Unit 3: Digital and Analog Transmission
Digital to Digital Conversion Analog to Digital Conversion Transmission Modes
Digital transmission
We shall understand, how we can represent digital data by using digital signals.
The conversion involves three techniques:
line coding block coding scrambling.
Digital Transmission
Line coding
Line coding is the process of convertingdigital data into digital signals
It is important to understand that digital data stored in digital
memory storage device as sequence of bits needs to be converted into a digital signal where level of a waveform signifies the digital signal Line coding is the process of converting this sequence of bits into digital signal
Signal element
A data element is smallest piece of information i.e. a bit
A signal element is the shortest unit (timewise) of a digital signal. Signal element carrydata elements
We define a ratio:
r = d s
Signals and data elements
Data rate and signal rate
Data rate is number of data elements (bits) transmitted per second
Units is bits per second (bps) Also calledbit rate
Signal rate is number of signal elements transmitted per second.
Units isbaud
Also calledpulse rate/modulation rate/ baud rate
Goal of signal communication is increase the data rate while decreasing the signal rate.
Relationships
IfS is signal rate andN is data rate then:
S = N r
S changes with bit pattern
S is different if we have all 1s, all 0s or alternate 1’s and 0’s Since there can be a lot of combinations of bits, data rate has a maximum, minimum and an statistical average.
Average signal rate:
Savg =c ×N×
Calculating signal rate
Suppose a signal is carrying data such that two data element is encoded as one signal element. If bit rate is 1000kbps, what is Sav if c = 0.7
Sav = 0.7×106×2 = 1.4Mbaud
It is the baud rateand not thebit rate, which determines the required bandwidth for a digital signal.
Find out the signal rate,r and calculate Sav of digital TV signal at your home. Also find out what happens when the signal is not received at this baud rate.
Minimum bandwidth (Bmin) for given data rate:
Bmin=c×N×
1 r
Also for a given bandwidth, Maximum data rate (Nmax):
Baseline wandering
While decoding, receiver calculates a running average is received signal power called baseline.
Incoming signal power is evaluated against this baseline to determine value of the data element
In this technique, a long list of 1s or 0s can cause problem by causing drift in baselinealso called baseline wandering
DC components
When voltage level in a digital signal is constant for a while, low frequencies are created (check using Fourier analysis)
These frequencies around zero are called DC (direct current) components becomes problem for systems which cannot pass low frequencies
Self-synchronization
For correct interpretation of sender’s signal, receiver must synchronize its clock
A self-synchronizing digital signal includes timing information in the data being transmitted.
If receiver’s clock is 0.1% faster than sender’s clock, how many extra bits per second does receiver receives for data rate of 1 kbps and 1 Mbps
Bits sent Bits received Extra bits
1,000 1,001 1
Line Coding
Unipolar NRZ
All signal levels are on one side of Amplitude axis.
NRZ schemes
Traditionally, unipolar scheme was designed as anon-return-to-zero (NRZ)scheme in which positive voltage defines bit 1 and zero voltage defines bit 0.
It is called NRZ because signal does not return to zero at the middle of the bit.
The scheme turned out to be costly energy-wise.
Polar NRZ-L and NRZ-I schemes
Polar Schemes are those where voltage levels extend on both sides of voltage axis.
NRZ-L
NRZ-L (level) indicates the fact that level of the voltage indicates the bit.
NRZ-I (Invert) indicates the fact that lack of change of level of the voltage indicates the value of bit.
Comparison of NRZ-L and NRZ-I
Baseline wandering is problem in both but it is more severe in NRZ-L.
For NRZ-L, when there is a long series of 0s or 1s, then the average power becomes skewed.
For NRZ-I, when there is a long series of 0s or 1s, then the problem occurs on;y for long series of 0s.
So the problem is twice as severe in NRZ-L than in NRZ-I
We employ mechanisms to avoid long series of 0s to overcome this problem in NRZ-I case.
