Syllabus:
Lecture component: Image Processing
Lecturer: MP
Hours: 20 Lectures with 4 interspersed problem classes
- 1 Introduction: definition of an image, digitisation, criteria for sampling
and quantization
- 2 Image transformations: matrix and vector representation of images,
orthonormal bases, linear operators, 2-D unitary transforms
- 3 singular value decomposition of matrices
- 4 Problem Class
- 5-6 Finite Fourier, Walsh, Hadamard and Haar transforms
- 7-8 Karhunen-Loeve transform and principal component analysis
- 9 Image enhancement: histogram modification, smoothing, sharpening
- 10 Problem Class
- 11 2-dim non-recursive filters & 2-D recursive filters: definition in terms of
z-transforms
- 12-14 Image restoration: prior knowledge required, inverse filtering, least
squares (Wiener) filtering, direct and constrained matrix inversion
- 15 Problem Class
- 16-17 Image segmentation: thresholding, choice of the optimal threshold,
split and merge algorithms, region growing
- 18-19 Edge detection: linear and non-linear methods, design of optimal
convolution filters, algorithms
- 20 Problem Class
Lecture component: Speech Analysis
Lecturer: EHSC
Hours: 10 Lectures with interspersed problem classes
- 1 Characteristics of speech signals: speech as statistical signal, mean,
variance, frequency range and dynamic range, quasi-stationarity,
voiced-unvoiced classification, periodicity in speech
- 2 Speech production: vocal tract description, source-filter model, origin
of periodicity, formants and anti-resonances in terms of physical model,
all-pole digital model of vocal tract, relationship between physical
model and phonemes
- 3 Speech perception: the structure of the ear, frequency and amplitude
response of ear
- 4-5 Signal processing techniques: auto-correlation of speech signal, pitch
estimation with low-pass filter, Fourier transform applied to speech,
spectral properties of speech signal, window length, resolution, power
spectrum, characteristics of voiced and unvoiced speech, spectral shape,
formants and anti-resonances, fine spectral structure, harmonics, phase
spectrum for speech, need for phase unwrapping
- 6-7 Speech analysis: linear prediction, definition as weighted sum of past
input/output samples, all-pole source filter, minimising mean square
error, the Yule-Walker equations, auto-correlation solution, Durbins
algorithm, covariance solution, the synthesis filter, spectral envelope
matching, prediction gain, error as prediction order, spectral flatness
measure, stability considerations
- 8 Inverse filtering of speech signal: separating source from excitation,
vocal tract response, formant estimation, the residual-pitch estimation,
robust linear prediction
- 9-10 Cepstral deconvolution: definition of real cepstrum, transforming
convolution to sum by non-linear operation, the complex logarithm,
the complex cepstrum, the frequency unit, pitch estimation via the
cepstrum, formant estimation via the cepstrum, comparison of spectral
envelope with that derived from linear prediction