference frequencies (lower and upper sidebands) due to each frequency component of the analogue signal.

16. If W and f-W do not overlap then it is possible to separate the group of frequencies at the receiving end.
This can be achieved by use of a low-pass filter with a cut-off frequency f = W.
The separated frequencies are then those of the analogue signal transmitted.
From this the following condition is derived

17. This means the repetition frequency must be at least twice the highest frequency component in the analogue signal.
The minimum sampling frequency is then
This is also called the Nyquist rate.
If the sampling rate is less than 2W the lower sideband will overlap the baseband and it will not be possible to separate them.
This effect is known as aliasing. It can be avoided by passing the signal through a filter before sampling.

18. Telephone siganls range from 300 Hz to 3
Telephone siganls range from 300 Hz to 3.4 kHz, the internationally agreed sampling frequency is 8kHz. It means there is a guard band of 1.2kHz between the lower side band and the baseband.
Comment:
It means W has an upper limit
The technique can only be used if the bandwidth can be restricted to W without destroying the essential information. To achieve this, band-limited signals are used.

19. Sampling Theorem
If a signal f(t) is sampled at regular intervals of time and at a rate higher than twice the highest frequency, then the samples contain all of the information of the original signal. The function f(t) may be reconstructed from these samples by the use of a low pass filter.

20. Sampler
An analogue sampler commonly known as the sample-and-hold is used in sampling the input analogue signal voltage and maintaining that voltage until the next sampling instant.

21. The FET (Field Effect Transistor) acts like a simple switch.
When turned "on," it provides a low‑impedance path to deposit the analogue sample voltage on capacitor.
The time that the FET is "on" is called the aperture or acquisition time.
Essentially, the capacitor is the hold circuit. When the switch FET is "Off," the capacitor does not have a complete path to discharge through and therefore stores the sampled voltage.

22. The storage time of the capacitor is also called the conversion time because it is during this time that the unit converts the sample voltage to a digital code.
The acquisition time should he very short. This assures that a minimum change occurs in the analogue signal while it is being deposited across the capacitor.
If the input to the sampler is changing while it is performing the conversion, distortion results. This distortion is called aperture distortion.

23. Thus, by having a short aperture time and keeping the input to the constant relatively constant, the sample‑and‑hold circuit reduces aperture distortion.
If the analogue signal is sampled for a short period of time and the sample voltage is held at constant amplitude during the conversion time, this is called flat‑top sampling.
If the sample time is made longer and the analogue‑to‑digital conversion takes place with a changing analogue signal, this is called natural sampling.
Natural sampling introduces more aperture distortion than flattop sampling and requires a faster A/D converter.

24. Pulse Code Modulation
PCM is the most commonly used technique in digital communications
Used in many applications:
Telephone systems
Digital audio recording
CD laser disks
voice mail
digital video etc.
They are a primary building block for advanced communication systems

25. Pulse Code Modulation Based on the sampling theorem
Each analog sample is assigned a binary code
Analog samples are referred to as pulse amplitude modulation (PAM) samples
The digital signal consists of block of n bits, where each n-bit number is the amplitude of a PCM pulse

26. Quantization
Is the process of converting the sampled signal to a binary value
Each voltage level will correspond to a different binary number
The magnitude of the minimum step size is called the resolution.
The error resulting from quantizing is called the quantization noise. Its value is 1/2 the resolution

27. Pulse Code Modulation

28. Dynamic Range
This is the ratio of the largest to smallest analogue signal that can be transmitted.
But Vmin is the resolution and can be written as
It follows that

29. If this is expressed in decibels
From
It can be observed that the DR is the
Maximum binary number for a system. With one code used for 0V which is not considered in calculating DR, it is observed that

30. Example
Given a PCM system with the following parameters:
Maximum analog input frequency 3kHz
A maximum decoded voltage at the receiver of +/- 1.27V
A minimum dynamic range of 35dB.
Find the minimum sample rate
The number of bits required
The resolution
The quantization error

31. Quantization Noise Root mean square error The effective voltage
The noise power is

32. Reasons for Growth of Digital Techniques
Growth in popularity of digital techniques for sending analog data
Repeaters are used instead of amplifiers
No additive noise, can be used over long distances
TDM is used instead of FDM
No intermodulation noise
For a given bandwidth the signal/noise ratio is superior
Conversion to digital signaling allows use of more efficient digital switching techniques
Fits in well with other digital systems

33. Problems
Large bandwidth required. Might consider using optical fibres
Circuits for implementation are costly
uneconomical over short distances less than 5km.
Might consider using integrated circuits to deal with last two.