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Signals – continuously and discretely indexed signals, important signal types, frequency-domain analysis (Fourier, Laplace and Z transforms), nonlinear transformations and harmonics, sampling;
Systems – viewing differential / difference equations as systems that process signals, the notions of input, output and internal signals, block diagrams (series, parallel and feedback connections), properties of input-output models (causality, delay, stability, gain, shift-invariance, linearity), transient and steady state behaviour;
Linear time-invariant systems – continuous and discrete impulse response; convolution operation, transfer functions and frequency response, time-domain interpretation of stable and unstable poles and zeros, state-space models (construction from high-order ODEs, canonical forms, state transformations and stability), and the discretisation of models for systems of continuously indexed signals.
- Sinusoids and Complex Numbers
- Spectrum Representation and Fourier Series
- Sampling and Aliasing
- FIR Filters
- Frequency Response of FIR Filters
- Discrete Time Fourier Transform
- Discrete Fourier Transform
- z-Transforms
- IIR Filters
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