Transcript Pulse Modulation

Chapter 3
Pulse Modulation
&
Digitized Speech Signal
Chapter Overview
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•
•
•
Pulse Modulation : PAM, PWM, PPM
Sampling Theorem, Sample and hold
Pulse Code Modulation
Delta Modulation
Introduction
• Voice signal specifications:
 SNR better than 30 dB.
 Harmonic distortion better than 26 dB.
 Frequency response of 300 Hz to 3400 Hz.
• Analog transmission is very susceptible
to noise and interference.
• Digital transmission is resistive to noise.
PULSE MODULATION
• Sampling analog information signal
• Converting samples into discrete pulses
• Transport the pulses over physical transmission
medium.
• Four (4) Methods
1.
PAM
2.
3.
4.
PWM
PPM
PCM

Analog Pulse Modulation
 Digital Pulse Modulation
Cont’d...
• Voice digitization is performed by
voice digitizers
 Storing, transmitting, switching.
 Wide band – standard telephone
applications.
 Narrow band – low data rate
transmission.
• Commonly used technique for voice
signal digitization is PCM.
Pulse Amplitude Modulation (PAM)
• The amplitude of the sampled signal is made
proportional to the analog input signal.
• Sampling Process
 The process by which an analog signal of specified
frequency is uniformly sampled at discrete intervals of
time.
• Sampling theorem
 The mathematical interpretation of sampling process.
• Result
 The generation of discrete output signals with
amplitudes proportional to the input signals.
Cont’d...
• An analog input signal, sampled at specific
intervals of time and an output signal composed
of uniform duration pulses related to clock pulse
and varying amplitudes proportional to the input
analog signal amplitude.
Cont’d...
• Mathematical relationship between
analog input signals and the sampling
frequency
Nyquist Theorem
fs > 2 BW
Where BW = bandwidth of the
sampled signal (Hz)
fs = clock frequency (Hz)
Cont’d...
• The relationship of the PAM signal to
information and sampling signals:
fs(t) = f(s) . f(t)
• In practice - non-ideal signal of
constant amplitude and finite width is
utilized.
Cont’d...
• PAM signal spectra representation :
sampled at rate f(s) > 2 f(t)
Cont’d...
• PAM signal spectra representation :
sampled at rate f(s) = 2 f(t)
Cont’d...
• PAM signal spectra representation :
sampled at rate f(s) < 2 f(t)
Cont’d...
• Sampling circuit
 Sampling analog circuit is the first step toward speech
signal digitization.
 The following figure illustrates the block diagram of a
sample and hold (S/H) circuit.
 Open–loop S/H circuit and Close-loop S/H circuit.
Pulse Position Modulation (PPM)
• The amplitude of the modulated signal is
maintained at a constant level while its
pulse position is shifted at a rate
proportional to the rate of change of the
input signal.
Pulse width modulation (PWM)
• Generates an output signal with constant
amplitude and pulse width proportional to
the input signal amplitude rate of change.
Pulse Code Modulation (PCM)
• Commonly used techniques for speech
signal digitization.
• Process whereby an analog signal is
converted to digital form in order to be
transmitted by digital means.
PCM Block Diagram Tx & RX
Tx
Rx
Cont’d...
• Minimize the impact of channel noise at
the final stage of the reconstruction
process – Quantizer
To determine whether the incoming digital
signal has a voltage corresponding to binary
zero or binary one
• Accuracy of generated signals
– Quantization noise and BER
Cont’d...
• Quantization
– Analog signal is quantized because:
• Easily separated from the channel noise
• Reconstructed to its original form
– The analog signal is confined between a minimum
and maximum value and divided into a number of
equal segments.
– Magnitude of the segments is called STEP SIZE.
Step size, S = (Vmax – Vmin) / M
Where M is number of steps
Cont’d...
• Quantization process
Quantization Error Power, Pqn
The noise power of the
quantized signal,
Where
• (ē)² = Mean square value
of error
• P(e) = probability density
function
Output Signal Power, Pso
Signal to Quantization Error Ratio, SQE
Cont’d...
• Non-linear quantization
– During the quantization process, an analog
input signal confined within its
predetermined boundaries reflects a
quantization error of ± S/2.
– When analog signal exceeds these
boundaries, the quantization error will
increase.
– Decrease the step size (S) will decrease
the quantization error, increase the number
of sample levels (M), increase the PCM
baseband bandwidth requirements.
Cont’d...
• To achieve better Pso/Pqn – NON
LINEAR QUANTIZATION
– The input analog signal is compressed
at the higher amplitude levels and
expanded at the lower amplitude levels
before quantization – COMPANDING
SCHEME.
Cont’d...
Instantaneous
companding
Companding
Methods
Uniform
distribution
Non-uniform
companding
Cont’d...
• Instantaneous companding
– The process whereby the multiplexed
signal is processed through a nonlinear
circuit prior to encoding process, while at
Rx end the reverse process is applied
before demultiplexing.
Cont’d...
• Non uniform companding
– The compression and expansion
circuitry is incorporated into the
encoding process and can be
implemented by either analog or digital
means.
Cont’d...
• Uniform distribution
– Incorporates a linear encoder and a digital
compressor at the Tx end and a digital
expander and linear decoder at the Rx end.
– Digital compressor reduces the high
resolution code into a lower resolution
uniform code with an acceptable degree of
accuracy , while the opposite process takes
place at the Rx end.
Cont’d...
Companding Functions
Method of Companding
• For the compression, two laws are adopted: the -law in US and
Japan and the A-law in Europe.
• -law
•
• A-law
Vout 
Vmax ln( 1   Vin Vmax )
ln( 1   )