Synchronization is a problem in both
More serious in NRZ-L than in NRZ-I A long series of 0s is problem in both A long series of 1s is problem in NRZ-L only
Comparison of NRZ-L and NRZ-I
Average signal rate is N/2 Bandwidth
Value os power density is very high for frequencies close to zero (DC component)
RZ schemes
Main issue with NRZ schemes is that of synchronization as receiver has no means to knowing when one bit has ended and other bit has started.
Polar RZ Scheme
Note that signal goes to zero voltage in the middle of each bit and remains there until the beginning of next bit.
RZ Scheme
Main disadvantage is that it requires two signal changes to encode a bit, which results inincreased bandwidth.
There isn’t any DC component problem here. Sudden change in polarity does create problem. Due to three voltage levels, it is complex
Manchester and Differential Manchester
Manchester and Differential Manchester
Manchester
Combines RZ and NRZ-L
Duration of bit is divided into two halves
Voltage remains at one level during first half and moves to second in second half
Transition in the middle of the bit provides synchronization.
Differential Manchester
Combines RZ and NRZ-I
There is always a transition at the middle of the bit but the bit values are determines at the beginning of beginning if bit.
If next bit is 0, there is a transition If next bit is 1, there isn’t any transition
Features of Manchester and Differential Manchester
No baseline wandering
There are transitions in each bit so continuous voltage levels are not created
There is no DC component
each bit has a positive and negative voltage contribution
Signal rate is double that of RZ scheme
Bipolar coding scheme
There are three voltage levels
Positive Zero Negative
Voltage level of one data element is at zero voltage and for other data element, it alternates between positive and negatives.
For this reason, it is also calledmultilevel binary. Two Schemes are popular
AMI & Pseudoternary
The wordmark comes from telegraphy and means 1.
0 is represented by zero voltage and 1 is represented alternatively by positive and negative voltages
In pseudoternary, 1 bit is encoded as zero voltage and 0 is represented alternatively by positive and negative voltages
Features of Binary Schemes
Alternative to NRZ scheme same signal rate as NRZ
AMI and Pseodoternary
Check out some more schemes from page 105 to 109
Summary
A2D- Pulsed Code Modulation
PCM
PCM encoder performs 3 processes:
Sampling Encoding Quantizing
Sampling
Analog signal is sampled everyTs s Ts is sampling interval or period
Sampling frequency is inverse of sampling period i.e
fs=
1
Ts
There are three kinds of samplings:
Three sampling types
Nyquist theorem
Which sampling rate is adequate to reproduce an analog signal reasonably
Nyquist provides an elegant answer:
Nyquist Theorem
Quantization
Sampling results in series of pulses with amplitude values between maximum and minimum values of the signal amplitude.
These set of values can be infinite in number andnon-integral in nature.
This presents a problem for encoding them digitally
Solution:
Assuming original analog signal has instantaneous amplitudes between
Vmax andVmin
Divide the range (Vmax,Vmin) intoLzones, each of height ∆ such that:
∆ = Vmax −Vmin
L
Quantization error
Quantization is an approximation process Hence these is an error due to approximation Quantization error changes theSNRdB:
SNRdB = 6.02nb+ 1.76
Uniform vs Non-uniform quantization
Amplitudes might change abruptly
One way out is to change ∆ as per requirement
Other way out is the process of companding and expanding
Companding refers to reduction to large amplitudes within a range and expanding is doing opposite
Encoding
Encoding is representation of quantized voltage in anb-bit code.
Number of bits are determined from quantization levels:
For 1 volt quantization resolution,±8 V signal would require 3 bit word for encoding because 23= 8→number of levels
For 0.5 volt quantization resolution,±8 V signal would require 4 bit word for encoding because 24= 16→number of levels.
Bit rate:
PCM decoder
PCM Bandwidth
Minimum bandwidth of a line-encoded signal is:
Bmax =
c ×N
r =
c×nb×fs
r =
c×nb×2×Banalog
r
Considering NRZ or bipolar signal, 1/r = 1 andc = 1/2, we get Bmin=nb×Banalog
This is the price of digitization one has to pay.
Delta Modulation
PCM is a complex technique
DM
Process records small positive and negative changes (δ)
Positive changes are recorded as 1 and negative changes are recorded as 0.
