Chapter 1: Deterministic signals

  1. Definitions
  2. Signal processing
  3. Signal classification 3.1 Phenomenological classification 3.2 Morphological classification 3.3 Symmetric classification
  4. Energy and power 4.1 Energy x(t) 4.2 Power of x(t)
  5. Some common deterministic signals 5.2 Unit scale function 5.3 Ramp function 5.5 Triangle function 5.6 Dirac impulse 5.7 Dirac’s Comb 5.8 Cardinal sine function
  6. Signal Operations 6.1 Time reversal 6.2 Change of scale (compression/dilatation) / Scaling 6.3 Convolution product
  7. Fourier series
  8. The Fourier Transform 8.1 Fourier transformation of functions 8.2 The inverse transform 8.3 Properties of the TF
  9. Parseval's theorem
  10. Questions

Chapter 2 :Sampling of analog signals

  1. Introduction
  2. Sampling 2.1 Definition 2.3 Shannon's theorem
  3. Reconstruction of an analog signal from its sampled version

Chapter 3: Discrete signals

  1. Definition
  2. Common discrete signals 2.1 Dirac impulse 2.2 Unit level 2.3 Rectangular window 2.4 Decreasing exponential
  3. Operations on discrete signals
  4. Energy and power of discrete signals
  5. Fourier transform of discrete-time signals (TFTD) 5.1 Definition 5.2 Periodicity 5.3 Examples from TFTD
  6. The inverse Fourier transform
  7. Poisson Formula
  8. Properties
  9. Parseval equality
  10. from TFTD to TFD
  11. ! FFT " : Fast Fourier Transform

Chapter 4:Random processes

  1. General
  2. Reminder on random variables
  3. Random signals
  4. Stationarity and ergodism
  5. Questions

Chapter 5:Signals and systems

  1. Linear and stationary systems 1.2 Linearity 1.3 Invariance over time 1.4 Memory 1.5 Causality 1.6 Stability 1.7 Impulse response 1.8 Index response
  2. The Z-transform 2.1 Definition 2.2 Cauchy criterion and the convergence region 2.3 Properties of the Z transform 2.4 Limit theorems 2.5 Table of Z Transformation of Usual Functions
  3. Inverse Z transform 3.1 Power series development 3.2 Development in partial fraction 3.3 Rational Z transform
  4. Representation of poles and zeros
  5. Stability of a discrete-time system
  6. Transformation de Hilbert
  7. Linear prediction 7.1 The prediction model 7.2 Linear Prediction for Speech Processing

Chapter 6:Synthesis of digital filters

  1. Filtering 1.2 Reminders on filtering theory 1.2.3 Synthesis of analog filters 1.2.4 Ideal filters
  2. Digital filters 2.1 Definition of a digital filter 2.2 Classification 2.3 Direct and transposed canonical structure
  3. Synthesis of a digital filter 3.1 Synthesis of FIR filters 3.2 Summary of R.I.I filters

Chapter 7: Introduction to spectral analysis and estimation

  1. What is spectral analysis?
  2. For what applications?
  3. What are the basic tools for spectral analysis?
  4. Spectral analysis of stochastic processes 4.1 Introduction 4.2 Useful informative signals 4.3 Noise and disturbances
  5. Spectrum of a random signal 5.1 Reminders 5.2 Power spectral density and the Wiener-Khintchine theorem
  6. Concepts of spectral estimation
  7. Parametric estimates

Annex A :canvas Annexe

 B : Fourier transform of usual signals Appendix

C:The discrete Fourier transform TFD Appendix

D:Taylor series Bibliography

Modifié le: mardi 7 mai 2024, 16:23