View
215
Download
0
Category
Preview:
Citation preview
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 1/45
SKKU J.D. Cho1
Lecture on Communication Theory
Chapter 6. Pulse Modulation
6.1 Introduction
CW modulation - AM, DSB-SC,SSB,VSB,FM,PM
Pulse modulation
Analog: discrete in time & continuous in amplitude
Digital : discrete in time & amplitude
6.2 Sampling Process
Time domain Frequency domain
W T s
2
1<
W T s
2
1=
W T s 2
1
>
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 2/45
SKKU J.D. Cho2
Lecture on Communication Theory
1. Notation
- : original analog signal
- : sampling period
- : sampling rate
2. Sampling
Sampling with δ (t)
; ideal sampled signal
where
; discrete Fourier Transform
If
W T s
2
1=
( ) ∑∞
−∞=δ
π−
=
n W
nf j
W
n g f G
2exp
2
( ) ( ) ( )∑∞
≠−∞=
δ −+=
0mm
s s s mf f G f f G f f G
)(t g
sT
s
s
T f
1=
( ) ( ) ( )∑∞
−∞=
−=n
snfT jnT g f G s
π2expδ
)()( f Gt g
⇔
( ) ( ) )(δδ
f GnT f G f f g n
s s∑∞
−∞=
=−⇔ let
( ) ( ) ( )∑∞
−∞=
−=n
snT t nT g f g δδ
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 3/45
SKKU J.D. Cho3
Lecture on Communication Theory
Under following conditions
has all information contained in g(t)
3. Reconstruction
Reconstruction
=> Interpolation formula
where : Interpolation function
( )
=
≥=
W f
W f f G
s 2
0 for
( ) ( ) W f W f GW
f G <<−= δ 21
( ) D.F.T. , ;2
exp22
1W f W
W
nf j
W
n g
W f G
n
<<−
π−
=∴ ∑
∞
−∞=
( )W n g 2∴
W
n g t g
2)( from
( )Wt 2sinc
∑∞
−∞=
=n
dt ft j f Gt g )π2exp()()(
∑
∑ ∫ ∫ ∑
∞
−∞=
∞
−∞=−
−
∞
−∞=
−−
=
−
=
−
=
n
n
W
W
W
W n
nWt
nWt
W
n g
df W
nt f j
W W
n g
df ft jW
nf j
W
n g W
)ππ2(
)ππ2sin(
2
)]2
(π2exp[2
1
2
)π2exp(π
exp22
1
( )∑∞
−∞=
=
n
n-Wt W n g t g sinc So, 22
)(
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 4/45
SKKU J.D. Cho4
Lecture on Communication Theory
4.Sampling Theorem
1) BW=W 로 band-limited signal 은 1/2W seconds 로 샘플링
한
value 로 완전하게 describe 된다 .
2) BW=W 로 band-limited signal 은 1/2W 로 샘플링한 샘플값
으로
완전하게 복원 가능하다
5. Aliasing
Anti - aliasing filter
Aliasing 없애는 방법
Nyquist rate 보다 높게 sampling
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 5/45
SKKU J.D. Cho5
Lecture on Communication Theory
6. Reconstruction filter
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 6/45
SKKU J.D. Cho6
Lecture on Communication Theory
6.3 Pulse-Amplitude Modulation
1. PAM
Instantaneous sampling
1) Sample and hold :Lengthening(T)
