TO DIGITAL MODULATION

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CHAPTER 4

• INTRODUCTION
• TO DIGITAL MODULATION

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From your syllabus

• 4.0 Introduction to Digital Modulation (12 hours)
• 4.1 Type of digital modulation
• 4.2 Pulse Modulation
• 4.3 Binary Modulation (Shift keying modulation)
• 4.4 Sampling theorem Nyquists theorem
• 4.5 Quantization uniform and non-uniform
• 4.6 Coding
• 4.5 Pulse Code Modulation
• 4.6 Other digital modulation such as delta
  modulation, DPCM, ADPCM
• 4.7 Line coding Manchester, NRZ
• 4.8 Multiplexing system, SDM, FDM, TDM
• 4.9 Digital Hierarchy PDH and SDH

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Rearranged syllabus

• 4.2 Pulse Modulation
• 4.4 Sampling theorem Nyquists theorem
• 4.5 Quantization uniform and non-uniform
• 4.6 Coding
• 4.5 Pulse Code Modulation
• 4.3 Binary Modulation (Shift keying modulation)
• 4.6 Other digital modulation such as delta
  modulation, DPCM, ADPCM
• 4.7 Line coding Manchester, NRZ
• 4.8 Multiplexing system, SDM, FDM, TDM
• 4.9 Digital Hierarchy PDH and SDH

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By the end of this chapter you should be able to

• Explain the concept of pulse modulation, and the
  various types of pulse modulation
• Explain the process of converting analog data
  into digital data using PCM
• Solve problems involving PCM

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Pulse Modulation

• Pulse Modulation is a process of sampling analog
  signal and then converting them into discrete
  pulses and transporting the pulses from a source
  to a destination over a transmission medium. A
  device to perform this is called ADC
  (Analog-to-Digital Converter) DAC
  (Digital-to-Analog Converter).

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PAM (Pulse Amplitude Modulation)

• It is used to describe the conversion of analog
  signal to pulse-type signal in which the
  amplitude of the pulse denotes the analog
  information. In addition, it is a series of
  pulses in which the amplitude of each pulse
  represents the amplitude of the information
  signal at a given time.

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Pulse Modulation

• PWM (Pulse Width Modulation)
• It is a pulse duration modulation (PDM) or
  pulse length modulation. The width of pulse is
  varied proportional to the Amplitude of the
  analog signal at the time signal is sampled.
• PPM (Pulse Position Modulation)
• It is a series of pulses in which the timing
  of each pulse represents the amplitude of the
  information signal at a given time.

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PCM (Pulse Code Modulation)

• It is a series of pulse in which the amplitude of
  the information signal at a given time is coded
  as a binary number. The pulses are of fixed
  length and fixed amplitude. Refer to Figure 10-1
  in the textbook for PWM, PPM, PAM PCM.
• PCM is generated by 3 processes Sampling,
  Quantization Encoding.
• An Integrated circuit that perform PCM
  encoding and decoding function is called CODER OR
  DECODER.

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Pulse Modulation
Analog signal
Pulse amplitude modulation
Pulse width modulation
Pulse position modulation
Pulse code modulation
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Sampling
A process of periodically sampling the
continually changing analog input voltage and
convert it to a series of constant amplitude
pulses
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Block diagram for digital transmission system
ASK, FSK, PSK
Sampling Quantization Coding
RZ, NRZ, AMI
Digital transmission
Analog
ADC
Line coding
Block diagram for digital transmission system
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Nyquist Sampling Theorem

• Nyquist Sampling Theorem states that an
  analogue signal is completely described by its
  samples, taken at equal time Intervals, the
  sampling frequency fs is greater than, or equal
  to, twice the maximum frequency component of the
  analogue signal

Nyquist theorem states that
fs 2 x (bandwidth of analogue signal) 2B Hz
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The choice of sampling frequency, fs must follow
the sampling theorem to overcome the problem of
aliasing and loss of information

• Shannon sampling theoremgt fs ? 2fm
• Nyquist frequency
• fs 2fm fN

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Nyquist theorem
m
m
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Therefore, the maximum frequency that can be
processed by the sampled data using sampling
frequency, fs (without aliasing) is
fs gt 2fm

