Week 7 Lecture 1+2
Digital Communications System
Architecture + Signals basics
Old Communication : Analog
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Today: we use “Digital”
Block Diagram on Digital
Communication Systems
Review: Why Digital Comm?
Continuous
Info. Source
Sampler
Quantizer
Source
Encoder
• The points may be considered as the input of a Digital
Communication System where messages consist of sequences
of "symbols" selected from an alphabet e.g. levels of a
quantizer or telegraph letters, numbers and punctuations.
• The objective of a Source Encoder (or data compressor) is to
represent the message-symbols arriving at point A2 by as few
digits as possible. Thus, each level (symbol) at point is A2
mapped, by the Source Encoder, to a unique codeword of 1s
and 0s and, at point B ,we get a sequence of binary digits.
There are two ways to reduce the channel noise/interference effects:
1. to introduce deliberately some redundancy in the sequence at point B and this is what
a Discrete Channel Encoder does. This redundancy aids the receiver in decoding the
desired sequence by detecting and many times correcting errors introduced by the
channel;
2. to increase Transmitter's power - point T often very expensive therefore
better to trade transmitter's power for channel bandwidth.
Interleaver
Discrete
Channel
Encoder
Channel Encoder
Digital
Modulation
DeInterleaver
Channel
Decoder
DeModulator
Receiver
Source
Decoder
The source decoder processes the sequence received from the output of the
channel decoder and, from the knowledge of the source encoding method used,
attempts to reconstruct the signal of the information source.
A SIMPLIFIED BLOCK STRUCTURE (Digital source)
Note: For Digital source -- Quality is measured as the Bit Error
Rate (BER)
An Internet System (Digital source) based on Cellular Network in
the core
Digital Transmission of Analogue Signals (voice)
Not BER (like in Digital Source case, previous case)
It is clear from the previous discussion that
signals (representing bits) propagate
through the networks.
Therefore the following sections are
concerned with the main properties and
parameters of communication signals.
Communication Signals
Frequency Domain (Spectrum): very important in Communications
Classification of Signals
according to their description
Classification of Signals:
according to their periodicity
according to their signal energy
according to their spectrum
TD/FD: OPERATIONS
More On Transformations
WOODWARD's Notation
•
The evaluation of FT, that is
•
involves integrating the product of a function and a complex exponential which can be difficult; so tables of useful transformations are frequently
used (next 2 slides).
However, the use of tables is greatly simplified by employing Woodward's
notation for certain commonly occurring situations.
main advantage of using Woodward's notation: allows periodic
time/frequency functions to be handled with FT rather than Fourier
Series
•
•
FOURIER TRANSFORMS - TABLES
FOURIER TRANSFORMS – TABLES (cont’d)
IMPORTANT SPECTRUM SHAPES
finite duration (i.e. Energy signals)
Modulation principle
Multiplication (TD) 
Convolution (FD)
In FD, it becomes
Shift operations!
Some frequently used signals
Some frequently used signals
Some frequently used signals
• we can generate any desired "rect" function by scaling and shifting;
see for instance the following table
effects of temporal scaling:
Bandwidth of a signal
Bandwidth: the range of the significant frequency components in a signal
waveform
Examples of message signals (baseband signals) and their bandwidth:
• television signal bandwidth 5.5MHz
• speech signal bandwidth 4KHz
• audio signal bandwidth 8kHz to 20kHz
Examples of transmitted signals (basepass signals) and their bandwidth:
• to be discussed latter on
•Note that there are various definitions of bandwidth, e.g. 3dB bandwidth,
null-to-null bandwidth, Nyquist (minimum) bandwidth (next slide)
Definitions: Signal Bandwidth
REDUNDANCY
The degree of similarity in a signal is provided by its Redundancy
autocorrelation function. For instance the autocorrelation function
of a signal
SIMILARITY
The degree of similarity between two signals is given by their crosscorrelation function. For instance the cross-correlation function
between two signals
On Comm Noise
• Usually people assume: Additive White Gaussian
Noise (AWGN)
Noise