电子科大-信号与系统1-1

Signals and systems

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Introduction1. What is the signal and the system? 2. Why shall we study the signals and systems? 3. How to deal with the complex signals and

systems?4. Arrangement of the text and excises.sas1-1 2

Definition of signals and systemsGeneral definition: Signal: any phenomena which changed with variables (time,space,…)

System: the interactions (operations) betweensignals

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Definition of signals and systemsStrict definition: Signal: functions of time: x t

y t

System:operations to the functions: y t Hx t

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Problem to be solved in signals and systemsSignal analyses System analyses

System construct

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Main method in signal and systemIn real world, most signals and systems are complex ! Any complex thing can be pide to its simple part ! Complex signal <==> combination of basic signals Complex system <==> connection of simple systemssas1-1 6

Main method in signal and systemThe properties of basic signals and simple

systems;The properties of these combinations and connections;Study the signals and systems in different domains !sas1-1 7

Key points in signal and systemThe representations of signals The characteristics of systems

Basic signals and their propertiesExpress the system in different formssas1-1 8

Teaching arrangementText book:Signals and systems(Oppenheim)

Software for experiment :MATLABTime-domain ( 1-2) : 30% Frequency-domain (3-4) : 40%

Complex-domain (9-10) : 30%sas1-1 9

Course Score RateHomeworkExperiment Middle exam

10%10% 20%

Final exam

60%

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Mathematics ReviewThe representations of numbersInteger : 2, 53, -27, n, mrational : 2.65, -31/56 , n/m real : include rational and irrational

All these numbers can be expressed on a line: number axis.sas1-1 11

Complex number

z a jb re

j

Imaginary note: j 1 Euler’number: e 2.71828 ...

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Rectangular form of complex number

z a jbReal part

Imaginary part

b Im z

a Re z

Both a and b are real numbers !sas1-1 13

Pole form of complex number

z reMagnitude phase

j

r z z

Both r and θ are real numbers !0 r sas1-1

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Complex planeEach complex number can be represented by a point in complex plane

a r cos

b r sin r sas1-1

1 2 2 2 a b 1

tg

b a

Example: Different forms for complex2 2ej0

3 3e j 2

j 4 4e

j

j 4 4ej

j

2

4 316

1 j 2e1 j 3 2 e sas1-1

j