Signals and systems. Discrete sequences and systems, their types and properties.
Linear time-invariant systems, convolution. Harmonic phasors are the eigen
functions of linear time-invariant systems. Review of complex arithmetic. Some
examples from electronics, optics and acoustics.
Fourier transform. Harmonic 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.
MATLAB: Some of the most important exercises in this course require writing small programs,
preferably in MATLAB (or a similar tool), which is available on PWF computers. A brief MATLAB
introduction was given in Part IB “Unix Tools”. Review that before the first exercise and also
read the “Getting Started” section in MATLAB’s built-in manual.
Finite and infinite impulse-response filters. Properties of filters, implementation
forms, window-based FIR design, use of frequency-inversion to obtain highpass
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 diagonalisation, eigen decomposition, Karhunen-Lo`eve transform,
principal/independent 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/μ-law coding, delta coding,
JPEG photographic still-image compression, motion compensation, MPEG
video encoding, MPEG audio encoding.