- Impulse 대신 lengthening with T 를 사용한 이유
to avoid the use of an excessive channel BW
)( sT
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 7/45
SKKU J.D. Cho7
Lecture on Communication Theory
2. PAM signal
PAM signal
where
Instantaneous sampled version of
==
<<
=
otherwise ,0
,0 ,2
1
0 ,1
)( T t t
T t
t h
)(t m
∑∞
−∞=
δ −δ=n
s s nT t nT mt m )()()(
∫
∞
∞−δ ττ−τ=∗ δ d t hmt ht m )()()()(
∫ ∑∞
∞−
∞
−∞=
ττ−−τδ=n
s s d t hnT nT m )()()(
∫ ∑∞
∞−
∞
∞−
ττ−−τδ= d t hnT nT m s s )()()(
∑∞
−∞=
−=n
s s nT t hnT m )()(
)()()( δ t ht mt s ∗= ,So
)()()( f H f M f S δ=
∑∞−∞=
−=n
s s nT t hnT mt s )()()(
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 8/45
SKKU J.D. Cho8
Lecture on Communication Theory
여기서
3. 로 부터 를 recover 하는 방법
Sample and Hold 의 전 달 함 수
( ) f S
∑∞
−∞=
−=k
s s kf f M f f M )()(δ
)(t m
∑∞
−∞=
−=∴k
s s f H kf f M f f S )()()(
Reconstruction
filter outputEqualizer 특성
Amplitude distortion
)exp(sinc)( fT j(fT)T f H π−=
Delay of T/2
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 9/45
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 10/45
SKKU J.D. Cho10
Lecture on Communication Theory
6.5 Pulse-Position Modulation
1. PDM = Pulse-width mod. = Pulse-length mod.
: Pulse duration ∝2. PPM (Pulse Position Mod)
To make strictly nonoverlapping
)( snT m
∑∞
−∞=
−−=n
s p s nT mk nT t g t s ))(()(
Standard Pulse
2)(
max
s p
T t mk <
Sensitivity of PPM
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 11/45
SKKU J.D. Cho11
Lecture on Communication Theory
3. Generation of PPM waves
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 12/45
SKKU J.D. Cho12
Lecture on Communication Theory
4. Detection of PPM waves
)(t m PAM PDM PPM
sample&Integrator
→→→
↑
Integrator & Sample
elayed Version
sliver output
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 13/45
SKKU J.D. Cho13
Lecture on Communication Theory
5. Noise in PPM
1) If the received pulses were perfectly rectangular
→no effects on pulse position
but infinite channel BW
∴ Finite rise time →affected by noise
Ex1. SNR of a PPM system using sinusoidal mod.
Standard Pulse : raised cosine pulse
where
( )[ ] T t T t B A
t g T ≤≤−+= πcos12
)(
T BT
1=
nV
τ
)/41(π2
)/π2sin()(
22
T
T
B f f
B f A f G
−=
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 14/45
SKKU J.D. Cho14
Lecture on Communication Theory
For sinusoidal message
Peak-to-peak swing : by Ts
Rms value of receiver output
where K : constant
Avg. signal power (with 1Ω )
If noise amplitude = , τ : positive error, : noise
22
s KT =
822
222
s s T K KT =
nV nV
; g(t) 의 slope
; error
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 15/45
SKKU J.D. Cho15
Lecture on Communication Theory
Avg. noise power
Avg. transmitted power P
(Avg. noise power in message BW = W) = WNo
∫ − == 2
2
22
4
3)(
1 S
S
T
T
S T T B
Adt t g
T P
0
222
32
π(
N
AT B S T =∴ oSNR)
24
π
)(
)( 322 W T B
SNR
SNR FOM sT
C
O ==
[ ][ ]
22
0
2
222
2
n
2
222
2
n2
22
π
4
π
VE4
π
4V
τ
A B
N K
A B
K
A B
E K
E K
T T T
==
=
=
[ ] )2
2(V 00
2
n
N B N B E T T ×←=∴
oT S
C WN BT
ASNR)
4
3(
2
=∴
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 16/45
SKKU J.D. Cho16
Lecture on Communication Theory
Assume ; Nyquist sampling rate
FOM > 1 if
3) 결론
– PPM 에서는 FOM 은 크게 하려면 BT 가 커 야 된 다 .
– Noise 가 너 무 크 면 noise 를 message 로 오인
⇒Threshold Effect
6.6 Bandwidth - Noise trade off
1. PPM 과 FM 의 유 사 한 점
1) FOM 가 (BT/W)2 에 비례
2) Threshold Effect
2. FOM 와 BT 간의 trade - off
22
199
π
=W
B FOM T
W T s
2
1=
W BT 41.4>
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 17/45
SKKU J.D. Cho17
Lecture on Communication Theory
6.7 Quantization Process
1. Memoryless Quantizer
1) Quantizer
Signal amplitude
k = 1,2,…..,L
mk : decision levels or decision thresholds
vk : representation levels or reconstruction levels
∆ = mk - m
k-1: quantum or step - size
Figure 6.16 Description of a memoryless quantizer
1: +≤<→ k k mmmk m if index
ϕ k
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 18/45
SKKU J.D. Cho18
Lecture on Communication Theory
2)
3) Qunatization 하는 이유 : human sense (ear or eye )
can detect only finite intensity differences
Uniform Quantizer
Non-uniform Quantizer
Midthread
Midrise
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 19/45
SKKU J.D. Cho19
Lecture on Communication Theory
2. Quantization Noise
1) Q = M - V ; quantization Error ≈ thermal noise
uniformly distributed r.v.
