University
of
Hertfordshire
STUDENT'S GUIDE
FROM ANALOG TO DIGITAL
OBJECTIVES
LECTURE 2
FROM ANALOG TO DIGITAL
This lecture should achieve the follow ing:
•
Introduce
sampling
, the Nyquist Limit (Shannon's
Sampling
Theorem) and representation
of
signals in
the frequency
domain
•
Introduce
basic
concepts
of
Analog-to-Digital Conversion and quantization noise
•
Consider
practical
ADC
and
DAC devices
•
Consider
the
functional blocks
of
the DSP Starter Kit
board
LECTURE 2
45
2-1
~
TEXAS
IN
SIRUMENTS
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University
of
Hertfordshire
STUDENT'S GUIDE
FROM ANALOG TO DIGITAL
SI
GNA
LS IN
TIM
E
AND
FR
EQU
EN
CY
DOM
A IN S
TIME
DO
MAIN
T ,=1 /f,
A MPLITUDE
:
_:
~
C\
~
d
c
V
~
V
T
I
M~
FR EQ U ENC Y
DOMA
IN
AM PLITUDE
--L-
r,
FREQU ENCY
T,
=1/f
,
AMP
LITUD E
:-..:
r
1\
1\
6
~
I\
{
vvv
v
vv
,
TIME
AM PLI TUDE
--lL
f,
F
REQUENCY
T
=
period
f
=
fre q u e n c y
All electronic signals can
be
visualized (signal representation) using two basic methods - the
time domain
and
the
frequency domain.
If we have an electronic signal running along a copper wire, we need
some
method
of
displaying what that signal is.
•
Time Domain
The time domain is the form
of
visualization that most people are familiar with.
This method shows
variations
of
a signal with time.
The most common time domain instrument is the oscilloscope, which has
graduations
of
volts on the Y axis and graduations
of
time on the X axis.
A pure sine wave is shown on the left side
of
the above diagram. The signal has
afreque ncy
(the number
of
times that the signal repeats itself in a second) and a
period
(the time duration
of
one complete signal cycle).
Frequency and period are not different quantities, but different methods
of
describing the time measurement
of
a signal.
The diagram shows two waveforms.
The lower one has a higher frequency
(more
cycles per a
second) and a shorter period (less time to complete one signal). Both signals have the same amplitude.
•
Freq
uency Domain
The frequency domain is not as well-known as the time domain, but is very important in the field
of
DSPs.
Instead
of
showing the variation of a signal with respect to time, we show the variation
of
the signal with
respect to frequency.
Most people are familiar with the graphical displays in music systems
that
show how
much bass or treble is
in
music; this is a frequency domain display.
The most common instrument for
displaying the frequency domain is the spectrum analyzer.
The right side
of
the diagram shows a frequency
domain display.
In the top graph, we see a single line representing a single pure frequency
(f.).
In the lower
graph, we see a higher-frequency signal
(f
2
) .
This line is further to the right on the frequency axis.
LECTURE 2
46
2-2
University
of
Hertfordshire
STUDENT'S GUIDE
REA
L S
IGNALS
FROM ANALOG TO DIGITAL
A MPL
ITUD
E
~~
7
'Z..<7
'
»
TIME
A
MPLITUDE
IAI
• REAL LIF E
SIGNALS
ARE A COMB INA TION
OF
MANY
FR
EQUENCI
ES
•
THE Y
HAVE
BA
ND WI DTH
2'.
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- Spring '08
- Walker
- Digital Signal Processing, Analog-to-digital converter, input signal, University of Hertfordshire
-
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