class_01_introduction.pdf

Chengbin Ma UM-SJTU Joint Institute

Class#1

- Administrative Information

- What is a signal? (1.1)

- What is a system? (1.2)

- Classification of signals (1.4)

- Basic operations on signals(1.5)

Slide 1


Administrative Information (1) Course name: Ve216-Introduction to Signals and Systems (4 Credits)

Instructors: Chengbin Ma, [email protected], Tel: 3420-6209

Office hours: Mon & Wed 2:00pm03:50pm, Room 219, JI Building (or reserve individual time in advance) Need to confirm in the class.

TAs: Yue Qiao and He Yin (PhD candidates, JI DSC Lab) Office hours?

3 labs started from week#5: 1) Linear Time Invariant System; 2) AM

Radio; 3) Feedback Systems

Major Contents: Modeling and Analysis of LTI Systems (# refer to syllabus)

Representation of Analog LTI systems (Signals/Differential/difference equations)

Frequency-domain Responses (Fourier Transform)

Time-domain Responses (Laplace Transform)

Discrete LTI systems (z-Transform)

Three exams:

Midterm#1: Mar. 18th (Differential/difference equations)

Midterm#2: Mar. 30th (Fourier Transform)

Final exam: Apr. 23th (Laplace and z-Transforms)

Slide 2


Administrative Information (2) Grading policy:

Homework: 20% (JI Honor Code), Quiz: 15%, Labs: 15%, Midterm Exam#1: 10%,

Midterm Exam#2: 10%, Final Exam: 30%

Attendance: will be randomly taken at least 5 times following SJTU

academic regulations.

Typical grading curve following past practice in the recent 3 years:

Slide 3


Resources in Sakai

Slide 4


Background of Instructor

Modeling, analysis and control of dynamic systems.

Dynamic Systems Control Lab (Web)

Slide 5
http://umji.sjtu.edu.cn/lab/dsc/


Examples of Real Systems

Slide 6

Power

amplifier

Power

sensor

Bidirectional

coupler

Coupling

system

NI

CompactRIO

Rectifier

IV sampling

board

DC/DC

converter

Electrical

load


Class#1






Slide 7


What is a system? (1)

Two keywords: signal and system #relationship?

Example: Anti-lock braking system (ABS)

Structure: components/elements and their

composition

Behavior: inputs/processing/outputs of material,

energy, information, etc.

Interconnectivity: functional and structural

relationships among parts

Functions

Slide 8

ABS system: 06_Reference\Videos\EV\Safety (6 mins)


ABS system

Slide 9

Wheel

Sensor

Control

Unit

Modulator

Unit

Brake

DiscWheel

Pulses

(Electrical Signal)Control

Command

(Electrical Signal)

Hydraulic

Pressure

(Mechanical Signal)

Braking Force

(Mechanical Signal)

Components, Signals, and the ABS System


What is a system? (2)

From Latin Systma

System is a set of interacting or interdependent

components forming an integrated whole.

A system is a set of ? and ? .

The relationships can be abstracted as signal flows

(electrical, magnetic, mechanical, optical, thermal,

etc.) #refer to the previous ABS system.

Slide 10

Wheel

Sensor

Control

Unit

Modulator

Unit

Brake

DiscWheel

Pulses

(Electrical Signal)Control

Command

(Electrical Signal)

Hydraulic

Pressure

(Mechanical Signal)

Braking Force

(Mechanical Signal)


What is a signal?

Slide 11

Keywords:

Act/event/physical quantity,

transmit/convey,

message/information, etc.,

i.e., a carrier of ? .

Relationship with system:

refer to the ABS system (synergetic integration of

hardware and software)


Information and Computer Science

Slide 12


Engineering and Physics

Slide 13


Social/cognitive sciences and

management research

Slide 14


Strategic Thinking

Slide 15

Colonel Warden as Commandant of

the Air Command and Staff College (1992)


Class#1






Slide 16


Continuous-time/Discrete-time Signals

Slide 17
MichaelDefined for all time tMichaelDefined only at discreteInstants of timeMichaelMichaelMichaelMichaelMichaelMichaelParentheses () are used to denote continuous-valued quantities, while brackets [] are used to denote discrete-valued quantities.


An Example: Integrator

(Analog) (Digital)

Slide 18

+

R

C

Vo

+

yk-1

xk-1 xk

(k-1)T kT 0

Av(s) = -Z1/Z2= -1/(RCs) Txx

yy kkkk2

11

Software-based (programmable)

Easy and flexible implementation

Tradeoff between accuracy and cost

,2,1,0,)(][ nnTxnx s


Even and Odd Signals Even signal (symmetric about the vertical axis): x(-t) = x(t)

Odd signal (anti-symmetric about the vertical axis): x(-t) = -x(t)

Even-odd decomposition: Given an arbitrary signal, we may

develop an even-odd decomposition of that signal.