( )⋅ g r.v. M
(continuous)
r.v. V
(discrete)
vm
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 20/45
SKKU J.D. Cho20
Lecture on Communication Theory
2) p.d.f of Q
where
∴ Variance
3. Bit 할당 및 SNR
R: bits per sample
=)( g f Q∆
1
22
∆≤<
∆− q
0 otherwise
L
mmax2Δ = , signal = [-m
max , m
max]
L = total # of levels
R
R
R
m
m
L R L
222
max
2
23
1Δ
12
1σ
2
2Δ
log,2
max
−==∴
=∴
==
2
Q
( ) [ ]
12
Δ
Δ
1
σ
2
2
Δ
2
Δ
2
2
Δ
2
Δ
222
==
==
∫
∫
−
−
dqq
Q E dqq f q QQ
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 21/45
SKKU J.D. Cho21
Lecture on Communication Theory
Output SNR (neglect receiver noise)
ex) Sinusoidal Modulating Signal
][68.1)(log10 10 dB RSNR o +=
R
Q
om P P 22max
2 23σ
( ==SNR)
)2(2
32
23
2
2
2
22
max
2
R
m
Rm
mm
A
A
Am A
P
==∴
==
O(SNR)
Level Bits SNR
32 5 31.8
64 6 37.8128 7 43.8
256 8 49.8
12 73.8
16 97.8
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 22/45
SKKU J.D. Cho22
Lecture on Communication Theory
6.8 PCM
1. PCM 구조
LPF : for anti-aliasing
2. Sampling : a train of narrow rectangular pulses,
Nyquist sampling theorem 에 의한 sampling
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 23/45
SKKU J.D. Cho23
Lecture on Communication Theory
3. Quantization : Discrete in both time & amplitude
1) Linear Quantizer
2) Nonlinear Quantizer
Voice signal 에서 사용하는 이유 :
loud talk : weak talk = 100 : 1
3) Nonlinear Q = Compressor + Uniform Quantizer
x µ - law
where µ > 0
- µ = 0 →Uniform Quantizer
weak talk →small step-size
loud talk → large step-size
⇒
)μ1log(
)μ1log(
++
=m
v
1 3 7 15 31
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 24/45
SKKU J.D. Cho24
Lecture on Communication Theory
- Reciprocal slope : quantum steps
≈→>>≈→<<
⇒
+×
+=
++
=
m
m
mmd
vd
m
vd
md
1
1μ
μ1
μ
)μ1log(
1
)μ1(
μ
)μ1log(
linear
logarithmic
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 25/45
SKKU J.D. Cho25
Lecture on Communication Theory
y A - law
- A = 1 →Uniform Quantizer
- Practical value of A ⇒A ≅ 100
- Reciprocal slope
z Compander = Compressor + Expander
=v
Am
A
m A 10,
log1≤≤
+
11
,log1
)log(1≤≤
++
m A
A
m A
=vd
md Am
A
A 10,
log1≤≤+
11
,)log1( ≤≤+ m A
m A
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 26/45
SKKU J.D. Cho26
Lecture on Communication Theory
4. Encoding
1) Encoding process : Translate the discrete set of
sample values to a more appropriate form of signal
to make the transmitted signal more robust to noise,
interference and other channel degradations
- Code : particular arrangement of discrete events
- Code element or symbol- Code word or character or alphabet
ex) 8 bit code word 256 levels.
R = 4 bits →16 level
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 27/45
SKKU J.D. Cho27
Lecture on Communication Theory
2) Binary symbols 을 나타내는 line codes.
x On - off signaling 1 →high, 0 →zero.y NRZ signaling 1 →+A
0 →-A
z RZ signaling 1 →half width
0 →no pulse
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 28/45
SKKU J.D. Cho28
Lecture on Communication Theory
Binary RZ 1 →+A,-A alternately
0 →no pulse
- no dc
| Split-phase (Manchester Code)
1 : +A → -A with half width
0 : -A →+A with half width
- no dc
Differential Encoding
1 : no transition
0 : transition
5. Regeneration ( Regenerative Repeater)
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 29/45
SKKU J.D. Cho29
Lecture on Communication Theory
Accumulation of distortion and noise Completely removed
if no error in decision making process.
Regenerated signal 에 error 가 생 길 경 우
Channel noise and interference →bit errors
Timing jitter →distortion →bit errors
6. Decoding →Quantized PAM signal
7. Filtering →LPF with BW = W (message BW)
8. Multiplexing ; TDM
9. Synchronization
- TDM 의 경우 수신기가 송신기에 synchronization- Frame Sync.
