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Signals and Systems

**Course Code**: B82006Y

**Course Name**: Signals and Systems

**Credits**: 3.0

**Level**: Undergraduate

**Pre-requisite**: Calculus, Linear algebra, Mathematical physical equation, Fundamentals of Electronic Circuits

**Lecture Time**: 15 weeks, 2 session/week, 2 hours/session

**Instructors**:

Prof. Zhi-bei Huang, University of Chinese Academy of Sciences

A.P. Fei Qin, University of Chinese Academy of Sciences

**Course Description**

This course is a required course for undergraduate students of Electronic Information Engineering. The basic concepts and basic analysis methods of signal and system theory are introduced, mainly focused on how to establish the mathematical model of signal and system, as well as how to solve and analyze the performance of the system and the output signal of the system through the mathematical analysis of the time domain and the transform domain. The results are interpreted by physics and endowed with physical meaning. Through this course, students should master the basic concepts and basic operations, and be flexible in their application.

**Topics and Schedule**

- Introduction (4 hrs)

1.1 Description, classification and typical examples of signals

1.2 Operation of signals

1.3 Models and classifications of systems

1.4 system analysis methods

- Time domain analysis of continuous time system (5 hrs)

2.1 The establishment and solution of differential equation

2.2 Definition and solution of zero input response and zero state response

2.3 Impulse response and step response

2.4 Definition and calculation of convolution

- Fourier transform and its application (13 hrs)

3.1 Fourier series of periodic signals

3.2 Fourier transform and spectral density function of aperiodic signals.

3.3 The properties and operations of Fourier transform

3.4 Fourier transform of periodic signals

3.5 Sampling theorem

3.6 Application of Fourier analysis for continuous time system

- Laplace Transform (8 hrs)

4.1 Laplace transform and its inverse transformation

4.2 The properties and operations of Laplace transformation

4.3 Laplace transform Solution of linear system

4.4 System function and impulse response

4.5 Laplace transform of periodic signal

4.6 S domain analysis and system zero-pole-analysis

4.7 Bilateral Laplace transform

4.8 Relationship between Laplace transform and Fourier transform

- Vector space analysis (5 hrs)

5.1 Orthogonal decomposition of signals

5.2 Parseval's theorem, energy spectrum and power spectrum

5.3 Correlation coefficient and correlation function, correlation and convolution, correlation theorem

5.4 Match filter

- Time domain analysis of discrete time systems (5 hrs)

6.1 Classification and operation of discrete time signals

6.2 Mathematical model and solution of discrete time systems

6.3 Unit sample response

6.4 Definition, property and operation of discrete convolution

- Z transform analysis of discrete time signals and systems (12 hrs)

7.1 Definition of Z transform and its inverse transform，region of convergent

7.2 The properties of Z transform

7.3 The relationship between Z transform and Laplace transform

7.4 Z transformation solution of difference equation

7.5 System function and frequency response

7.6 DTFT, DFT and FFT

7.7 Basic principles and structures of filter

- State equation analysis of the system (6 hrs)

8.1 Establishment and solution of system state equation

8.2 The establishment, solution and performance analysis of S domain flow graph

8.3 The establishment, solution and performance analysis of Z domain flow graph

8.4 Controllability and observability

- Overview and summary (2 hrs)

**Grading**

A weekly homework will be given during the 15 weeks of the class. The homework will be graded and their scores will count for 15% of the total. Course experiment counts for 15%. Mid-term and final examination count for 20% and 50% respectively.

**Textbook**

Jun-li Zheng, Signals and Systems, 3st ed., Higher Education Press, 2011.

**References**

[1] Alan V. Oppenheim，Alan S.Willsky，S.Hamid Nawab, Signals and Systems, 2st ed., Electronic Industry Press, 2013.

[2] Simon Haykin, Barry Van Veen, Signals and Systems, 2st ed., Electronic Industry Press, 2013.

**Course Website: **http://sep.ucas.ac.cn/portal/site/16/801