This subject provides a mathematical analysis ofAnalogue Communication Systems. In particular, Fourier Series and Fourier Transforms are introduced and used to analyse a selection of communications systems. Information Theory is reviewed and developed, and the Lempel Ziv is introduced. An integrated Project contributes towards the final mark of this subject.
Qualitative Introduction
Overview of Communications Systems; fundamentallimitations; signals and spectra, baseband and passband; modulation andbenefits of modulation.
Fourier Series
Complex exponential Fourier series, Trigonometric Fourierseries, Phasors and one and two sided line spectra (explanation of negativefrequency), hermitian symmetry for real signals, Gibb's phenomenom, Averagenormalized power of periodic signals, dc component, Parsevals Theorem. Use ofthe generating function to determine the Fourier coefficients.
Fourier Transform
Development of the Fourier transform from the Fourier series, Dirichletconditions, The inverse Fourier transform and interpretation, hermitiansymmetry for real signals, the sinc function, Properties of the Fouriertransform, Fourier transform of various common functions, inverse relationshipbetween time and frequency domains, the delta function, Rayleigh's energytheorem, Fourier transform of periodic signals.
Transmission of Signals Through Linear Systems
Linear time invariant systems,Impulse response, convolution integral, causal signals, tapped delay line filter,convolution sum, application of convolution theorem, geometric interpretationof convolution, frequency response of LTI systems, transfer functions, logarithmof transfer function, bandwidth, analysis of practical circuits. Signal distortionin transmission, distortionless transmission, amplitude and phase distortion,constant phase delay, equalisation. Ideal filters, step response, pulse response,risetime, pulse resolution. Quadrature filters and Hilbert transforms.
CW Modulation
Analysis of AM, DSB, SSB, FM,and PM signals, FDM. FM stereo.
Noise Figure and Noise temperature
Noise: Introduction to noise, thermal noise, shot noise, noise figure, measurement of noise figure, noise in a multistage amplifier, Friis formula, noise temperature, noise figure of a lossy transmission line, application to various systems.
Information Theory and Coding
Information sources, discrete memory-lesssource, information measure, information content of a symbol, Entropy,information rate, Channel matrix, joint probability matrix, lossless channel,deterministic channel, noiseless channel, binary symmetric channel, conditionalentropies, equivocation and mutual information, channel capacity.
Source Coding
Code length and efficiency, source coding theorem,classification of codes, Kraft inequality. Entropy coding, Shannon-Fano coding,Huffmann coding, Lempel-Ziv algorithm.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 30 |
| Formal Examination | 70 |