ENGINEERING TRIPOS PART IB - 2012/2013

PAPER 6 - INFORMATION ENGINEERING (2)

Communications
Fourier Transforms &
Signal & Data Analysis

Leader: Prof SJ Godsill

Timing: Weeks 1-8 Lent term

Structure: 14 lectures: 1 lecture per week (wks 1-4 and wk 8); 3 lectures per week (wks 5-7)

Fourier Transforms, Signal and Data Analysis

AIMS

The aims of this section of the course are to:

• Introduce the Fourier Transform as an extension of Fourier techniques on periodic functions and to see how the Fourier Transform is applied to real problems
• Introduce discrete Fourier methods and to develop skills in analysing discrete data.

OBJECTIVES

The objectives of this section of the course are to:

• To develop the ability to discuss and manipulate signals in terms of their frequency content.
• To be able to relate properties of signals in the time domain to those in the frequency domain.
• To be familiar with the difference in behaviour/properties of continuous signals compared to sampled signals, and the basic rules that apply to the latter.

Communications

AIMS

The aims of this section of the course are to:

• Introduce the basic elements of typical Communications Systems.
• Explain the problems associated with matching the characteristics of typical signals, such as audio, video and data, to typical transmission paths, such as the telephone network, radio paths (including satellites), and optical fibres.
• Provide an understanding of bandwidth, as it applies to signals and transmission channels.
• Discuss digitisation of signals and how it affects their properties.

OBJECTIVES

As specific objectives for this section of the course, students should:

• Understand what are the key elements of a Communications System.
• Know the typical bandwidths of speech, music, television, and data signals; and understand how to calculate these for television and data.
• Know the typical pass bands for copper cables, radio paths ranging from Long Wave to UHF and microwaves, and optical fibres.

And be able to:

• Interpret the characteristics of signals and paths in the frequency domain.
• Understand how amplitude modulation and frequency modulation can be used to match the characteristics of signals to those of the required transmission path; and appreciate the relative merits of these two modulation methods.
• Understand how digitisation affects the characteristics of a signal; and in particular understand the separate effects of sampling (in time) and quantisation (in amplitude), so that an appropriate sampling rate and quantiser word length may be specified for a given signal.
• Understand broadly how typical analog-to-digital and digital-to-analog converters work and what are their limiting parameters.

SYLLABUS

Fourier Transforms, Signal and Data Analysis Prof. S. Godsill

1. Introduction and preliminaries
   • 1.1 Motivation for signal analysis. Examples of typical datasets.
   • 1.2 Power and energy
   • 1.3 Revision and extension of delta functions
   • 1.4 Revision of Fourier series

2. The Fourier Transform (FT)
• 2.1 Mathematical formulation of the FT
• 2.2 Interpretation of the FT
• 2.3 The inverse Fourier transform (IFT)
• 2.4 Some important Fourier transforms
3. Properties of the Fourier Transform
• 3.1 Linearity and scaling
• 3.2 Time and frequency shifts (modulation)
• 3.3 Duality, Parseval's Theorem, convolution
• 3.4 Relationship to Laplace transforms
4. Sampling Theory
• 4.1 The sampling theorem and aliasing
• 4.2 The discrete time Fourier transform
• 4.3 Signal reconstruction and the Nyquist frequency
5. The Discrete Fourier Transform
• Derivation of DFT and inverse DFT
• Examples of using the DFT
• The spectrogram

Communications Dr A.G.I Fabregas

1. Typical Signals
   • Signal Properties (energy, power, bandwidth)
   • Digitisation of signals (sampling, quantisation)
   • Representation of Digital Signals


2. Communications Channels
   • Data rate, error probability, channel capacity, spectral efficiency
   • Mobile radio channels (fading, coherence time, coherence bandwidth)


3. Signals Through Channels and Modulation
   • Analogue modulation (amplitude, phase, frequency)


4. Digital Modulation
   • Amplitude, phase and frequency shift keying
   • Multicarrier modulation


5. Multiple Access
   • Frequency-division multiple access
   • Time-division multiple access
   • Code-division multiple access
   
   

REFERENCES

Please see the Booklist for Part IB Courses for references for this module.