**Course Name: Signals and Systems**

Course Number: 40220653

Program: Undergraduate program

Type: Required

Credits: 3

Term Offered: Spring

Prerequisite(s): Mathematics (Differential and Integral Calculus), Principles of Electric Circuits

Instructor(s): Weidong Liu, Chao Lu

Textbook(s):

**Weidong Liu, Foundation of Signal and System Alanysis, Tsinghua University Press, 2008.**

**Reference(s): **

**A. V. Oppenheim, Signals and Systems (Second edition), Prentice-Hall, 1997.**

**Course Description: **

** This course provides the students a fundamental understanding on the principles, concepts and applications of signal and system analysis. The class hour of 48 is suggested. It involves in the course 11 chapters: **

**(1)Introduction on signals and systems;**

**(2)Analysis of Continuous-Time Linear Time-Invariant (LTI) System;**

**(3)Analysis of Discrete-Time LTI System;**

**(4)The Fourier Series (FS) Representation of Continuous-Time Periodic Signals;**

**(5)The Continuous-Time Fourier Transform (FT);**

**(6)The Laplace Transform;**

**(7)The Discrete-Time Fourier Series (DFS);**

**(8)The Discrete-Time Fourier Transform (DTFT);**

**(9)The Z Transform;**

**(10)The Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT);**

**(11)Basic Introduction of Analog and Digital Filter.**

**Course Objectives and Outcomes: **

** Numbers in brackets are linked to department educational outcomes.**

**1.Students could master the basic concepts, principles and algorithms on signal and system analysis, and use the knowledge to solve the practical problems. [2, 5, 11]**

**2.Students could not only know the basic methods and the algorithms related to signal and system analysis, but also know how they were established. A deep understand is required so that the students could put forward their own new ideas to solve practical problems. [5, 11]**

**3.Training on the ability of abstract thinking. Although signals or systems can investigated through experiments by observing the related waveforms, the deep understanding of the signal and system analysis method mostly depends on abstract thinking ability because the transform on a signal usually makes it difficult to be observed. [1]**

** **

Course Topics:

**1.An introduction on signals and systems: Signal properties and important special signals; System properties and examples; Main analysis methods for signals and systems in time domain, frequency domain and complex frequency domain.**

**2.Analysis of Continuous-Time Linear Time-Invariant (LTI) System: System representation through differential equations; Input-output behavior; Unit impulse response; Convolution.**

**3.Analysis of Discrete-Time LTI System: System representation through difference equations; Input-output behavior; Unit impulse response; Convolution-sum.**

**4. The Fourier Series (FS) Representation of Continuous-Time Periodic Signals: Establishment of FS representation of continuous-time periodic signals based orthogonal decomposition of signals in finite time intervals.**

**5.The Continuous-Time Fourier Transform (FT): Establishment of FT of continuous-time absolute integrable signals based orthogonal decomposition of signals in infinite time intervals; Properties of FT; FT of continuous-time non-absolute integrable signals; FT of periodic signals: FT of impulse-train sampling and square-train sampling signals; Relations between FT and FS; System analysis in frequency domain based on FT; Frequency characterization of signals and systems.**

**6.The Laplace Transform: Establishment of The Laplace Transform; Properties of The Laplace Transform; Relation between The Laplace Transform and FT; System analysis using The Laplace Transform.**

**7.The Discrete-Time Fourier Series (DFS): Establishment of DFS representation of discrete-time periodic signals based orthogonal decomposition of discrete-time signals in finite discrete-time intervals; Relation between DFS and FS; Error analysis when using sampling and DFS calculation to gain FS of continuous-time periodic signals.**

**8.The Discrete-Time Fourier Transform (DTFT): Establishment of DTFT of discrete-time absolute summable signals based orthogonal decomposition of signals in infinite discrete-time intervals; Properties of DTFT; Relations between DTFT and FT for signals after and before sampling; Error analysis when using sampling and DFFT calculation to gain FT of continuous-time signals; Discrete-time system analysis in frequency domain based on DTFT; Frequency characterization of discrete-time signals and systems.**

**9.The Z Transform: Establishment of The Z Transform; Properties of The Z Transform; Relation between The Z Transform and DTFT; Relation between The Z Transform and The Laplace Transform for signals after and before sampling; Discrete-time system analysis using The Z Transform.**

**10.The Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT): Concept and definition of DFT algorithm; Relations between DFT and DFS as well as DTFT; Properties of DFT; Fast calculation of DFT; FFT and its basic application.**

**11. Basic Introduction of Analog and Digital Filter: Concepts of analog and digital filtering; Design of Butterworth filter, an example of analog filtering; Digital filtering, Infinite Impulse Response (IIR) filter and Finite Impulse Response (FIR) filter.**

**Course Assessment: **

**Middle-term examination, 30 points + End-term examination, 60 points + Assignment, making 10 points = 100 points**