Example 3. T1 System
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 30/45
SKKU J.D. Cho30
Lecture on Communication Theory
x bit 193 : framing bit, for sync
y Voice channels
- 8 bit PCM used on five of six frames- 7 bit PCM used on every of six frames.
Bit 8 of each channel is a signaling bit
Voice signal : 300 ~ 3100 Hz
LPF for anti-aliasing = cut off = 3100 Hz
Standard Sampling = 8KHz
Compression law = approximate µ -law with µ =255
Mbps544.1125
1193 =
µ×
64
128
5121024
2048
4096
256
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 31/45
SKKU J.D. Cho31
Lecture on Communication Theory
MSB = 1 if +8bit word MSB = 0 if -
Next 3 bits : segments
LSB 4 bits : amplitude within a segment
6.9 Noise Considerations in PCM Systems
1. Channel noise
- Additive, white, Gaussian
- Bit error
- Error Rate = Average probability of symbol error
2. Quantization Noise : signal dependent
3. Error threshold
PCM using NRZ (Binary PCM)
Assume 105 bps = 100 Kbps
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 32/45
SKKU J.D. Cho32
Lecture on Communication Theory
Note: Thresho ld of visibility
(TOV) has been me asured to
occur at a S/N of 14.9dB w hen
there are 2.5 segme nt errors per
second which is a segment
error rate (SER) of 1.93x10-4.
SER at TOV
S/N db (RM S)
1E+01
1E+00
1E-01
1E-02
1E-03
1E-04
1E-05
1E-06
1E-07
1E-08
8 9 10 11 12 13 14 15
P r o b a b i l i t y
o f E r r o r
16 17 18
Segment error probability, 8 VSB with 4 state trellis, RS
(207,187)
Error threshold (at about 11dB)
≈ 60 - 70 dB required using AM
Regenerative Repeater
: Effects of amplitude, phase, and nonlinear
distortions in one link have practically no effect
on the regenerated input signal to the next link
Cliff Effects
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 33/45
SKKU J.D. Cho33
Lecture on Communication Theory
16 VSB error probability
S/N db (RM S)
1E+01
1E+00
1E-01
1E-02
1E-03
1E-04
1E-05
1E-06
1E-07
1E-08
8 12 16 20 24 28 32 36
16-VSB
Sym bol Error Rate
Segm ent Error
Rate After Reed-
Solom on FEC
P r o b a b i l i t y
o f E r r o r
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 34/45
SKKU J.D. Cho34
Lecture on Communication Theory
6.10 Virtues, Limitations, and Modifications of PCM1. PCM 의 장점
1) Ruggedness to channel noise & interference
2) Efficient regeneration of a coded signal
3) Efficient exchange of increase channel BW for improved SNR
4) Uniform format → integration with other forms of digital datain a common network
5) Comparative ease in TDM system
6) Secure communication ex ) encryption
2. 단점
1) Increased channel BW ←
2) Increased system complexity ←VLSI or Delta modulationwide band : satellite,optic fiber
data compression
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 35/45
SKKU J.D. Cho35
Lecture on Communication Theory
6.11 Delta Modulation
1. DM System
Oversampling → to increase the correlation between adjacent
samples.
