Signals and Systems Notes

520.214


0. Introduction

0.1 Introductory Comments
0.2 Complex-Arithmetic Background
0.3 Analysis Background

1. Signals

1.1 Mathematical Definitions of Signals
1.2 Elementary Operations on Signals
1.3 Elementary Operations on the Independent Variable  
1.4 Energy and Power Classifications  
1.5 Symmetry-Based Classifications of Signals
1.6 Additional Classifications of Signals
1.7 Discrete-Time Signals: Definitions, Classifications, and Operations

2. Continuous Time Signals

2.1 The Class of CT Exponential Signals
2.2 The Class of CT Singularity Signals
2.3 Linear Combination of Singularity Signals and Generalilzed Calculus

3. Discrete Time Signals

3.1 The Class of DT Exponential Signals
3.2 The Class of DT Singularity Signals  

4. Systems

4.1 Introduction to Systems
4.2 System Properties
4.3 Interconnections of Systems - Block Diagrams
 

5. Discrete Time LTI Systems

5.1 DT LTI Systems and Convolution  
5.2 Properties of Convolution - Interconnections of DT LTI Systems
5.3 DT LTI System Properties
5.4 Response to Singularity Signals  
5.5 Response to Exponentials (Eigenfunction Properties)  
5.6 DT LTI Systems Described by Linear Difference Equations

6. Continuous Time LTI Systems

6.1 CT LTI Systems and Convolution  
6.2 Properties of Convolution - Interconnections of CT LTI Systems  
6.3 CT LTI System Properties  
6.4 Response to Singularity Signals  
6.5 Response to Exponentials (Eigenfunction Properties)  
6.6 CT LTI Systems Described by Linear Differential Equations

7. Introduction to Signal Representation

7.1 Introduction to CT Signal Representation  
7.2 Orthogonality and Minimum ISE Representation  
7.3 Complex Basis Signals  
7.4 DT Signal Representation

8. Periodic CT Signal Representation (Fourier Series)

8.1 CT  Fourier Series
8.2 Real Forms, Spectra, Convergence  
8.3 Operations on Signals  
8.4 CT LTI Frequency Response and Filtering

9. Periodic DT Signal Representation (Fourier Series)

9.1 DT Fourier Series
9.2 Real Forms, Spectra, and Convergence
9.3 Operations on Signals
9.4 DT LTI Frequency Response and Filtering

10. Fourier Transform Representation for CT Signals

10.1 Introduction to CT Fourier Transform
10.2 Fourier Transform for Periodic Signals
10.3 Properties of Fourier Transform
10.4 Convolution Property and LTI Frequency Response
10.5 Additional Fourier Transform Properties
10.6 Inverse Fourier Transform
10.7 Fourier Transform and LTI Systems Described by Differential Equations
10.8 Fourier Transform and Interconnections of LTI Systems

11. Unilateral Fourier Transform


11.1 Introduction
11.2 Properties of the Unilateral Laplace Transform
11.3 Inverse Unilateral Laplace Transform
11.4 Systems Described by Differential Equations
11.5 Introduction to Laplace Transform Analysis of LTI Systems

12. Application to Circuits

12.1 Circuits with Zero Initial Conditions
12.2 Circuits with Nonzero Initial Conditions