There is no encoding stage here Bits are sent one after another
Adaptive Delta Modulator changes the δ as per magnitude of amplitude of analog signal
Delta Modulation
Delta Demodulation
Transmission Modes
Parallel and Serial modes
Asynchronous
Timing of signal is unimportant
Instead, the information is received and translated by agreed upon partners
Pattern of transmission is group-wise (byte-level) serial streaming We send one start bit (0) at the beginning and 1 or more stop bits (1s) at the end of each byte
There may be gaps between bytes
Gap can be represented either by an idle channel or by a stream if additional stop bits
”Asynchronous” nature is only at byte level
Asynchronous
Synchronous
Bit stream is combined into longer frames which may contain multiple bytes
Without start or stop bits
It is the responsibility of receiver to group the bits
Receivercounts the bits and group them into bytes (8 bits)
Synchronous
Isochronous
Data arrives at a fixed rate
Analog Transmission
D2A
A sine waves has 3 characteristics
Amplitude Frequency Phase
Changing any one characteristic of a wave, results in anew version of that wave
D2A Schemes
Aspects of D2A
Data element versus signal element
Although the definition of both are same but nature of signal element is different as it is continuous in nature
Relationship between data rate and signal rate:
S = N r
Unit is baud,N is data rate (bps) and r is number of data elements in one signal elements
Carrier Signal
Sender produces a high-frequency signals which acts as a abase for information signal
This is calledcarrier signal/frequency
Receiver is tuned to carrier frequency
Amplitude Shift Keying
Amplitude of carrier signal is varied to create signal element
Both frequency and phase remains as original, only amplitude changes
Binary ASK
ASK with two levels (hence the word binary) Also called ON-Off Keying (OOK)
Peak level amplitude of 0 is zero voltage and for 1 it remains same as carrier frequency
Bandwidth:
The carrier wave is single frequency sine wave
modulation produces non-periodic composite signal having continuous set of frequencies
Bandwidth is proportional to signal rate (baud rate) Another variabled ∈(0,1) is defined
Depends onmodulationandfiltering process
Relationship:
B = (1 +d)S Bmin=S andBmax = 2S
Implementation of ASK
Digital data = unipolar NRZ (High=1V, Low=0V)
Multiply NRZ with signal coming from oscillator (Carrier frequency)
FSK
Frequency Shift Keying
Frequency of carrier signal modulates according to digital data Peak amplitude and phase remains as original
Binary and Multi-level FSK
Binary FSK uses two carrier frequencies
Binary FSK
Bandwidth for FSK
Carrier signals are simple sine waves
Modulation creates a non-periodic composite signal with continuous frequencies
One can imagine a FSK signal as two ASK signals, each with its own carrier frequencies f1 and f2.
If the difference between two frequencies is 2∆f the bandwidth is:
B = (1 +d)S+ 2∆φ
Implementations of BFSK
Two implementations of BFSK
Noncoherent
There may be discontinuities in the phase when one signal element ends and next begins
Same as two ASK modulations using two different carrier frequencies
Coherent
There aren’t any discontinuities in the phase when one signal element ends and next begins
BPSK
PSK involves modulation of phase
PSK is more common than ASK and PSK BPSK has only two signal elements:
With phase 00
With phase 1800
Features of PSK
Noise
Noise can change amplitude easier than it can change the phase Hence PSK is less susceptible to noise than ASK
But PSK needs moresophisticated hardware than ASK Bandwidth
Implementation of PSK
Polar NRZ is mixed with oscillator output
QPSK
Quadrature PSK
Using 2 bits at the same time in each signal element
Decreasing baud rate
Hence decrease bandwidth requirement two separate BPSK modulations
One is in-phase Other is out-of-phase
QAM
Quadrature Amplitude Modulation
PSK limits in distinguishing small difference in phase which limits its bit rate
IN QAM we combine ASK and PSK
Use two carriers, one in-phase and other quadrature with different amplitude levels for each carrier
There can be any number of combinations
4-QAM
4 different signal element types
using NRZ signal to modulate each carrier
A2A
Analog-to-analog conversion
