Microsoft PowerPoint - COMMI_lec7Chih-Wei Liu
Commun.-Lec7
[email protected] 2
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.
Commun.-Lec7
[email protected] 4
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
Commun.-Lec7
[email protected] 5
Commun.-Lec7
[email protected] 6
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)
Commun.-Lec7
[email protected] 10
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
Commun.-Lec7
[email protected] 16
Solution to Overload
based on xc(t).
⇒ make δ0 ↓.
⇒ make δ0↑. Method: Detect the “trend” of signal
Commun.-Lec7
[email protected] 17
ADM Receiver
Transmit step-size or regenerate the step-size at the receiver
according to pre-decided “rules”.
Commun.-Lec7
[email protected] 19
Pulse-Code Modulation (PCM)
Main advantages of digital communication
– more reliable communication
– complicated circuits ( cost reduced by VLSI)
Commun.-Lec7
[email protected] 20
PCM Signal Generation
Commun.-Lec7
[email protected] 21
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.
Commun.-Lec7
[email protected] 25
Example: Stereophonic FM
Commun.-Lec7
[email protected] 26
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)
Commun.-Lec7
[email protected] 27
<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 + +
⇒ = − →
Commun.-Lec7
[email protected] 28
Time-Division Multiplexing (TDM)
Each message signal occupies a small time slot in every Ts
second.
Commun.-Lec7
[email protected] 29
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
