Course material 2010–11
Digital Signal Processing
Lecturer: Dr M.G. Kuhn
No. of lectures: 12
Prerequisite courses: Probability, Mathematical Methods for Computer Science
The last lecture of Unix Tools (MATLAB introduction) is a prerequisite for the practical exercises. Some of the material covered in Floating-Point Computation will also help in this course.
Aims
This course teaches the basic signal-processing principles necessary to understand many modern high-tech systems, with digital-communications examples. 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.
- Phasors. Eigen functions of linear time-invariant systems.
Review of complex arithmetic. Some examples from electronics, optics
and acoustics.
- Fourier transform. 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).
- Digital modulation. IQ representation of band-pass signals,
in particular AM, FM, MSK, QAM, and OFDM signals. Clock recovery,
symbol detection, matched filter, software-defined radio.
- 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
diagonalization, eigen decomposition, Karhunen-Loève transform,
principal 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.
- Quantization, image coding standards. A/
-law coding, delta coding, JPEG.
Objectives
By the end of the course students should be able to
- apply basic properties of time-invariant linear
systems;
- understand sampling, aliasing, convolution, filtering, the
pitfalls of spectral estimation;
- explain the above in time and frequency domain representations;
- use filter-design software;
- visualize and discuss digital filters in the z-domain;
- use the FFT for convolution, deconvolution, filtering;
- implement, apply and evaluate simple DSP applications in MATLAB;
- apply transforms that reduce correlation between several signal
sources;
- understand the basic principles of several widely-used
modulation and image coding techniques.
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.