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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 Information Theory and Coding and 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 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.**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).**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 and audio coding standards.**A/-law coding, delta coding, JPEG photographic still-image compression.**MPEG standards.**Motion compensation, video coding, MP3.

**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
- be able to explain the above in time and frequency domain representations
- be competent to use filter-design software
- be able to visualize 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.

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