Microsoft PowerPoint - COMMI_lec7Chih-Wei Liu
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Message waveform is represented by regularly spaced sample values (sample signals) – discrete in time.
Historically, these methods are the early attempts to achieve modern communications. They are in the twilight zone between analog and digital modulations.
Today, their basic forms can still be found in some electronic components such as ADC.
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Analog/Digital Pulse-coded
Analog pulse modulation: A pulse train is used as the carrier wave. Some characteristic feature of each pulse (e.g., amplitude, duration, or position) is used to represent message samples. PAM – pulse amplitude PDM – pulse duration PPM – pulse position
Digital Pulse Modulation: Messages are discrete-amplitude (finite levels) samples. DM – delta modulation PCM – pulse-code modulation
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Pulse-Amplitude Modulation (PAM)
The amplitude of each pulse corresponds to the value of the message signal m(t) (at the leading edge of the pulse).
The pulse generator can be considered as a “filter”.
( 0.5 )( ) ( )
Wtt W
τ τ
M f M f H f H f f e
m t m nT t nT
δ
Equalizer: Recover distorted signals particularly when the distortion method is known or estimated.
1/H(f) LPF
Pulse width ∝ the values of message Spectrum: complicated (Fourier-Bessel spectra)
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Spectrum: complicated
Demodulation: (1) LPF & integration
(2) convert PPM to PWM → LPF Conversion of PPM or PWM to PAM: a ramp generator (re)starts at kTs and stops at tk. (next page)
( ) ( )n n
=−∞
= −∑
(1)
(2)
(3)
(4)
δ δ
= ∞ =−∞
= ∞
Slope Overload
The message signal m(t) has a slope greater than can be followed by the stair-step approximation ms(t).
Assume step-size = δ0 → slope (max) = δ0/Ts
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Solution to Overload
based on xc(t).
⇒ make δ0 ↓.
⇒ make δ0↑. Method: Detect the “trend” of signal
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ADM Receiver
Transmit step-size or regenerate the step-size at the receiver according to pre-decided “rules”.
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Pulse-Code Modulation (PCM)
Main advantages of digital communication
– more reliable communication
– complicated circuits ( cost reduced by VLSI)
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PCM Signal Generation
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BW of PCM
Message BW = W
Sampling rate = 2W
⇒ transmission BW ≈ knW, k=constant
Hence, B ≈ k2Wlog2q
Recovered message error is due to mainly quantization error. Thus, q↑ error↓ B↑
1 2nW
A number of data sources share the same communication channel.
Frequency-Division Multiplexing (FDM)
Quadrature Multiplexing (QM)
Time-Division Multiplexing (TDM)
FDM Several message signals are translated, using modulation, to different spectral locations and added to form a baseband signal.
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Example: Stereophonic FM
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Quadrature Multiplexing (QM)
Quadrature-carrier multiplexing: transmit two signals on the same carrier frequency. (not exactly FDM)
Note that cos and sin are orthogonal. QM Quadrature Amplitude Modulation (QAM)
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<Modulation> ( ) [ ( )cos ( )sin ].
<Coherent Demodulation> If the receiver has a carrier phase error, i.e.,
( ) 2cos( ). ( ) 2cos( )
LO t t x t t
A m t m t A m t t
ω ω
ω θ
c
m t t y t A m t m t
ω θ θ θ θ + +
⇒ = − →
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Time-Division Multiplexing (TDM)
Each message signal occupies a small time slot in every Ts second.
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BW of TDM
1
1
Baseband message BW = . There are channels. Samples per second = 2 .
Total samples per second: 2 . Or,
Total samples per second = 2 .
Total baseband BW to accommodate all sources
i
TDM: less crosstalk (in memoryless channels),
difficult to keep synchronization (frame structure, header), “digital” (sampled) signals