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SIGNAL AND SYSTEM
LECTURES SUMMARY

General Introduction
 What are they?
 Signal
 System

Fundamentals of Signals and Systems
 Signal: a function of one or more variables that convey
information on the nature of a physical phenomenon.
Examples: v(t),i(t),x(t),heartbeat, blood pressure,
temperature, vibration.
• One-dimensional signals: function depends on a single
variable, e.g., speech signal
• Multi-dimensional signals: function depends on two or
more variables, e.g., image

Fundamentals of Signals and Systems
 System: an entity or operator that manipulates
one or more signals to accomplish a function,
thereby yielding new signals.
• Commonly encountered systems:
communications systems
Automatic speaker recoginition system
Aircraft landing system
.
Input signal Output signal
System

 1. CT and DT signals:
Classification of signals

Classification of signals (cont.)
 For many cases, x[n] is obtained by sampling
x(t) as:
 x[n] = x(nT) , n =0,+1,+2,…
 Are there any requirements for the sampling?

 2. Even and odd signals:
Even:
x(−t) = x(t)
x[−n] = x[n]
Odd:
x(−t) = −x(t)
x[−n] = −x[n]
 Any signal x(t) can be expressed as
x(t) = xe(t) + xo(t) )
x(−t) = xe(t) − xo(t)
where
xe(t) = 1/2(x(t) + x(−t))
xo(t) = 1/2(x(t) − x(−t))

 3. Periodic and non-periodic signals:
 CT signal: if x(t) = x(t + T), then x(t) is periodic.
 Smallest T=Fundamental period: To
 Fundamental frequency fo = 1/To (Hz or cycles/second)
 Angular frequency: o = 2 /To (rad/seconds)
 DT signal: if x[n] = x[n + N], then x[n] is periodic.
 min(No): fundamental period
 Fo = 1/No (cycles/sample)
 =2 /N (rads/sample). If the unit of n is designated as
dimensionless,
 then is simply in radians.
 Note: A sampled CT periodic signal may not be DT periodic.
Any Condition addition of two periodic CT signals, resultant
must be periodic signal ?





 4. Deterministic and random signals.
• Deterministic signal: No uncertainty with respect
to its value at any time
• Completely specified at any time
• Random signal: Uncertain before it occurs. E.g.,
thermal noise.

 Energy and power signals:
• CT signal x(t):
 Energy: E =
 Power: P =
2
( )
x t dt



2
1
( )
2
lim
T
T T
x t dt
T
 


• DT signal x[n]:
 Energy: E =
 Power:
 Energy signal: if 0 < E <
 Power signal: if 0 < P <
 
2
x n



 
2
1
2 1
lim
N
N n N
x n
N
 





 Analog Signal and Digital Signal

Basic operations on signals
Basic Operations on Signal

• Rule for time shifting and time scaling:
 See figure below. Find y(t) = x(2t + 3).
Basic Operations on Signal(cont.)

Elementary signals
1. Exponential
2-Sinusoidal

Elementary signals(cont.)
3. Step function

5.Unit ramp function
Elementary signals(cont.)
4.Unit impulse function

2.Memory /Memoryless
• Memory system: present output value depend on
future/past input.
• Memoryless system: present output value
depend only on present input.
• Example
System Properties(cont.)

 Invertibility
x(t)
x(t)
y(t)
H
1

H
System Properties(cont.)

 Series(cascade) Interconnection
 Parallel, Interconnection
Interconnection of systems
System 1 System 2
System 1
System 2
+
Input Output
Input
Output

Interconnection of systems
•Feedback Interconnection
System
1
System
2
Input Output

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