A Vin Vmax
Vin 1
V
0


 max
1  ln A
Vout A

Vout  
Vin
1

ln(
A
1 Vin
Vmax )


1
 1  ln A
A Vout
Vmax= Max uncompressed
analog input voltage
Vin= amplitude of the input
signal at a particular of
instant time
Vout= compressed output
amplitude
A, = parameter define the
amount of compression
• The typical values used in practice are: =255 and A=87.6.
• After quantization the different quantized levels have to be
represented in a form suitable for transmission. This is done via an
encoding process.
μ-law
A-law
DELTA MODULATION (DM)
• DM circuit – the circuit capable of
performing analog signal quantization with
smaller bandwidth requirements.
• Binary output representing the most recent
sampled amplitude will be determined on
the basis of previous sampled amplitude
levels.
 0 bit : amplitude level to be quantized
SMALLER than amplitude of the previous level.
 1 bit : amplitude level to be quantized LARGER
than amplitude of the previous level.
Cont’d...
• DM circuits can easily perform the
encoding & decoding function BUT very
difficult to combine with other signals &
difficult to multiplexed.
DM Wave representation
Cont’d...
• The block diagram of DM circuit
Cont’d...
• LPF provides bandwidth restriction for
the input analog signal, a comparator, a
staircase generator and a clock
generator.
• Analog input at the comparator noninverting input is compared with the
staircase output
– Analog input LARGER – comparator output
logic 1
– Analog input LOWER – comparator output
logic 0
DM Circuit’s Problems
• Slope overload
– Due to the input analog signal
amplitude changes faster than the
speed of the modulator
– To minimize : the product of the
sampling step size and the sampling
rate must be equal to or larger than the
rate of change of the amplitude of the
input analog signal.
Cont’d...
• Granule noise
– Due to the difference between step size
and sampled voltage.
– To minimize : increase the sampling
rate, decrease the step size of
modulator
ADAPTIVE DELTA MODULATOR (ADM)
• The improvement of DM performance
• Continuously variable slope delta
modulation (CVSDM)
– the step size of the modulator does not
remain constant but adapts to the input
signal amplitude variations.
– Improvement in their dynamic range and
noise levels.
Cont’d...
• ADM Block Diagram
Homework !!!
Explain the ADM process
based on given block diagram.
Quantization noise in DM
• Two fundamental parameters for a DM are
sampling rate & step size.
• If the circuit is to follow the variations of
faster input analog signals, either the
sampling rate or the step size must be
increased.
 Increase the sampling rate – violate set
bandwidth restrictions.
 Increase in step size – quantization error.
Cont’d...
S²/3
DM Signal Power
• The signal power, Pso
DM Signal to Quantization Noise Ratio
PCM & DM COMPARISON
• Evaluated in terms of signal to
quantization noise power ratio
• Example:
– A linear PCM encoder operating with 8 bit
a 4 KHz voice base band bandwidth
exhibits a signal to quantization noise
power ratio given by:
Pso/Pqn = 6 (N+1) = 54 dB
Cont’d...
– At the same time, if the same voice signal is
converted to a digital signal through the DM
process, the signal to quantization noise ratio
is given by:
Pso/Pqn = 0.04 x [ (fb/fc)3 ] = 22 dB
