# Department of Computer Science and Technology

Course pages 2017–18

# Digital Signal Processing

Principal lecturer: Dr Markus Kuhn
Taken by: Part II
Past exam questions

No. of lectures: 12
Suggested hours of supervisions: 3
Prerequisite courses: Mathematical Methods I and III from the NST Mathematics course, Mathematical Methods for Computer Science, LaTeX and MATLAB (recommended).

## 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 and properties of the Fourier transform. Convolution theorem.

• Dirac’s delta function. Fourier representation of sine waves, impulse combs in the time and frequency domain.

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

• Digital modulation. IQ representation of band-pass signals, in particular AM, FM, PSK, and QAM signals.

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

• Spectral estimation. Short-time Fourier transform, leakage and scalloping phenomena, windowing, zero padding.

• Finite 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.

• Infinite impulse-response filters. Sequences as polynomials, z-transform, zeros and poles, some 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.

## 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;

• explain the basic principles of some widely-used modulation and image-coding techniques.