Component
École Nationale Supérieure d'Électrotechnique d'Électronique d'Informatique d'Hydraulique et des Télécommunications
Objectives
Two parts in this course: 1) Introduce theoretical tools for signal processing, 2) Digital signal processing (implementation).
Objectives for the first part (theoretical tools) :
- Understand the different classes of deterministic and random signals with the definitions of the autocorrelation function and the power spectrum density
- Understand the concept of linear filtering and the Wiener Lee relationships
- Understand the principles of sampling and the Shannon theorem
- Understand the interest of non-linear transformations applied to deterministic and random signals and how to apply Price’s theorem
Objectives for the second part (digital signal processing) :
- To be able to correctly sample a signal and to generate simple digital signals.
- To be able to estimate digitally the aucorrelation function and to perform a frequency representation (Fourier transform, Power Spectral Density) of a signal.
- To be able to determine impulse responses for simple filters (Finite Impulse Response, or FIR, filters) and to synthesize them, meaning to choose their parameters to meet some requirements.
- To be able to filter a signal and to analyze the obtained result.
Description
For the first part (theoretical tools) :
- Autocorrelation and power spectral density
- Sampling
- Linear Filtering
- Non-linear transformations and Price’s theorem
For the second part (digital signal processing) :
- Sampling and quantization.
- From theoretical to digital tools for the autocorrelation function and the Fourier transform : what are the approximations to be done ? what are their consequences ?
- Digital filters (FIR and IIR) and FIR synthesis.
Pre-requisites
Bases on deterministic signals (energy, power, periodicity)
Random variables and vectors