Fourier Analysis.
Ceschi, Roger.
Fourier Analysis. - 1st ed. - 1 online resource (271 pages)
Cover -- Title Page -- Copyright -- Contents -- Preface -- 1. Fourier Series -- 1.1. Theoretical background -- 1.1.1. Orthogonal functions -- 1.1.2. Fourier Series -- 1.1.3. Periodic functions -- 1.1.4. Properties of Fourier series -- 1.1.5. Discrete spectra. Power distribution -- 1.2. Exercises -- 1.2.1. Exercise 1.1. Examples of decomposition calculations -- 1.2.2. Exercise 1.2 -- 1.2.3. Exercise 1.3 -- 1.2.4. Exercise 1.4 -- 1.2.5. Exercise 1.5 -- 1.2.6. Exercise 1.6. Decomposing rectangular functions -- 1.2.7. Exercise 1.7. Translation and composition of functions -- 1.2.8. Exercise 1.8. Time derivation of a function -- 1.2.9. Exercise 1.9. Time integration of functions -- 1.2.10. Exercise 1.10 -- 1.2.11. Exercise 1.11. Applications in electronic circuits -- 1.3. Solutions to the exercises -- 1.3.1. Exercise 1.1. Examples of decomposition calculations -- 1.3.2. Exercise 1.2 -- 1.3.3. Exercise 1.3 -- 1.3.4. Exercice 1.4 -- 1.3.5. Exercise 1.5 -- 1.3.6. Exercise 1.6 -- 1.3.7. Exercise 1.7. Translation and composition of functions -- 1.3.8. Exercise 1.8. Time derivation of functions -- 1.3.9. Exercise 1.9. Time integration of functions -- 1.3.10. Exercise 1.10 -- 1.3.11. Exercise 1.11 -- 2. Fourier Transform -- 2.1. Theoretical background -- 2.1.1. Fourier transform -- 2.1.2. Properties of the Fourier transform -- 2.1.3. Singular functions -- 2.1.4. Fourier transform of common functions -- 2.1.5. Calculating Fourier transforms using the Dirac impulse method -- 2.1.6. Fourier transform of periodic functions -- 2.1.7. Energy density -- 2.1.8. Upper limits to the Fourier transform -- 2.2. Exercises -- 2.2.1. Exercise 2.1 -- 2.2.2. Exercise 2.2 -- 2.2.3. Exercise 2.3 -- 2.2.4. Exercise 2.4 -- 2.2.5. Exercise 2.5 -- 2.2.6. Exercise 2.6 -- 2.2.7. Exercise 2.7 -- 2.2.8. Exercise 2.8 -- 2.2.9. Exercise 2.9 -- 2.2.10. Exercise 2.10. 2.2.11. Exercise 2.11 -- 2.2.12. Exercise 2.12 -- 2.2.13. Exercise 2.13 -- 2.2.14. Exercise 2.14 -- 2.2.15. Exercise 2.15 -- 2.2.16. Exercise 2.16 -- 2.2.17. Exercise 2.17 -- 2.3. Solutions to the exercises -- 2.3.1. Exercise 2.1 -- 2.3.2. Exercise 2.2 -- 2.3.3. Exercise 2.3 -- 2.3.4. Exercise 2.4 -- 2.3.5. Exercise 2.5 -- 2.3.6. Exercise 2.6 -- 2.3.7. Exercise 2.7 -- 2.3.8. Exercise 2.8 -- 2.3.9. Exercise 2.9 -- 2.3.10. Exercise 2.10 -- 2.3.11. Exercise 2.11 -- 2.3.12. Exercise 2.12 -- 2.3.13. Exercise 2.13 -- 2.3.14. Exercise 2.14 -- 2.3.15. Exercice 2.15 -- 2.3.16. Exercise 2.16 -- 2.3.17. Exercise 2.17 -- 3. Laplace Transform -- 3.1. Theoretical background -- 3.1.1. Definition -- 3.1.2. Existence of the Laplace transform -- 3.1.3. Properties of the Laplace transform -- 3.1.4. Final value and initial value theorems -- 3.1.5. Determining reverse transforms -- 3.1.6. Approximation methods -- 3.1.7. Laplace transform and differential equations -- 3.1.8. Table of common