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Analog and Digital Signals,
Analog and Digital Signals,
Time and Frequency
Time and Frequency
Representation of
Representation of Signals
Signals
CSE 3213, Fall 2010
Instructor: N. Vlajic
Required reading:
Garcia 3.1, 3.2
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Analog and Digital Signals: Understanding Data Representation and Transmission, Study notes of Voice
An in-depth analysis of analog and digital signals, their representation, and transmission. It covers the concepts of data vs. signal, analog vs. digital, signal representation, and periodic vs. aperiodic signals. The document also discusses the classification of analog signals, Fourier analysis, and the frequency spectrum of analog signals.
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Analog and Digital Signals,
Analog and Digital Signals,
Time and Frequency
Time and Frequency
Representation of
Representation of Signals
Signals
CSE 3213, Fall 2010
Instructor: N. Vlajic
Required reading:
Garcia
Data vs. Signal Data vs. Signal
Analog vs. Digital
Analog Signals
Simple Analog Signals
Composite Analog Signals
Digital Signals
Signal Representation
Signal Representation
Signal Representation
- typically in 2D space, as a function of
time, space or frequency
when horizontal axis is time, graph displays the value of a signal at one particular pointin space as a function of time
when horizontal axis is space, graph displays the value of a signal at one particular point intime as a function of space
time
space
The time- and space- representation of a signal often resemble each other,
though the signal envelope in the space-representation is different (signal attenuates over distance).
Signal Representation
(cont.)
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=
Example
[
signal in time and space
]
Analog vs. Digital
Analog vs. Digital Data
Analog vs. Digital Data
analog data
analog data
- representation variable takes
on continuous values in some interval, e.g.voice, temperature, etc.
digital data
digital data
- representation variable takes
on discrete (a finite & countable number of)values in a given interval, e.g. text, digitizedimages, etc.
Analog vs. Digital Signal
Analog vs. Digital Signal
analog signal
analog signal
- signal that is continuous
in time and can assume an infinite numberof values in a given range (continuous intime and value)
discrete (digital) signal
discrete (digital) signal
- signal that is
continuous in time and assumes only alimited number of values (maintains aconstant level and then changes to anotherconstant level)
Analog vs. Digital
(cont.)
Both analog and digital data can be transmitted
using either analog or digital signals.
example:
analog signaling of analog and digital data
… will talk more about this later …
Data vs. Signal
Analog vs. Digital
Analog Signals Analog Signals
Simple Analog Signals
Composite Analog Signals
Digital Signals
measured in degrees or radians
π
rad
π
/360 rad
1 rad = (360/
π
phase shift of 360º = shift of 1 complete period
phase shift of 180º = shift of 1/2 period
phase shift of 90º = shift of 1/4 period
φ
= 0º or 360º
φ
= 90º
φ
= 180º
Simple Analog Signals
Phase in Simple
Phase in Simple
Analog Signals
Analog Signals
5V
1s
http://hermes.eee.nott.ac.uk/teaching/cal/h61sig/sig0001.html
Analog Signals
Example
[ period and frequency ]
10
12
Hz
terahertz (THz)
10
s
picoseconds (ps)
10
9
Hz
gigahertz (GHz)
10
s
nanoseconds (ns)
10
s
10
s
1 s
Equivalent
10
6
Hz
megahertz (MHz)
microseconds (
μ
s)
10
3
Hz
kilohertz (KHz)
milliseconds (ms)
1 Hz
hertz (Hz)
seconds (s)
Equivalent
Unit
Unit
(a)
Express a period of 100 ms in microseconds.100 ms = 100
×
s = 100
×
×
6
μ
s = 10
5
μ
s
(b)
Express the corresponding frequency in kilohertz.100 ms = 100
×
s = 10
s
f
Hz = 10
×
KHz = 10
KHz
units of period and respective frequency
One ‘spike’ in frequency domain
shows two characteristics
of the signal:
spike position = signal frequency,
spike height = peak amplitude.
Analog signals are best represented in the frequency domain.
Analog signals are best represented in the frequency domain.
Simple Analog Signals
Simple Analog Signals
http://hermes.eee.nott.ac.uk/teaching/cal/h61sig/sig0002.html
Example
[
time vs. frequency domain
]
Composite Analog Signals
(cont.)
Angular Frequency
Angular Frequency
aka radian frequency – number of 2
π
revolutions
during a single period of a given signal
simple multiple of ordinary frequency
f
T
[
]
∑
∞
=
1
n
0
n
0
n
0
t)
sin(n
B
t)
cos(n
A
A
s(t)
ω
ω
n
t)dt
n
s(t)cos
T
A
T
0
n
∫
0
n
t)dt
n
s(t)sin
T
B
T
0
n
∫
0
Composite Analog Signals
(cont.)
Example
[ periodic square wave ]
...
(5f)t)
sin(
5
π
4A
(3f)t)
sin(
3
π
4A
ft)
sin(
π
4A
s(t)
=
π
π
π
three harmonics
adding three harmonics
With three harmonics we get an approximation of a square wave.
To get the actual square, all harmonics up to
should be added.
With three harmonics we get an approximation of a square wave.
To get the actual square, all harmonics up to
should be added.
http://www.nst.ing.tu-bs.de/schaukasten/fourier/en_idx.html
http://www.phy.ntnu.edu.tw/java/sound/sound.html
No DC component!!!