# EE2S11 Signals and systems

Topics: Theory of signal transformations and LTI systems
Starting from complex function theory, the course presents the theory of signal transformations and linear time-invariant systems, preparing for courses on signal processing, systems theory, and telecommunication.

### Part 1: continuous-time signals

• Linear time-invariant systems (LTI), eigenfunctions and eigenvalues of an LTI system, Dirac delta function, Heaviside unit step function. Convolution.
• Laplace transform, region of convergence. Properties. Convoluton and product, inverse transform.
• Periodic signals. Fourier series, line spectrum.
• Fourier transform (continuous time).
• Transformations of a pulse, sinc function, sign function, step function. Duality of the Fourier transform. Shift and modulation, Parseval's theorem.

### Part 2: discrete-time signals

• Ideal sampling. impulse train, periodic spectrum. Sampling theorem (Nyquist, Shannon). Ideal reconstruction
• Discrete signals and systems, convolution.
• Z-transform
• Realizations (direct form for FIR, IIR)
• Fourier transform (discrete time)
• Filter design (analog and digital), frequency transformations.

## Teachers

### prof.dr.ir. Alle-Jan van der Veen

Array signal processing; Signal processing for communications

### dr.ir. Rob Remis

Electromagnetic and acoustic wavefield modeling, imaging, and inversion