LOCAL THEORETICAL MODELS IN ALGEBRA LEARNING
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Nombre de lectures
36
- leçon - matière potentielle : an unknown
- leçon - matière potentielle : the equations
- cours - matière potentielle : methods
- exposé
- expression écrite
- leçon - matière potentielle : that teenagers
- algebraic substitution
- children progress along the list of items
- theoretical models
- word problems
- cognitive processes
- algebra
- line to line
- line for line
- line-line
- line upon line
- line by line
- analysis
- problem
Publié par
Intro to Practical
Digital Communications
Lecture 2
Vladimir Stojanovi ć
6.973 Communication System Design – Spring 2006
Massachusetts Institute of Technology
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
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Discrete data transmission
Messages are encoded into signal points
signal points
signal waveforms
Signal points are mapped to signal waveforms
Modulation
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
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6.973 Communication System Design 18‰
Modulation and de-modulation
e.g. Binary Phase-Shift Keying (BPSK) x (t)
0
x (t)
1
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
6.973 Communication System Design 19‰
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Vector signal representation
Maps continuous signals to discrete vectors
Significantly simplifies system analysis
signal
signal points
waveforms
basis functions
Modulator
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
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6.973 Communication System Design 20‰
BPSK example
Signal constellation
What is the information rate (R) of this modulation?
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
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6.973 Communication System Design 21‰
Manchester modulation example (Ethernet)
Different waveforms can have same vector representations
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
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6.973 Communication System Design 22More constellations
Quadrature Amplitude Modulation
(QAM)
Pulse Amplitude Modulation
ϕ ()t
2
(PAM)
3
ϕ()t
1
1
ϕ()t
1
-3 -1 1 3 -3 -1 1 3
-1
e.g. PAM4
-3
e.g. 16-QAM
PAM and QAM have pulses as basis functions
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
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6.973 Communication System Design 23„
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How do we choose basis functions?
Need to be orthonormal – (b/c of demodulation)
Inner products
Continuous
Discrete
Invariant to choice of basis functions
Average energy of the constellation
Invariant to the choice of basis functions
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
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6.973 Communication System Design 24‰
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Constellation energy
Implications of the inner product invariance to
basis functions
If energy is a signal, it is the same regardless of
the mod waveform used
As long as basis functions are orthogonal
Parseval’s identity
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
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6.973 Communication System Design 25‰
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Correlative demodulator
Demodulator
Modulator
Straightforward demodulator implementation
Use the fact that basis functions are orthogonal
Collect the signal energy
Hard to build in practice
Cite as: Vladimir Stojanovic, course materials for 6.973 Communication System Design, Spring 2006.
MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology.
Downloaded on [DD Month YYYY].
6.973 Communication System Design 26
