This course introduces the basic tools of Fourier analysis of signals (both in continuous and discrete time), the analysis of linear systems and the representation of signals from their samples.
- Signals: properties and classification.
- Systems: properties and classification.
- Linear and time-invariant systems (LTI).
PART 1: Fourier series (FS) representation of periodic signals
- Response of LTI systems to complex exponentials.
- FS representation of continuous-time signals. Properties.
- FS representation of discrete-time signals. Properties.
PART 2: Fourier transform (FT)
- FT of signals in continuous time. Properties and examples.
- Linear systems characterised by ordinary differential equations.
- FT of discrete time signals. Properties and examples.
- Linear systems characterised by difference equations.
PART 3: Representation of signals from their samples
- The sampling theorem.
- Interpolation and decimation.
- Discrete-time processing of continuous-time signals.
- The discrete Fourier transform.
PART 4: Z Transform (ZT)
- The ZT.
- Region of convergence.
- Analysis of LTI systems.