Week 7 Lecture 1+2Week 7 Lecture 1+2

Digital Communications System Digital Communications System Architecture + Signals basicsArchitecture + Signals basics

Old Communication : Analog

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Today: we use “Digital”Today: we use “Digital”

Block Diagram on Digital Block Diagram on Digital Communication SystemsCommunication Systems

Review: Why Digital Comm?Review: Why Digital Comm?

• 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.

Continuous Info. Source Sampler Quantizer Source

Encoder

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.

Discrete Channel Encoder

InterleaverDigital Modulation

Channel Encoder

Channel Decoder

DeInterleaverDe-Modulator

Source Decoder

Receiver

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 Signalsaccording 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 signalsSome frequently used signals

Some frequently used signalsSome frequently used signals

Some frequently used signalsSome 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 BandwidthDefinitions: Signal Bandwidth

REDUNDANCYThe degree of similarity in a signal is provided by its Redundancyautocorrelation function. For instance the autocorrelation function of a signal

SIMILARITYThe degree of similarity between two signals is given by their cross-correlation function. For instance the cross-correlation function between two signals

On Comm NoiseOn Comm Noise• Usually people assume: Additive White Gaussian

Noise (AWGN)

NoiseNoise