1/21 chapter 5 – signal encoding and modulation techniques
TRANSCRIPT
1/21
Chapter 5 – Signal Encoding and Chapter 5 – Signal Encoding and Modulation Techniques Modulation Techniques
2/21
Analog Data, Digital SignalAnalog Data, Digital Signal
Digitization is conversion of analog data into digital data which can then:
be transmitted using NRZ-L (digital signal) be transmitted using code other than NRZ-L be converted to analog signal by using modulation
techniques (ASK, PSK, FSK)
signal
3/21
Codec (Coder-decoder)Codec (Coder-decoder)
Analog to digital conversion done using a codec (coder-decoder). Two techniques:
1. Pulse Code Modulation (PCM)
2. Delta Modulation (DM)
4/21
Pulse Code Modulation (PCM)Pulse Code Modulation (PCM)
Sampling Theorem:“If a signal is sampled at regular intervals at a rate
higher than twice the highest signal frequency, the samples contain all information in original signal”
Samples can be used to reconstruct the original signal
e.g., 100-4000Hz voice data, requires 2*4000=8000 sample per sec
These are analog samples, called Pulse Amplitude Modulation (PAM) samples
To convert to digital, each of these analog samples must be assigned a binary code
5/21
Pulse Code Modulation (PCM) ExamplePulse Code Modulation (PCM) Example
The signal is assumed to be band-limited with bandwidth B The PAM samples are taken at a rate of 2B, or once every
Ts=1/(2B) seconds Each PAM sample
is quantized into one of 16 levels
Each sample is then represented by 4 bits.
8 bits→256 level →better quality
4000Hz voice→(8000sample/s)*8bits/sample=64Kbps
6/21
Pulse Code Modulation (PCM)Pulse Code Modulation (PCM)Block DiagramBlock Diagram
By quantizing the PAM samples, the resulting signal is an approximation of the original one
This effect is known as quantization error or quantization noise
The Signal-to-Noise-Ratio (SNR) for quantizing noise:
bitsofnumberndBnSNRdB :,76.102.6
Linear Versus Non-Linear EncodingLinear Versus Non-Linear Encoding
7/21
Linear Encoding (uniform quantization): Equally spaced quantization steps Lower amplitude values are relatively more distorted
Non-Linear Encoding (non-uniform quantization): Non-equally spaced quantization steps Large number of quantization steps for signals with low amplitude, and smaller number of
quantizing steps for signals with large amplitude
8/21
Companding (Compressing-Companding (Compressing-Expanding)Expanding)
Instead of non-linear encoding, use companding+linear encoding
Companding gives more gain to weak signals than to strong signals on the input. At output, the reverse operation is performed
10000104010000log*1010000
100010301000log*101000
1001020100log*10100
10101010log*1010
)10()log*10()(
10/4010
10/3010
10/2010
10/1010
10/10
XYX
XYX
XYX
XYX
XExpandedXYcompressedXvalueNormal Y
Compressing ExpandingXY
X
9/45
Delta Modulation (DM)
An analog input is approximated by a staircase function that moves up or down by one quantization level () at each sampling interval (Ts).
A 1 is generated if the staircase function is to go up during the next interval; a 0 is generated otherwise.
The staircasefunction tracks the original waveform
10/21
Delta Modulation Operation For transmission: the analog input is compared
to the most recent value of the approximating staircase function.
If the value of the analog input exceeds that of the staircase function, a 1 is generated; otherwise, a 0 is generated.
Thus, the staircase is always changed in the direction of the input signal.
For reception: The output of the
DM process is therefore a binary sequence that can be used at the receiver to reconstruct the staircase function.
Staircase
11/21
Pulse Code Modulation (PCM) Versus Delta Modulation (DM)
DM has simplicity compared to PCMDM has worse SNR compared to PCMPCM requires more bandwidth
eg., for good voice reproduction with PCM want 128 levels (7 bit) & voice bandwidth 4khz need 8000 sample/s x 7bits/sample = 56kbps
PCM is more preferred than DM for analog signals
12/21
Analog Data, Analog Signal
Modulate carrier signal with analog data (voice)Why modulate analog signals?