Cont’d...
• PCM system using nonlinear quantization
reflect a constant signal to quantization
noise ratio about 30 dB over an input signal
dynamic range of approximately 40 dB.
• ADM schemes are preferable in some
applications that are intended to further
enhance system capacity.
Cont’d...
• Frame time, t(s) = 1 / (2 BW) = A
• T1(24-voice-channel) = (1/A) / number of bits = B
• Bit rate = 1/B
• Example :
The BW of a voice signal is rounded off to 4KHz.
Calculate the bit rate if each time slot accommodating
193 bits of information.
Cont’d...
• Jitter
– Short terms variations of the significant
instants of a digital signal from their ideal
positions in time. Signal instants referred to
any variation of the pulse from its original
position in time @
– A form of unwanted phase modulation which
ultimately contributes to system performance
degradation.
Cont’d...
– Common measure of the amplitude of the jitter
is in unit intervals (UI)
Jp=p = m/П
Where Jp=p = jitter amplitude peak to peak
m = index of modulation
Cont’d...
• Bit-stream variations
Δfb = m x fj
where
Δfb = Bit stream variations
fj = jitter frequency
Cont’d...
• Jitter function
Cont’d...
• System degradation
– If the jitter not controlled to acceptable
levels, it will accumulate over a period
of time, resulting in system degradation.
– Amplitude distortion, increase the error
probability
Cont’d...
• Source of jitter
– Multiplexers/demultiplexers, digital
degradators, regenerators & electronic
components.
– Regenerators is a major source of
jitters in digital transmission system.
• the incoming signals altered, distorted
through the transmission path
Cont’d...
• Block diagram of regenerator circuit.
Cont’d...
• Incoming signal applied to the input equalizer.
• Equalizer amplify and restores the incoming
signal to its original level.
• The bipolar to unipolar converter is required to
convert the signal for clock recovery.
• Decision circuit will determine the presented bit
either bit 1 or bit 0.
• The timing circuit will reconstruct the binary
signal.
• The unipolar to bipolar circuit will generate the
final signal for transmission to the next
generator.
Cont’d...
•
Other jitter sources which do not
depend on the digital regenerator:
1. Cross talk
2. tuned circuit mistuning
3. differential pulse delays
Cont’d...
• Cross talk
– Occurs when more than one digital transmission utilizes
the same transmission medium.
– Can be divided into two major categories : near end
and far end.
– Near end cross talk is measured at the input of the
transmission medium and must maintain a level
approximately 30 dB below the signal level, BER 10-8
– Far end cross talk is measured at the output of the
medium and must maintain a level 15 dB below the
signal level.
Cont’d...
• Tuning circuit mistuning
– LC component mistuning
– Cause a static phase shift
– Introduce a transmission delay in
regenerator
– Dynamic phase shift proportional to the
data bit stream
Cont’d...
• differential pulse delays
– Conversion of a unipolar to a bipolar signal
is implemented of semiconductor devices
operating at saturation or cutoff modes.
– Saturation mode : a slight variation of the
base to emitter junction Capacitance, Cb will
result a shift in time of the output pulse.
END OF CHAPTER 3