Ve216 LECTURE NOTES
Dianguang Ma Spring 2009
Course Information
Code: Ve216 Credits: 4 Prerequisite: Applied Calculus Required Textbook: Signals and Systems, 2/e, by Simon Haykin and Barry Van Veen, Wiley, 0471-37851-8. Lecturer: Dianguang MA TA: Hao WAN
Ve216 Lecture Notes
Dianguang Ma Spring 2009
The Discrete-Time Unit Step Function Definition
1, n 0 u[n] = 0, n < 0
The Discrete-Time Unit Step Function
The Continuous-Time Unit Step Function
Definition
1, t > 0 u (t ) = 0, n < 0
Figure 1.38 (p. 44)
Con
Ve216 Lecture Notes
Dianguang Ma Spring 2009
2.1 Introduction
In this chapter, we examine several methods for describing the relationship between the input and output signals of linear time-invariant (LTI) systems in time domain.
Convolution sum/integra
Ve216 Lecture Notes
Dianguang Ma Spring 2009
2.9 Differential/Difference Equations
An important class of continuous-time/discretetime systems is that for which the input and output are related through a linear constantcoefficient differential/difference
Ve216 Lecture Notes
Dianguang Ma Spring 2009
Chapter 3
Fourier Representations of Signals and LTI Systems
3.1 Introduction
In this chapter, we represent a signal as a weighted superposition of complex sinusoids. If such a signal is applied to an LTI syst
Ve216 Lecture 10
Dianguang Ma Spring 2008
Chapter 3 (Part II)
Fourier Representations of signals and LTI Systems
3.5 The Fourier Series
Example 3.14 Square-wave partial-sum approximation: In 1898, an American physicist, Albert Michelson, constructed a ha
Ve216 Lecture Notes
Dianguang Ma Spring 2009
Chapter 3 (Part III)
Fourier Representations of Signals and LTI Systems
3.6 The Discrete-Time Fourier Transform The discrete-time Fourier transform (DTFT) is used to represent a discretetime nonperiodic signal
Ve216 Lecture Notes
Dianguang Ma Spring 2009
Chapter 3 (Part IV)
Fourier Representations of Signals and LTI Systems
3.8 Periodicity Properties of Fourier Rrepresentations In general, representations that are continuous in one domain are nonperiodic in the
Ve216 Lecture Notes
Dianguang Ma Spring 2009
Chapter 4
Applications of Fourier Representations to Mixed Signal Classes
4.1 Introduction
When we use Fourier methods to (1) analyze the interaction between signals and systems or (2) numerically evaluate pro
Ve216 Lecture Notes
Dianguang Ma Spring 2009
Chapter 6 (Part I)
Representing Signals by Using Continuous-Time Complex Exponentials: The Laplace Transform
6.1 Introduction
The Laplace transform is a generalization of the continuous-time Fourier transform.
Ve216 Lecture Notes
Dianguang Ma Spring 2009
Chapter 6 (Part II)
Representing Signals by Using Continuous-Time Complex Exponentials: The Laplace Transform
6.3 The Unilateral Laplace Transform
There are many applications of Laplace transforms in which it
Ve216 Lecture Notes
Dianguang Ma Spring 2009
Chapter 7 (Part I)
Representing Signals by Using Discrete-Time Complex Exponentials: The z-Transform
7.1 Introduction
The z-transform is a generalization of the DTFT. It provides a broader characterization of
Ve216 Lecture Notes
Dianguang Ma Spring 2009
Chapter 7 (Part II)
Representing Signals by Using Discrete-Time Complex Exponentials: The z-transform
7.6 The Transfer Function
Having defined the transfer function as the ztransform of the impulse response, w