Laplace transforms -- 3.1.9. Transient state and steady state -- 3.2. Exercise instruction -- 3.2.1. Exercise 3.1 -- 3.2.2. Exercise 3.2 -- 3.2.3. Exercise 3.3 -- 3.2.4. Exercise 3.4 -- 3.2.5. Exercise 3.5 -- 3.2.6. Exercise 3.6 -- 3.2.7. Exercise 3.7 -- 3.2.8. Exercise 3.8 -- 3.2.9. Exercise 3.9 -- 3.2.10. Exercise 3.10 -- 3.3. Solutions to the exercises -- 3.3.1. Exercise 3.1 -- 3.3.2. Exercise 3.2 -- 3.3.3. Exercise 3.3 -- 3.3.4. Exercise 3.4 -- 3.3.5. Exercise 3.5 -- 3.3.6. Exercise 3.6 -- 3.3.7. Exercise 3.7 -- 3.3.8. Exercise 3.8 -- 3.3.9. Exercise 3.9 -- 3.3.10. Exercise 3.10 -- 4. Integrals and Convolution Product -- 4.1. Theoretical background -- 4.1.1. Analyzing linear systems using convolution integrals -- 4.1.2. Convolution properties -- 4.1.3. Graphical interpretation of the convolution product -- 4.1.4. Convolution of a function using a unit impulse. 4.1.5. Step response from a system -- 4.1.6. Eigenfunction of a convolution operator -- 4.2. Exercises -- 4.2.1. Exercise 4.1 -- 4.2.2. Exercise 4.2 -- 4.2.3. Exercise 4.3 -- 4.2.4. Exercise 4.4 -- 4.2.5. Exercise 4.5 -- 4.2.6. Exercise 4.6 -- 4.3. Solutions to the exercises -- 4.3.1. Exercise 4.1 -- 4.3.2. Exercise 4.2 -- 4.3.3. Exercise 4.3 -- 4.3.4. Exercise 4.4 -- 4.3.5. Exercise 4.5 -- 4.3.6. Exercise 4.6 -- 5. Correlation -- 5.1. Theoretical background -- 5.1.1. Comparing signals -- 5.1.2. Correlation function -- 5.1.3. Properties of correlation functions -- 5.1.4. Energy of a signal -- 5.2. Exercises -- 5.2.1. Exercise 5.1 -- 5.2.2. Exercise 5.2 -- 5.2.3. Exercise 5.3 -- 5.2.4. Exercise 5.4 -- 5.2.5. Exercice 5.5 -- 5.2.6. Exercice 5.6 -- 5.2.7. Exercise 5.7 -- 5.2.8. Exercice 5.8 -- 5.2.9. Exercise 5.9 -- 5.2.10. Exercise 5.10 -- 5.2.11. Exercise 5.11 -- 5.2.12. Exercise 5.12 -- 5.2.13. Exercise 5.13 -- 5.2.14. Exercise 5.14 -- 5.3. Solutions to the exercises -- 5.3.1. Exercise 5.1 -- 5.3.2. Exercice 5.2 -- 5.3.3. Exercise 5.3 -- 5.3.4. Exercice 5.4 -- 5.3.5. Exercise 5.5 -- 5.3.6. Exercise 5.6 -- 5.3.7. Exercise 5.7 -- 5.3.8. Exercise 5.8 -- 5.3.9. Exercise 5.9 -- 5.3.10. Exercise 5.10 -- 5.3.11. Exercise 5.11 -- 5.3.12. Exercise 5.12 -- 5.3.13. Exercise 5.13 -- 5.3.14. Exercise 5.14 -- 6. Signal Sampling -- 6.1. Theoretical background -- 6.1.1. Sampling principle -- 6.1.2. Ideal sampling -- 6.1.3. Finite width sampling -- 6.1.4. Sample and hold (S/H) sampling -- 6.2. Exercises -- 6.2.1. Exercise 6.1 -- 6.2.2. Exercise 6.2 -- 6.2.3. Exercise 6.3 -- 6.2.4. Exercise 6.4 -- 6.2.5. Exercise 6.5 -- 6.2.6. Exercise 6.6 -- 6.2.7. Exercise 6.7 -- 6.2.8. Exercice 6.8 -- 6.3. Solutions to the exercises -- 6.3.1. Exercise 6.1 -- 6.3.2. Exercise 6.2 -- 6.3.3. Exercise 6.3 -- 6.3.4. Exercice 6.4 -- 6.3.5. Exercise 6.5 -- 6.3.6. Exercise 6.6. 6.3.7. Exercise 6.7 -- 6.3.8. Exercise 6.8 -- Bibliography -- Index -- Other titles from iSTE in Digital Signal and Image Processing -- EULA.
9781119372233
Fourier analysis.
Electronic books.