• fm fs / 2
• 1 / 2Ts

fs lt 2fm
fs 2fm
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Types of sampling

• 2 types of sampling
• 1. Natural Sampling
• tops of the sample pulses retain their natural
  shape, making it difficult for ADC to convert to
  PCM codes
• 2. Flat-top Sampling
• input voltage is sampled with narrow pulses and
  then held relatively constant until next sampling
  

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Information signal
Pulse signal
Sampled signal (PAM)
Natural Sampling
Flat-top Sampling
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A method used to represent an analog signal in
terms of digital word
Constitutes 3 processes

• Sampling the analog signal- convert analog signal
  into PAM
• Quantization of the amplitude of the sampled
  signal rounding off of the voltage value
• Coding of the quantized sample into digital
  signal representing the quantized value as codes

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Pulse code modulation

• Sampling
• An analog signal must be sampled at Nyquist rate
  to avoid aliasing
• Quantization Coding
• Process of estimating the sampled amplitude into
  a value suitable for coding (ADC).
• A fixed number of levels including the maximum
  and minimum value of the analog signal
• Number of levels is determined by the number of
  bits used for coding

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Quantization

• Quantization level, L 2N
• Quantization level depends on the number of
  binary bits, N used to represent each sample.
• For exampleFor N 3 Quantization level, L 23
  8 level.
• In this example, first level (level 0) is
  represented by 000, whereas bit 111 represents
  the eigth level

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Quantization

• Quantization Interval (?V)
• Represent the voltage value for each quantized
  level
• For example For a sampled signal that has 5V
  amplitude, Vpp 10 V divide by the quantized
  level, L 8 level,
• Therefore, quantized interval ,

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mp
1 11
1 10
?V
1 01
1 00
0
t
0 00
0 01
0 10
0 11
-mp
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Quantization value, Vk
The middle voltage for each quantized level For
example for n 3, quantized level, L 8 and a
sampled sinusoidal signal with 5 V , The middle
quantized value for level 0, In this example,
for a sample that is in level 0 segment will be
represented by bit 000 with a voltage value of
4.375 V. The difference between the sampled
value and the quantized value results in
quantization noise.
?V
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Folded binary code

• The binary codes used for PCM are n-bit codes
  (sign-magnitude code) where the MSB bit is the
  sign bit.
• A code for a sample voltage value can be found
  from
• Folded PCM code sample voltage
• quantization interval

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Folded binary code

• If PCM is 3-bit codes, then the sign and
  magnitude are shown below
• In terms of Voltage, the maximum signal voltages
  are 3 V or -3 V and the minimum signal voltages
  are 1 V or -1 V.

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4.6.3.1 Uniform Quantization using Folded Binary
Code (sign bit)
The same code representing several samples with
different amplitudes
mp
1 11
1 10
Quantization error Qe
1 01
?
Step size
1 00
0
t
0 00
0 01
0 10
0 11
-mp
Sign but
value
PCM code
t
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UNIFORM QUANTIZATION
Uniform quantization is a quantization process
with a uniform (fixed) quantization interval.
Example N 3 , L 8 , signal 5 V gt ?V
1.25 V . Bit rate
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Problem 0

• What is the quantization interval for this
  system?
• Can you find the code for 2.3V?

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UNIFORM QUANTIZATION
What about using this system? Can you find the
code for -3.4V??
Example N 3 , L 8 , signal 5 V gt ?V
1.25 V . Bit rate
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Problem 1
Input analog signal
Sampling pulse
PAM signal
PCM code
What is the PCM code for 2.6 V??
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Problem 2
Question What is the quantized interval and PCM
code for 1.75 V??
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Problem 3

• The maximum signal voltages for this PCM system
  are 3 V or -3 V and the minimum signal voltages
  are 1 V or -1 V. How do we improve PCM, to handle
  analog signal with maximum peak voltage of 5V??