higher frequency can give more efficient transmissionpermits frequency division multiplexing (chapter 8)
Types of modulationAmplitude Modulation (AM)Frequency Modulation (FM)Phase Modulation (PM)
Demodulator)(tm)(tsModulator
analog data
)(tm
carrier signal)2cos( tfA cc
modulated signal)(ts
13/21
Amplitude Modulation (AM)
AM is the simplest form of analog modulationUsed in AM radio with carrier Used also in analog TV broadcastingAnalog data modulates a carrier signalMathematically, the AM wave can be expresses as
frequencycarrierf
indexModulationn
signaldatainputtmtxn
where
tftxnts
c
a
a
ca
:
:10
:)()(
)2cos()](1[)(
MHzfMHz c 605.1535.0
11/45
Time Domain description of AM Signal Derive an expression for the AM wave if the input signal:
Envelope of AM signal:
cmma fftfntm ),2cos()(
)2cos()]2cos(1[
)2cos()](1[)(
tftfn
tftmts
cma
c
Modulationn
AA
AAn
n
n
A
A
tfwhen
tfwhen
tfn
a
a
a
a
m
m
ma
%:%100*
1
1
1)2cos(.min
1)2cos(.max
)]2cos(1[
minmax
minmax
min
max
15/21
Frequency Domain description of AM Signal
The Double SideBand Transmitted Carrier (DSBTC):
)])(2cos())(2[cos(2
)2cos()(
)]cos()[cos(2
1)cos()cos(:
)2cos()2cos()2cos(
)2cos()]2cos(1[)(
tfftffn
tfts
identityrictrigonomettheemploying
tftfntf
tftfnts
mcmca
c
cmac
cma
cfmc ff mc ff 0f
)( fS
Upper Side Band(USB)
Lower Side Band(LSB)
Carrier
11/45
Frequency Domain description of AM Signal Consider a voice signal m(t) with a
bandwidth that extend from 300Hz to 3000Hz being modulated on a 60 KHz Carrier
KHzatCarrier
KHzKHzSideBandLower
KHzKHzSideBandUpper
containssignalresultingThe
KHzfcarrier
KHzBBandwidth
c
60
7.5957:
633.60:
:
60
3
17/21
Variations of AM signal
Double Side Band Transmitted carrier (DSBTC)wast of power as the carrier is transmitted with the side
bandswast of bandwidth as both upper and lower side bands are
transmitted (each side band contains the complete spectrum of the message signal m(t) ): Transmitted bandwidth=BT=2B
Double Side Band Suppressed Carrier (DSBSC)Less power is required as no carrier is transmittedwast of bandwidth as both upper and lower side bands are
transmitted: Transmitted bandwidth=BT=2BSingle Side Band (SSB)
Less power is required as no carrier is transmittedLess bandwidth as one side band is transmitted: BT=B
18/21
Angle Modulation
Frequency Modulation (FM) and Phase Modulation (PM) are special cases of angle modulation
Used in FM radio with carrier The angle modulated signal is expressed as:
Phase Modulation (PM): - Example: find s(t) if
MHzfMHz c 10888
))(2cos()( ttfAts cc
)(.max
.
:)(
:
)()(
tmoftheisAwhere
AndeviationphaseMax
signalmessageinputtm
indexModulationphasen
where
tmnt
m
mp
p
p
pmp
mpcc
mp
nAndeviationphaseMax
tfntfAts
tfnt
.
)]2cos(2cos[)(
)2cos()(
19/21
Frequency Modulation (FM)
The angle modulated signal is expressed as:
FM when: - Example: find s(t) if
))(2cos()( ttfAts cc
)(.max
2/..
2/)()(
)](2[)(2
:
:
)()(
tmoftheisAwhere
AnFdeviationfreqMax
tmnftf
ttfdt
dtf
timeanyatfrequencyThe
indexModulationfrequencyn
tmndt
td
m
mf
fci
ci
f
f
])2cos(2
2cos[)(
)2cos(2
)2sin()(
)2sin()(
tff
ntfts
tff
n
dttfnt
tfndt
td
mm
fc
mm
f
mf
mf
20/21
Transmitted Bandwidth for AM, PM and FM
Transmitted bandwidth for AM:
Transmitted bandwidth for PM and FM:
Thus, both PM and FM require greater bandwidth than AM
bandwidthsignalmessagetheisBwhere
BBT 2
FMforB
AnPMforAn
where
BB
mf
mp
T
2
)1(2
21/21
AM, PM, FM