Transcript Chapter 1

‫ذبذبات‬
‫أنظمة‬
Input Signal
Output Signal
System
System operte on input signal to produce output signal
Input Signal
Output Signal
System
Input Signal
Output Signal
System
A signal is a set of information or data that can be modeled as
a function of one or more independent variables (e.g.tR)
Examples  Speech, image, weather information, sales information, voltage in a circuit,
video, music, etc.
A system modifies signals or extracts information.
It can be considered a transformation that operates on a signal.
Examples : electronics, radio or TV, guidance system, communication system, etc.
Audio System
‫محول‬
Transducer that convert
Audio intensity to electric signal
Example : The microphone
Visual System
Transducer that convert
light intensity to electric signal
Receiving
Transducer that convert
electric signal to light intensity
Transmitting
Temprture System
Transducer that convert
Temprture to electric signal
Temprture
Sensor
Pressure System
Input Signal
Output Signal
System
Types of Signals
1-Continuous-time signals
- Signal that has a value for all points in time
- Function of time
- Written as x(t) because the signal x is a function of
2- Discrete-Time Signals
- Signal that has a value for only specific points in time
- Function of the sample value, n
- Written as x[n]
Input Signal
Output Signal
System
System
- A collection of items that together performs a function
- Modifies / transforms an input to give an output
Represented by
T[ ]
Output Function y(t)
Input Function x(t)
Consider The following Input/Output relations
i(t)
i(t)
R

VR (t )

C

VC (t )

VR (t )  Ri (t )
i(t)
1
VC (t ) 
C
t
 i ( )d 

L

VL (t )

VL (t )  L
di (t )
dt
i(t)
i(t)
i(t)
R

VR (t )

L

VL (t )

C

VC (t )

We can think or consider i(t) as the input or excitation which is
usually known
We can think of VR(t), VC(t), VL(t) as the output or response
In general we can represent the simple relation between
the input and output as:
x(t )
Input
T[ ]
y(t )
Output
y(t) = T[ x(t) ]
Were T[ ] is an operator that map the function x(t) to
another function y(t) .( Function to Function mapping)
i(t)

VR (t )

R
VR (t )  Ri (t )
TR [ ] = R[ ]
i(t)
L

VL (t )

VL (t )  L
di (t )
dt
d
TL [ ] = L [ ]
dt
i(t)
C

VC (t ) VC (t )  1
C

t
 i ( )d 

TC [ ] 
1
t

C 
[ ]dt '
Example
d
[]
Differential Operator
dt
Let the input x(t) = 2sin(4pt) then the output y(t) be
Let the operator
T[ ] =
d
[2sin(4p t )] = 8cos(4pt )
dt
Function 2sin(4pt)
Function 8cos(4pt)
mapped
y(t) = T[x(t)] =
x(t )
Input
H[ ]
y(t )
Output
H[ ]
Output Function space
y(t)
Input Function space
x(t)
Note operator map function x(t) to another function y(t)
In comparison to functions , it maps Domain (numbers)
to Range (domain)
i (t )
R
Input
Input

x (t )


V (t )
C
Output
x (t )  Ri V c (t )
C

dV c (t )
i (t ) C
dt
dV c (t )
x (t )  RC
 V c (t )
dt
The operator or relation T can be defined as
- Linear / Non linear
- Time Invariant / Time Variant
- Continuous-Time / Discrete-Time
- Causal / Non Causal