lect chapter1 part1
TRANSCRIPT
-
8/4/2019 Lect Chapter1 Part1
1/16
Introduction:Fundamental Concepts
Br. Khaizuran Abdullah
Department of Electrical and
Computer Engineering
International Islamic University Malaysia
ECE 2221 : Signals and Systems (Analysis) Sem. II (04/05)
Lecture Chapter 1 (Part 1)
-
8/4/2019 Lect Chapter1 Part1
2/16
1-2
Questions?
Whats signal?
Whats system?
-
8/4/2019 Lect Chapter1 Part1
3/16
1-3
Introduction:Signals and Systems: What are they?
A time-varying physical phenomenon to convey
information/message
Signal:
a dogs barking, traffic lights, a cars signal, emergency
light, a red light on top of a building, a heartbeat of a
patient, a blood pressure of a patient
Examples:
-
8/4/2019 Lect Chapter1 Part1
4/16
1-4
Introduction:Signals and Systems: What are they?
System:
a combination of several components to
perform a desired task. It processes
input signal to produce output signal
a communication system, a human sense system,
a traffic controller. Refer to CommSys.doc
Examples:
http://commsys.doc/http://commsys.doc/ -
8/4/2019 Lect Chapter1 Part1
5/16
1-5
Classification of signals
CT or DT
Deterministic Random/stochastic
Periodic Aperiodic
Complex Transient Almostperiodic
Sinusoid
Power, Energy
Even or Odd
-
8/4/2019 Lect Chapter1 Part1
6/16
1-6
CT and DT Signals
Examples of CT and DT are shown in these figures
A signal x(t) is said to be a continuous-time signal if it is defined for all time t.Example of a continuous signal? A sine wave signal
Example of a NOT continuous signal? A unit pulse signal
Is defined only at discrete instant of time
Is obtained by sampling the CT signal at a uniform rate
sampling means that acquiring the values of a signal at discrete pointsin time and not between them.
Is a function of an argument that takes values from a discrete set
~x[n] wheren {...-3,-2,-1,0,1,2,3...}~We sometimes use index instead of time when discussing
discrete-time signals~Values forx may be real or complex
Continuous-time signal:
Discrete-time signal:
http://ct_dt.doc/http://ct_dt.doc/ -
8/4/2019 Lect Chapter1 Part1
7/16
1-7
Deterministic and Random Signals
Deterministic signal:
Signal which can be completely modeled as function of
time.
Random signal:
Signal which is processed using probability theory.
Examples: x1(t) = sin(20t) for all tx2(t) = cos(20t) for all t
Examples ofdeterministic and random signals
http://det_random.doc/http://det_random.doc/ -
8/4/2019 Lect Chapter1 Part1
8/16
1-8
Periodic and Aperiodic Signals
Periodic signal has the property that x(t)=x(t+T) for all t.
The smallest value ofT that satisfies the definition is called
the fundamental period.
Below is an example of a periodic signal with T = 0.2 s :
Periodic Signal?
-
8/4/2019 Lect Chapter1 Part1
9/16
1-9
Periodic and Aperiodic Signals
Aperiodic Signal?
Any signal x(t) for which no value of T satisfies the
condition of x(t) = x(t+T)
Below is an example of aperiodic signal:
-
8/4/2019 Lect Chapter1 Part1
10/16
1-10
How to prove Periodic or Aperiodic
To prove periodic, we need to determine T first:
For a simple sinusoid signal such as x(t)=10 sin(12t), T= 1/6 (rational
number)
Then use x(t + 1/6) = x(t) to confirm that its periodic:
txandwheret
ttt
ttx
02sin12cos12sin10
12cos2sin2cos12sin10212sin10
6
112sin10
6
1
-
8/4/2019 Lect Chapter1 Part1
11/16
1-11
How to prove Periodic or Aperiodic
For a sum or a product of 2 signals, such as the following examples, it is periodicif the ratio of their respective periods can be expressed as a rational number.
Try these:
1. x(t)=10 sin(12t) + 4 cos (18t)
=> periodic, T1 =1/6 (rational) T2 =1/9 (rational) , T = 1/32. x(t)=10 sin(12t) + 4 cos (18t)
=> aperiodic, T1 =1/6 (rational) T2 = /9 (irrational), T = undetermined
3. x(t)=10 cos(t) + sin (4t)
=> periodic, T1 = 2 (rational) T2 = 1/2 (rational), T = 2
Then, for those which are periodic, use x(t + T) = x(t) to confirm that they areperiodic. (try confirming them !)
-
8/4/2019 Lect Chapter1 Part1
12/16
1-12
Even and Odd Signals
Even Signal:
x(t) is an even signal if it is satisfies
For example,
tfortxtx
txtxThus
ttttx
ttx
,
2cos2cos2cos
2cos
-
8/4/2019 Lect Chapter1 Part1
13/16
1-13
Even and Odd Signals
Odd Signal:
x(t) is an odd signal if it is satisfies
For example,
tfortxtx
txtxThus
ttttx
ttx
,
2sin2sin2sin
2sin
-
8/4/2019 Lect Chapter1 Part1
14/16
1-14
Energy and Power Signals
dttxE
2
2
2
21lim
T
TT
avedttx
TP
T
Tt
t
avedttx
Tdttx
TP
22 110
0
For periodic signal :
If x(t) is a CT signal, its signal energy is
However, this energy integral will not converge if it is infinite. An example of a
CT signal with infinite energy would be the sinusoidal signal
In this case, it is convenient to deal with the average signal power of the signalinstead of the signal energy. The average signal power of a CT signal is
tAtx0
cos
-
8/4/2019 Lect Chapter1 Part1
15/16
1-15
Energy and Power Signals
Examples:
A) Find the total energy of the rectangular pulse shown in the figure below.
x(t)
t
T
A
B) Find the average power of the square wave shown in the figure below.
x(t)
0.2 0.4-0.2 0
B
-B
Answer: A2T
Answer: B2
-
8/4/2019 Lect Chapter1 Part1
16/16
1-16
Thank You