Prerequisite courses: Continuous Mathematics, Numerical Analysis I, Probability
Some of the material covered in Information Theory & Coding will also help in this course.

Aims

This course teaches the basic signal processing principles necessary
to understand many modern high-tech systems, with a particular view on
audio-visual data compression techniques. Students will gain practical
experience from numerical experiments in MATLAB-based programming
assignments.

Lectures

Signals and systems.
Discrete sequences and systems, their types and properties. Linear
time-invariant systems, convolution. Harmonic phasors are the eigen
functions of linear time-invariant systems. Review of complex
arithmetic. Some examples from electronics, optics and acoustics.

MATLAB.
Use of MATLAB on PWF machines to perform numerical experiments and
visualise the results in homework exercises.

Fourier transform.
Harmonic phasors as orthogonal base functions. Forms of the Fourier
transform, convolution theorem, Dirac's delta function, impulse combs
in the time and frequency domain.

Discrete sequences and spectra.
Periodic sampling of continuous signals, periodic signals, aliasing,
sampling and reconstruction of low-pass and band-pass signals,
spectral inversion.

Discrete Fourier transform.
Continuous versus discrete Fourier transform, symmetry, linearity,
review of the FFT, real-valued FFT.

Spectral estimation.
Leakage and scalloping phenomena, windowing, zero padding.

Finite and infinite impulse-response filters.
Properties of filters, implementation forms, window-based FIR design,
use of frequency-inversion to obtain high-pass filters, use of
modulation to obtain band-pass filters, FFT-based convolution,
polynomial representation, z-transform, zeros and poles, use of
analog IIR design techniques (Butterworth, Chebyshev I/II, elliptic
filters).

Random sequences and noise.
Random variables, stationary processes, autocorrelation,
crosscorrelation, deterministic crosscorrelation sequences, filtered
random sequences, white noise, exponential averaging.

Correlation coding.
Random vectors, dependence versus correlation, covariance,
decorrelation, matrix diagonalisation, eigen decomposition,
Karhunen-Loève transform, principal/independent component
analysis. Relation to orthogonal transform coding using fixed basis
vectors, such as DCT.

Lossy versus lossless compression.
What information is discarded by human senses and can be eliminated by
encoders? Perceptual scales, masking, spatial resolution, colour
coordinates, some demonstration experiments.

be able to apply basic properties of
time-invariant linear systems

understand sampling, aliasing, convolution,
filtering, the pitfalls of spectral estimation

be able to explain the above in time and frequency domain
representations

be competent to use filter-design software

be able to visualise and discuss digital filters in the z-domain

be able to use the FFT for convolution, deconvolution, filtering

be able to implement, apply and evaluate simple
DSP applications in MATLAB

apply transforms that reduce correlation between several
signal sources

understand and explain limits in human perception that are
exploited by lossy compression techniques

provide a good overview of the principles and characteristics
of several widely-used compression techniques and standards
for audio-visual signals

Recommended reading

* Lyons, R.G. (2004). Understanding digital signal processing. Prentice-Hall (2nd ed.).
Oppenheim, A.V. & Schafer R.W. (1999). Discrete-time digital signal processing. Prentice-Hall (2nd ed.).
Stein, J. (2000). Digital signal processing - a computer science perspective. Wiley.
Salomon, D. (2002). A guide to data compression methods. Springer.