SIGNALS & SYSTEMS
LECTURER:
MUZAMIR ISA
049798139
muzamir@kukum.edu.my
PLV:
MUHAMMAD HATTA HUSSEIN
049852853
muhdhatta@kukum.edu.my
EVALUATION
Coursework :


50 %
30 % Practical:
(i) 70 % from Lab Report
(ii) 30% from Lab Test
20 % :
(i) 15 % from Written Test 1 & Written Test 2
(ii) 5 % from Tutorial
Final Exam :
50 %
REFERENCES
Simon Haykin, Barry Van Veen; Signal &
System, 2nd Edition, 2003, Wiley (main
textbook)
MJ Robert; Signal & System, 2003,
McGraw Hill
Charles L Philips et.al; Signal, System and
Transform, Pearson.
Signals and Systems
Signals are variable that carry
information
Systems process input signals to
produce output signals
What Are “Signals”?
A function of one or more variable,
which conveys information on the
nature of a physical phenomenon.
A function of time representing a
physical or mathematical quantities.
e.g. : Velocity, acceleration of a car,
voltage/current of a circuit.
Even Signal
Deterministic Signal
Odd Signal
Random Signal
Classification of Signals
Continuous-Time and Discrete-Time
Signals
Even and Odd Signals
Periodic and Nonperiodic Signals
Deterministic and Random Signals
Energy and Power Signals
Continuous Time (CT) and Discrete-Time (DT)
Signals

Continuous-time signals
Examples: Signals in cars and circuits
Signals described by differential equations, e.g.,
dy/dt = ay(t) + bf(t)
Signal itself could have jumps (discontinuities) in
magnitude
y(t)
t

Discrete-time signals
Examples: money in a bank account, daily stock
prices
No derivative exists
Signals described by difference equations, e.g.,
y(k+1) = ay(k) + bf(k)
y(k)
k
Even and Odd Signals
Periodic and A-periodic Signals
Right and Left-Sided Signals
Bounded and Unbounded Signals
OPERATION ON SIGNALS
Operations performed on the independent
variable



Time scaling
y(t) = x(at)
Reflection
y(t) = x(-t)
Time shifting
y(t) = x(t – t0)
where t0 is the time shift.
TIME SCALING
y(t) = x(at) ;
Compress the signal x(t) by a.
This is equivalent to plotting the signal
x(t) in a new time axis tn at the location
given by t = atn or tn = t/a
REFLECTION OR FOLDING
y(t) = x(- t)
Just scaling operation with a = -1. It
creates the folded signal x(- t) as a
mirror image of x(t) about the vertical
axis through the origin t = 0.
TIME SHIFTING
y(t) = x(t – a)
Displaces a signal x(t) in time without
changing its shape. Simply shift the
signal x(t) to the right by a. This is
equivalent to plotting the signal x(t) in a
new time axis tn at the location given
by t = tn - a or tn = t + a.
EXAMPLE
A CT signal is shown, sketch and label
each of this signal;
a) x(t -1)
b) x(2t)
c) x(-t)
x(t)
2
t
-1
3
x(t)
x(t-1)
2
2
t
t
0
4
-1/2
3/2
x(-t)
2
t
-3
1
A discrete-time signal, x[n-2]
A delay by 2
x(n-2)
4
2
0
1
2
3
4
5
n
A discrete-time signal, x[2n]
Down-sampling by a factor of 2.
x(2n)
4
2
0
1
2
3
n
A discrete-time signal, x[-n+2]
Time reversal and shifting
x(-n+2)
4
2
-1
0
1
2
n
A discrete-time signal, x[-n]
Time reversal
x(-n)
4
2
-3
-2
-1
0
1
n
Exercises
1.A continuous-time signal x(t) is shown
below, Sketch and label each of the
following signal
a.x(t – 2)
b. x(2t) c.x(t/2) d. x(-t)
x(t)
4
0
4
t
Continue…
2.A discrete-time signal x[n] is shown below,
Sketch and label each of the following
signal
a. x[n – 2]
b. x[2n] c. x[-n+2] d. x[-n]
x[n]
4
2
0
1
2
3
n
Basic Operation on Signals
Operations performed on dependent
variable





Amplitude scaling
Addition
Multiplication
Differentiation
Integration
Exponential Signals
x(t) = Beat ;
B is the amplitude
Decaying Exponential (a < 0)
Growing Exponential (a > 0)
Sinusoidal Signals
x(t) = A cos(t + )
where A = amplitude
 = frequency (rad/s)
 = phase angle (rad)
Unit Impulse Function
Narrow Pulse Approximation
Intuiting Impulse Definition
Uses of the Unit Impulse
Unit Step Function
Successive Integrations of the Unit
Impulse Function