QA403.5.C473 2017
Fourier Analysis. - 1st ed. - 1 online resource (271 pages)
Cover -- Title Page -- Copyright -- Contents -- Preface -- 1. Fourier Series -- 1.1. Theoretical background -- 1.1.1. Orthogonal functions -- 1.1.2. Fourier Series -- 1.1.3. Periodic functions -- 1.1.4. Properties of Fourier series -- 1.1.5. Discrete spectra. Power distribution -- 1.2. Exercises -- 1.2.1. Exercise 1.1. Examples of decomposition calculations -- 1.2.2. Exercise 1.2 -- 1.2.3. Exercise 1.3 -- 1.2.4. Exercise 1.4 -- 1.2.5. Exercise 1.5 -- 1.2.6. Exercise 1.6. Decomposing rectangular functions -- 1.2.7. Exercise 1.7. Translation and composition of functions -- 1.2.8. Exercise 1.8. Time derivation of a function -- 1.2.9. Exercise 1.9. Time integration of functions -- 1.2.10. Exercise 1.10 -- 1.2.11. Exercise 1.11. Applications in electronic circuits -- 1.3. Solutions to the exercises -- 1.3.1. Exercise 1.1. Examples of decomposition calculations -- 1.3.2. Exercise 1.2 -- 1.3.3. Exercise 1.3 -- 1.3.4. Exercice 1.4 -- 1.3.5. Exercise 1.5 -- 1.3.6. Exercise 1.6 -- 1.3.7. Exercise 1.7. Translation and composition of functions -- 1.3.8. Exercise 1.8. Time derivation of functions -- 1.3.9. Exercise 1.9. Time integration of functions -- 1.3.10. Exercise 1.10 -- 1.3.11. Exercise 1.11 -- 2. Fourier Transform -- 2.1. Theoretical background -- 2.1.1. Fourier transform -- 2.1.2. Properties of the Fourier transform -- 2.1.3. Singular functions -- 2.1.4. Fourier transform of common functions -- 2.1.5. Calculating Fourier transforms using the Dirac impulse method -- 2.1.6. Fourier transform of periodic functions -- 2.1.7. Energy density -- 2.1.8. Upper limits to the Fourier transform -- 2.2. Exercises -- 2.2.1. Exercise 2.1 -- 2.2.2. Exercise 2.2 -- 2.2.3. Exercise 2.3 -- 2.2.4. Exercise 2.4 -- 2.2.5. Exercise 2.5 -- 2.2.6. Exercise 2.6 -- 2.2.7. Exercise 2.7 -- 2.2.8. Exercise 2.8 -- 2.2.9. Exercise 2.9 -- 2.2.10. Exercise 2.10. 2.2.11. Exercise 2.11 -- 2.2.12. Exercise 2.12 -- 2.2.13. Exercise 2.13 -- 2.2.14. Exercise 2.14 -- 2.2.15. Exercise 2.15 -- 2.2.16. Exercise 2.16 -- 2.2.17. Exercise 2.17 -- 2.3. Solutions to the exercises -- 2.3.1. Exercise 2.1 -- 2.3.2. Exercise 2.2 -- 2.3.3. Exercise 2.3 -- 2.3.4. Exercise 2.4 -- 2.3.5. Exercise 2.5 -- 2.3.6. Exercise 2.6 -- 2.3.7. Exercise 2.7 -- 2.3.8. Exercise 2.8 -- 2.3.9. Exercise 2.9 -- 2.3.10. Exercise 2.10 -- 2.3.11. Exercise 2.11 -- 2.3.12. Exercise 2.12 -- 2.3.13. Exercise 2.13 -- 2.3.14. Exercise 2.14 -- 2.3.15. Exercice 2.15 -- 2.3.16. Exercise 2.16 -- 2.3.17. Exercise 2.17 -- 3. Laplace Transform -- 3.1. Theoretical background -- 3.1.1. Definition -- 3.1.2. Existence of the Laplace transform -- 3.1.3. Properties of the Laplace transform -- 3.1.4. Final value and initial value theorems -- 3.1.5. Determining reverse transforms -- 3.1.6. Approximation methods -- 3.1.7. Laplace transform and differential equations -- 3.1.8. Table of common Laplace transforms -- 3.1.9. Transient state and steady state -- 3.2. Exercise instruction -- 3.2.1. Exercise 3.1 -- 3.2.2. Exercise 3.2 -- 3.2.3. Exercise 3.3 -- 3.2.4. Exercise 3.4 -- 3.2.5. Exercise 3.5 -- 3.2.6. Exercise 3.6 -- 3.2.7. Exercise 3.7 -- 3.2.8. Exercise 3.8 -- 3.2.9. Exercise 3.9 -- 3.2.10. Exercise 3.10 -- 3.3. Solutions to the exercises -- 3.3.1. Exercise 3.1 -- 3.3.2. Exercise 3.2 -- 3.3.3. Exercise 3.3 -- 3.3.4. Exercise 3.4 -- 3.3.5. Exercise 3.5 -- 3.3.6. Exercise 3.6 -- 3.3.7. Exercise 3.7 -- 3.3.8. Exercise 3.8 -- 3.3.9. Exercise 3.9 -- 3.3.10. Exercise 3.10 -- 4. Integrals and Convolution Product -- 4.1. Theoretical background -- 4.1.1. Analyzing linear systems using convolution integrals -- 4.1.2. Convolution properties -- 4.1.3. Graphical interpretation of the convolution product -- 4.1.4. Convolution of a function using a unit impulse. 4.1.5. Step response from a system -- 4.1.6. Eigenfunction of a convolution operator -- 4.2. Exercises -- 4.2.1. Exercise 4.1 -- 4.2.2. Exercise 4.2 -- 4.2.3. Exercise 4.3 -- 4.2.4. Exercise 4.4 -- 4.2.5. Exercise 4.5 -- 4.2.6. Exercise 4.6 -- 4.3. Solutions to the exercises -- 4.3.1. Exercise 4.1 -- 4.3.2. Exercise 4.2 -- 4.3.3. Exercise 4.3 -- 4.3.4. Exercise 4.4 -- 4.3.5. Exercise 4.5 -- 4.3.6. Exercise 4.6 -- 5. Correlation -- 5.1. Theoretical background -- 5.1.1. Comparing signals -- 5.1.2. Correlation function -- 5.1.3. Properties of correlation functions -- 5.1.4. Energy of a signal -- 5.2. Exercises -- 5.2.1. Exercise 5.1 -- 5.2.2. Exercise 5.2 -- 5.2.3. Exercise 5.3 -- 5.2.4. Exercise 5.4 -- 5.2.5. Exercice 5.5 -- 5.2.6. Exercice 5.6 -- 5.2.7. Exercise 5.7 -- 5.2.8. Exercice 5.8 -- 5.2.9. Exercise 5.9 -- 5.2.10. Exercise 5.10 -- 5.2.11. Exercise 5.11 -- 5.2.12. Exercise 5.12 -- 5.2.13. Exercise 5.13 -- 5.2.14. Exercise 5.14 -- 5.3. Solutions to the exercises -- 5.3.1. Exercise 5.1 -- 5.3.2. Exercice 5.2 -- 5.3.3. Exercise 5.3 -- 5.3.4. Exercice 5.4 -- 5.3.5. Exercise 5.5 -- 5.3.6. Exercise 5.6 -- 5.3.7. Exercise 5.7 -- 5.3.8. Exercise 5.8 -- 5.3.9. Exercise 5.9 -- 5.3.10. Exercise 5.10 -- 5.3.11. Exercise 5.11 -- 5.3.12. Exercise 5.12 -- 5.3.13. Exercise 5.13 -- 5.3.14. Exercise 5.14 -- 6. Signal Sampling -- 6.1. Theoretical background -- 6.1.1. Sampling principle -- 6.1.2. Ideal sampling -- 6.1.3. Finite width sampling -- 6.1.4. Sample and hold (S/H) sampling -- 6.2. Exercises -- 6.2.1. Exercise 6.1 -- 6.2.2. Exercise 6.2 -- 6.2.3. Exercise 6.3 -- 6.2.4. Exercise 6.4 -- 6.2.5. Exercise 6.5 -- 6.2.6. Exercise 6.6 -- 6.2.7. Exercise 6.7 -- 6.2.8. Exercice 6.8 -- 6.3. Solutions to the exercises -- 6.3.1. Exercise 6.1 -- 6.3.2. Exercise 6.2 -- 6.3.3. Exercise 6.3 -- 6.3.4. Exercice 6.4 -- 6.3.5. Exercise 6.5 -- 6.3.6. Exercise 6.6. 6.3.7. Exercise 6.7 -- 6.3.8. Exercise 6.8 -- Bibliography -- Index -- Other titles from iSTE in Digital Signal and Image Processing -- EULA.
9781119372233
Fourier analysis.
Electronic books.
QA403.5.C473 2017