Slide 19

component odd:2

)()()(

componenteven :2

)()()(

2

)()(

2

)()()(

txtxtx

txtxtx

txtxtxtxtx

o

e

#class1_decomposition.m


Even and Odd Signals Conjugate symmetry: A complex-valued signal x(t) is said to

be conjugate symmetric if

Slide 20

*( ) ( )x t x t

*

*

( ) ( ) ( )

( ) ( ) ( ), ( ) ( ) ( )

( ) ( ) ( ) ( ), ( ) ( )

x t a t jb t

x t a t jb t x t a t jb t

x t x t a t a t b t b t


Periodical/Non-periodical Signals

Continuous-time signal:

for all t;

fundamental period: the smallest T

Discrete-time signal:

for all n;

fundamental period: the smallest N

Examples: x(t)=cos(2t): periodic, with fundamental period of

x[n]=cos[2n]: non-periodic (Why?)

x[n]=cos[2n] : periodic, with fundamental period of 1 sample

Slide 21

)()( Ttxtx

][][ Nnxnx

#class1_period.m


Energy and Power of Signals (1)

The (normalized) instantaneous power of a

signal:

Total energy of the signal:

Slide 22

dttxdttxE

T

TT

22)()(lim

n

n

nxE2

][

,)()(2

txtp 2

][][ nxnp



Average power of the signal:

# For a periodic signal, its average power is defined as:

Slide 23

T

TT

dttxT

P2

)(2

1lim

N

NnN

nxN

P2

][12

1lim

1

0

2

0

2][

1or )(

1 N

n

T

nxN

PdttxT

P



Root Mean Square (RMS) value of the

periodic signal (IMPORTANT)

the square root of the average power

An AC voltage (or current) is often expressed as a

root mean square (RMS) value, written as Vrms,

because

Ptime average = Vrms2/R

Slide 24

2

1

2

12

)(T-

1X

T

T

rms dttxT


Deterministic/Random signals

Deterministic signal: a signal about which there is no uncertainty with respect to its value at any time. Namely,

deterministic signals may be modeled as completely specified

functions of time.

Random signal: a signal about which there is uncertainty before it occurs. A random signal has a certain probability of

occurrence.

Slide 25

Three examples of EEG

(electroencephalography) signals

recorded from the hippocampus of

a rat. Neurobiological studies

suggest that the hippocampus plays

a key role in certain aspects of

learning and memory.


Class#1






Slide 26


Dependent/Independent Variables

For example, x and y. If every value of x is associated

with exactly one value of y, then y is said to be a

function of x.

It is customary to use x for what is called the

"independent variable", and y for what is called the

"dependent variable" because its value depends on the

value of x.

Namely, for y=f(x), y is dependent variable and x is

the independent variable.

Slide 27


Basic Operation on Signals

Operations for dependent variables:

1. Amplitude scaling

2. Addition

3. Multiplication

4. Differentiation

5. Integration

Operations for independent variables:

1. Time scaling

2. Reflection (Time reversal)

3. Time shifting

Slide 28


Amplitude Scaling

The signal resulting from amplitude scaling

applied to a signal is defined by

Slide 29

][][

)()(

ncxny

tcxty


Addition

The signal obtained by the addition of two

signals is defined by

Slide 30

][][][

)()()(

21

21

nxnxny

txtxty


Multiplication

The signal resulting from the multiplication of

two signals is defined by

Slide 31

][][][

)()()(

21

21

nxnxny

txtxty


Differentiation/Difference

The derivative/first difference of a signal with

respect to time is defined by

Slide 32

( ) ( )

[ ] [ ] [ 1]

dy t x t

dt

y n x n x n


Integration/Accumulation

The integral/running sum of a signal with

respect to time is defined by

Slide 33

( ) ( )

[ ] [ ]

t

n

k

y t x d

y n x k


Time Scaling

Definition

Slide 34

0],[][

)()(

kknxny

atxty

- Time-scaling operation; (a) continuous-time signal x(t), (b) version of x(t)

compressed by a factor of 2, and (c) version of x(t) expanded by a factor

of 2.


Reflection

Definition

Slide 35

][][

)()(

nxny

txty

- Operation of reflection: (a) continuous-time signal x(t) and (b) reflected

version of x(t) about the origin.


Time Shifting

Definition

Slide 36

][][

)()(

0

0

nnxny

ttxty

Time-shifting operation: (a) continuous-time signal in the form of a

rectangular pulse of amplitude 1.0 and duration 1.0, symmetric about the

origin; and (b) time-shifted version of x(t) by 2 time shifts.


Combination of Time Shifting and Time Scaling

Precedence rule for time shifting and time

scaling: The time-shifting operation is

performed first on signal, but why?

3-min Quiz: for x(t), what are the results when

First time-shifting by b, then time scaling by a,

First time scaling by a, then time shifting by b,

Respectively?

Slide 37


An Example

Slide 38


Homework Problem 1.9 from (a) to (h)

Problem 1.42 (a)(c)(d)(e)

- Due: 2:00PM next Thursday

Slide 39

class_01_introduction.pdf

Documents

previous abs system

sakai slide

latin systma system

linear time invariant

analysis of lti systems

sjtu academic regulations

ztransforms slide

control of dynamic systems