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Problem 4
6 bit code (5 bits for magnitude and 1 bit for
sign
Vpp 31.5 V

• No of levels
• quantized interval, ?V
• Voltage value for 101101
• Voltage value for 011001
• PCM Code for input 13.62 V
• (g)PCM Code for input 9.37 V

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Solution
6 bit code (5 bits for magnitude and 1 bit for
sign
Vpp 31.5 V

• No of levels 26 64
• quantized interval, ?V 31.5/64 0.492 V
• Voltage value for 101101 (13 x 0.492) 6.4
  V
• Voltage value for 011001 (25 x 0.492) -12.3
  V
• Code for input 13.62 V
• 13.62/0.492 27.68 ? 28 gt 111100
• (g)Code for input 9.37 V
• 9.37/0.492 19.04 ? 19 gt 010011

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Quantization Error

• Folded PCM code sample voltage
• resolution
• For input at 2.6 V, the PCM code is therefore
• 2.6/1 2.6
• But since there is no code for 2.6, the
  magnitude is rounded off to the nearest valid
  code, which is 111 (3V)
• Thus there is difference of 0.4
• ?QUANTIZATION ERROR (Qe)
• or also known as quantization noise (Qn)
• Qe sample voltage - original analog signal

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• Maximum magnitude Qe is equal to one-half a
  quantum
• Resolution , more accurate the quantized signal
  will resemble the original analog sample

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Linear input-output transfer curve
Linear
Error
Quantization
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Dynamic Range

• Ratio of the largest possible magnitude to the
  smallest (other than 0) magnitude that can be
  decoded by the digital-to-analog converter (DAC)
  in the receiver

DR dynamic range (unitless) Vmin the quantum
value Vmax the maximum voltage magnitude of the
DACs n number of bits in a PCM code (excl.
sign bit)
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• Number of bits used for a PCM code depends on the
  dynamic range
• DR 2N -1
• Thus 2N DR 1
• And therefore, The minimum number of bit used
• N log ( DR 1 )
• log 2

For n gt 4
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Dynamic Range
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Coding Efficiency
Coding efficiency is a numerical indication of
how efficiently a PCM code is utilized
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EXAMPLE

• A PCM systems has the following specification
• Maximum Analog Input Frequency 4 kHz
• Maximum decoded voltage at the receiver ? 2.55
  V
• The dynamic range 46 dB
• Determine the following
• (a) Minimum Sampling Rate
• (b) Minimum number of bits used in PCM code
• (c) Resolution
• (d) Quantization Error
• (e) Coding Efficiency

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Solution

• (a) The minimum sampling rate
• fs 2fa 2(4 kHz) 8 kHz
• (b) Calculate the Dynamic range
• 46 20log(Vmax / Vmin)
• Vmax / Vmin antilog (46/20) 199.5
• Thus, the minimum number of bit used
• n log (199.5 1) / Log 2 7.63
• (c) Resolution is defined as
• Vmax / 2n - 1 0.01 V
• (d) Quantization Error
• Q resolution / 2 0.01 V / 2 0.005
  V

(e) Coding Efficiency Coding efficiency
(8.63/9)(100) 95.89
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Non uniform quantization
nonuniform to improve SNR (SQR)

• More levels is available for low level amplitudes
  compared to high amplitude
• Increase SNR for low level amplitude and decrease
  SNR for higher amplitudes

analog compression is done to the input signal
before sampling and quantization at the
transmitter Expansion is done at the
receiver COMPANDING (compression and expanding)
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Signal-to-Quantization Noise Efficiency
Occurs when the signal at minimum amplitude
SQR is not constant even the magnitude of the
Qe remains constant
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Non Uniform Quantization
example Non-Linear Quantization
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Companding gt Compress - Expanding
A method used to produce a uniform SNR for all
input signal range is compression-expansion
(Companding). Input signal is compressed at the
transmitter and expanded at the receiver
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Companding gt Compress - Expanding
gt Analog Compression process is done on the
input signal before sampling and coding gt
Digital compression process is done after the
signal is sampled
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2 Popular companding system (standardized by ITU)

• EUROPE gt A - Law
• USA/NORTH AMERICA gt ? - Law

A - compressor paramater. Usually the value of A
is 87.6.
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?-law compression
Vmax max uncompressed analog (volts) Vin
amplitude of the input signal at a particular
instant of time (volts) µ parameter used to
define the amount of compression (unitless) Vout
compressed output amplitude (volts)