# Signaalanalyse

## WB3230

### ECTS:

6### Responsible Instructor:

Dr.-Ing. S. Wahls (Sander)### Instructor:

dr.ing. R. Van de Plas (Raf)### Contact Hours / Week x/x/x/x:

0/0/4/0### Education Period:

3### Start Education:

3### Exam Period:

3### Course Language:

English### Expected prior knowledge:

WI2030WBMT Wiskunde 3 (Differentiaalvergelijkingen)WI2031WBMT Wiskunde 4 (Kansrekening en Statistiek)

WB2230 Systeem en Regeltechniek

WB2231 Project Mechatronica

### Course Contents:

This course treats the analysis, filtering and detection of signals influenced by linear time-invariant systems as they occur in typical mechanical and mechatronic applications. Signals will be considered in both deterministic and stochastic formulations. Special emphasis is put on discrete-time techniques that can be easily implemented in practice. The main topics of the course are:1. Elementary properties of signals and systems (even, odd, linear, stable, causal, linear-phase, group-delay, all-pass, minimum-phase)

2. Fourier and Hilbert transform, one and two-sided Laplace and Z-transforms

3. Bode plots and Bodes phase-gain relationship

4. Continuous-time low-pass filters

5. Modulation and demodulation

6. Analog-to-digital and digital-to-analog conversion

7. Design of discrete-time filters using windowing and impulse invariance

8. Elementary properties of random processes (i.i.d., w.s.s., joint w.s.s., independence); key indicators such as mean, auto and cross-correlation/covariance, and spectral densities

9. Identification of linear time-invariant discrete-time systems in the frequency domain

10. Discrete-time Wiener filtering (finite impulse response and non-causal)

11. Detection of discrete-time signals in Gaussian noise

### Study Goals:

Students can1. Evaluate if a signal or system possesses an elementary property; utilize these in simple problems; give examples that exhibit desired elementary properties

2. Compute Fourier, Laplace, z and Hilbert transforms, both directly and using transform pairs and properties

3. Sketch Bode plots for rational transfer functions

4. Determine the specifications of continuous-time low-pass filters from their frequency response; design low-pass filters that fulfill given specifications

5. Analyze typical modulation and demodulation schemes; add missing components

6. Evaluate the impact of A/D and D/A conversion schemes; choose sampling intervals

7. Design discrete-time filters using impulse invariance, windowing, and Wiener techniques

8. Evaluate if a random process possesses an elementary property; utilize them in simple problems; determine key indicators of random processes

9. Identify the frequency response of a linear time-invariant discrete-time system from actual measurements; specify the bias and the variance

10. Derive optimal detection rules for a known signal in Gaussian noise

### Education Method:

Lectures, problem sets and practice sessions (werkcolleges).### Literature and Study Materials:

- A.V. Oppenheim, A.S. Willsky and S. Hamid, Signals and Systems, Pearson New International Edition, 2nd ed, 2013.- A.V. Oppenheim and G. Verghese, Signals, Systems and Inference, Class Notes for 6.011: Introduction to Communication, Control and Signal Processing, MIT, Spring 2010. Available online: http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-011-introduction-to-communication-control-and-signal-processing-spring-2010/readings/

- For some parts of the lecture, external materials will be used. These materials will either be available online from within the network of TU Delft, or be provided via Blackboard.