# EE2S31 Signal processing

Topics: Digital signal processing; stochastic processes

Signal processing plays an important role in many applications, such as consumer electronics (mp3 player, mobile phone, CD player, TV (HD)), radar and medical applications. This course covers two topics: an introduction into random signals (processes), and a first course on digital signal processing (following the Signals and Systems course EE2L11).

In this course the following topics are discussed:

Digital signal processing

The part on signal processing considers in particular one-dimensional signals and discusses digital filter design, filter structures, the DFT spectral analysis, filter implementation, and multirate filters.

1. Repetition ((discrete-time) signal processing, poles and zeros, filter functions)
2. Discrete Fourier transform (frequency domain sampling, properties, convolution using DFT (FFT))
3. Spectral analysis
4. Sampling and reconstruction
5. Time Discrete filter structures
6. Digital Filter Design
7. Multirate filters
8. Quantization and rounding errors

Stochastic processes

The part on stochastic processes introduces the concept of stochastic models and random processes to describe systems and signals that are not deterministic in nature.

1. Pairs of random variables
2. Random vectors & conditional probability models
3. Sums of random variables,
4. Derived random variables
5. moment generating function
6. central limit theorem.
7. Deviation of RVs from its expected value:Markov ineq., Chebyshev ineq. and the Chernoff bound.
8. Sample mean, unbiased estimators, consistency.
9. Estimation of Random variables, blind estimation, conditional estimation, MMSE, MAP and ML estimators.
10. Stochastic processes.
11. Estimation of autocorrelation functions, ergodicity, the autocorrelation function & signal processing for WSS signals.
12. The autocorrelation function & signal processing, PSD, CPSD & frequency domain relationships.

## Teachers

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

Array signal processing; Signal processing for communications

Biomedical signal processing, Tensor decompositions

### Details

Credits: 5 EC 0/0/0/6 Alle-Jan van der Veen