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Appendix. Useful Formulas
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Appendix. Useful Formulas
by Luis Chaparro
Signals and Systems using MATLAB
Cover image
Table of Contents
Front Matter
Copyright
Dedication
Preface
Acknowledgements
Chapter 0. From the Ground Up!
0.1. Signals and Systems and Digital Technologies
0.2. Examples of Signal Processing Applications
0.3. Analog or Discrete?
0.4. Complex or Real?
0.5. Soft Introduction to MATLAB
Chapter 1. Continuous-Time Signals
1.1. Introduction
1.2. Classification of Time-Dependent Signals
1.3. Continuous-Time Signals
1.4. Representation Using Basic Signals
1.5. What Have We Accomplished? Where Do We Go from Here?
Chapter 2. Continuous-Time Systems
2.1. Introduction
2.2. System Concept
2.3. LTI Continuous-Time Systems
2.4. What Have We Accomplished? Where Do We Go from Here?
Chapter 3. The Laplace Transform
3.1. Introduction
3.2. The Two-Sided Laplace Transform
3.3. The One-Sided Laplace Transform
3.4. Inverse Laplace Transform
3.5. Analysis of LTI Systems
3.6. What have We Accomplished? Where Do We Go from Here?
Chapter 4. Frequency Analysis
4.1. Introduction
4.2. Eigenfunctions Revisited
4.3. Complex Exponential Fourier Series
4.4. Line Spectra
4.5. Trigonometric Fourier Series
4.6. Fourier Coefficients from Laplace
4.7. Convergence of the Fourier Series
4.8. Time and Frequency Shifting
4.9. Response of LTI Systems to Periodic Signals
4.10. Other Properties of the Fourier Series
4.11. What Have We Accomplished? Where Do We Go from Here?
Chapter 5. Frequency Analysis
5.1. Introduction
5.2. From the Fourier Series to the Fourier Transform
5.3. Existence of the Fourier Transform
5.4. Fourier Transforms from the Laplace Transform
5.5. Linearity, Inverse Proportionality, and Duality
5.6. Spectral Representation
5.7. Convolution and Filtering
5.8. Additional Properties
5.9. What have we Accomplished? What is Next?
Chapter 6. Application to Control and Communications
6.1. Introduction
6.2. System Connections and Block Diagrams
6.3. Application to Classic Control
6.4. Application to Communications
6.5. Analog Filtering
6.6. What have we accomplished? What is next?
Chapter 7. Sampling Theory
7.1. Introduction
7.2. Uniform Sampling
7.3. The Nyquist-Shannon Sampling Theorem
7.4. Practical Aspects of Sampling
7.5. What Have We Accomplished? Where Do We Go from Here?
Chapter 8. Discrete-Time Signals and Systems
8.1. Introduction
8.2. Discrete-Time Signals
8.3. Discrete-Time Systems
8.4. What have we accomplished? Where do we go from here?
Chapter 9. The Z-Transform
9.1. Introduction
9.2. Laplace Transform of Sampled Signals
9.3. Two-Sided Z-Transform
9.4. One-Sided Z-Transform
9.5. One-Sided Z-Transform Inverse
9.6. What Have We Accomplished? Where Do We Go from Here?
Chapter 10. Fourier Analysis of Discrete-Time Signals and Systems
10.1. Introduction
10.2. Discrete-Time Fourier Transform
10.3. Fourier Series of Discrete-Time Periodic Signals
10.4. Discrete Fourier Transform
10.5. What Have We Accomplished? Where Do We Go from Here?
Chapter 11. Introduction to the Design of Discrete Filters
11.1. Introduction
11.2. Frequency-Selective Discrete Filters
11.3. Filter Specifications
11.4. IIR Filter Design
11.5. FIR Filter Design
11.6. Realization of Discrete Filters
11.7. What have we Accomplished? Where do we go from here?
Chapter 12. Applications of Discrete-Time Signals and Systems
12.1. Introduction
12.2. Application to Digital Signal Processing
12.3. Application to Sampled-Data and Digital Control Systems
12.4. Application to Digital Communications
12.5. What Have We Accomplished? Where Do We Go from Here?
Appendix. Useful Formulas
References
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Appendix. Useful Formulas
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