Department of Computer Science and Technology

Course pages 2021–22

# Digital Signal Processing

Principal lecturer: Dr Ali Ozgur Yontem
Taken by: Part II CST 75%
Term: Michaelmas
Hours: 16
Format: In-person lectures
Class limit: max. 24 students
Prerequisites: Mathematical Methods I and III from the NST Mathematics course (or equivalent), LaTeX and MATLAB (recommended)
timetable

## Aims

This course teaches the basic signal-processing principles necessary to understand many modern high-tech systems, with application examples focussing on audio processing, image coding, communication systems and software-defined radio. Students will gain practical experience from numerical experiments in programming assignments (in MATLAB, NumPy or Julia).

## Lectures

• Signals and systems. Discrete sequences and systems: types and properties. Amplitude, phase, frequency, modulation, decibels, root-mean square. Linear time-invariant systems, convolution. Some examples from electronics, optics and acoustics.
• Phasors. Eigen functions of linear time-invariant systems. Review of complex arithmetic. Phasors as orthogonal base functions.
• Fourier transform. Forms and properties of the Fourier transform. Convolution theorem. Rect and sinc.
• Dirac’s delta function. Fourier representation of sine waves, impulse combs in the time and frequency domain. Amplitude-modulation in the frequency domain.
• Discrete sequences and spectra. Sampling of continuous signals, periodic signals, aliasing, interpolation, sampling and reconstruction, sample-rate conversion, oversampling, spectral inversion.
• Discrete Fourier transform. Continuous versus discrete Fourier transform, symmetry, linearity, FFT, real-valued FFT, FFT-based convolution, zero padding, FFT-based resampling, deconvolution exercise.
• Spectral estimation. Short-time Fourier transform, leakage and scalloping phenomena, windowing, zero padding. Audio and voice examples. DTFM exercise.
• 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.
• Infinite impulse-response filters. Sequences as polynomials, z-transform, zeros and poles, some analog IIR design techniques (Butterworth, Chebyshev I/II, elliptic filters, second-order cascade form).
• Band-pass signals. Band-pass sampling and reconstruction, IQ up and down conversion, superheterodyne receivers, software-defined radio front-ends, IQ representation of AM and FM signals and their demodulation.
• Digital communication. Pulse-amplitude modulation. Matched-filter detector. Pulse shapes, inter-symbol interference, equalization. IQ representation of ASK, BSK, PSK, QAM and FSK signals. [2 hours]
• Random sequences and noise. Random variables, stationary and ergodic processes, autocorrelation, cross-correlation, deterministic cross-correlation sequences, filtered random sequences, white noise, periodic averaging.
• Correlation coding. Entropy, delta coding, linear prediction, dependence versus correlation, random vectors, 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, audio masking, spatial resolution, colour coordinates, some demonstration experiments.
• Quantization, image coding standards. Uniform and logarithmic quantization, A/µ-law coding, dithering, JPEG.

## Objectives

• 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;
• familiarity with a number of signal-processing concepts used in digital communication systems

## Assessment - Part II students

• Three homework programming assignments, each comprising 20% of the mark
• Written take-home assignment, comprising 40% of the total mark.