Staircase approximation → ±∆
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 36/45
SKKU J.D. Cho36
Lecture on Communication Theory
))1()()](sgn[)(
)()()(
sq sq sq
s sq
s sq s s
nT eT nmnT mnT enT e
T nT mnT mnT e
+−=∆=
−−= ; error signal
; quantized error signal
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 37/45
SKKU J.D. Cho37
Lecture on Communication Theory
2. DM Quantization error
1) Slope overload distortion
2) Granular Noise3) Slope overload distortion 을 없애는 조건
4) Slope overload Granular Noise
5) Adaptive DM: 입력 신호의 크기에 따라 adaptive
하게 결정
dt
t dm
T s
)(max≥
∆
→← Trade off
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 38/45
SKKU J.D. Cho38
Lecture on Communication Theory
3. Delta-Signal Modulation (D -Σ M)
; 수신기의 integrator 을 송신기로 이동
1) DM 의 단점 : 수신기에 error 의 accumulation
2) Delta-Sigma Mod 의 영향
x Low frequency content of input signal is pre-emphasized
y Adjacent sample 간의 correlation 이 증가하여 overall
system performance 증가
z Receiver 가 simple
3) Smoothed version of 1 bit PCM
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 39/45
SKKU J.D. Cho39
Lecture on Communication Theory
6.12 Differential PCM
1. High correlation between adjacent samples
→ Redundant information
2. DPCM System
redundancy in spatial
redundancy in entropy
redundancy in temperal
ex) Video
pitch frequency
temporal redundancy Voice
sq T ne )1(( −
sq T nm )1( −
)( sq nT m
Ts
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 40/45
SKKU J.D. Cho40
Lecture on Communication Theory
Prediction error
Quantizer output
Prediction filter input
)(ˆ)()( s s s nT mnT mnT e −=
)()()( s s s nT qnT enT eq −=
Quantization
error
)()(ˆ)( s s sq nT enT mnT m q+=)()()(ˆ s s s nT qnT enT m
++=)()( s s nT qnT m +=
)( snT mq is independent of )(ˆ snT m
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 41/45
SKKU J.D. Cho41
Lecture on Communication Theory
3. Processing Gain
- Processing Gain ; Predictor 를 사용해서 생기는 Gain
- Optimum adv. of DPCM over PCM = ≈ 4 ~ 11dB
- For constant signal-to quantization noise ratio
DPCM → saving of about 8 - 16kbps over PCM (T s= 8KHz )
where : Variance of prediction error
E
2σ
: signal to quantization noise ratioQSNR )(
Q
M
OSNR 2
2
σ
σ
)( =
QO SNRGSNR p
Q
E
E
M )()(
2
2
2
2
=
σ
σ
σ
σ=
where : Variance of with zero mean)( snT m
: Variance of with zero mean)( snT q
E
M pG
2
2
σ
σ=
QSNR)(
QSNR)(
2σ M
2σ Q
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 42/45
SKKU J.D. Cho42
Lecture on Communication Theory
6.13 Coding Speech at low bit rates. (32, 16, 8, 4 kbps)
1. Design Philosophy
1) Remove redundancies by statistical characteristics
of speech waveforms
2) Properties of hearing →Phychoaccoustic Modeling
2. 오디오 압축의 원리
Psychoacoustic model
- Masking curve 이하는 감지 불능 .
- 큰 소리는 주변의 작은 소리를 Mask 함 .
1KHz sinewave masker
Masking threshold
Threshold in quiet
0.02 0.05 0.1 0.2 0.5 1 2 5 10 20KHz
0
10
20
30
40
50
60
70
frequency
Sound
pressure
lev
el(dB)
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 43/45
SKKU J.D. Cho43
Lecture on Communication Theory
2. Adaptive Differential PCM ; Time-domain codes
1) Adaptive quantization : time-varying step size
where φ : constant
: estimate of
x Adaptive quantization with forward estimation (AQF)
unquantized samples of the input signal
→ forward estimates of
Buffer 필요 : ∆ (nT s) 를 정할 동안 unquantized
sample 저장
TX of level information
Delay in encoding(≈ 16msec) ⇒AQB 를 더 많 이 사 용
y Adaptive quantization with backward estimation (AQB)samples of quantized output
→backward estimates of
Buffer 없음 , delay 없음
)(ˆ)( s s nT nT M σφ=∆
)(ˆ snT M σ )( snT M σ
)( snT M σ
)( snT M σ
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 44/45
SKKU J.D. Cho44
Lecture on Communication Theory
2) Adaptive Prediction
speech signals are inherently nonstationary
→ Autocorrelation function & p.s.d of speech signals are
time-varying
x Adaptive prediction with forward estimation (APF)
y Adaptive prediction with backward estimation (APB)
- Logic for adaptive prediction : LMS algorithm
- 32 kbps 에서 impressive
8/8/2019 comm6
http://slidepdf.com/reader/full/comm6 45/45
Lecture on Communication Theory
3. Adaptive Subband Coding ; Freq-domain code
- 16kbps ≈ 64 kbps PCM
- 16kbps, 8kbps, 4kbps
Quasi - periodic nature of voice signal
pitch frequency →pitch prediction
Noise Masking Phenomenon
동일 band 의 signal 보다 15dB 낮은 noise 는 human ear 가
감지하지 못한다 .
즉format frequency (resonance freq of the vocal track tube)
근처에서는 large coding error 를 허용한다 .
Psychoaccoustic modeling
- Adaptive subband coding
- Complexity of 16kbps ≅ 100 × (that of 64k PCM)
- Processing delay ≈ 25 msec
¯ Voice mail 에는
문제없음
Recommended