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Lecture # 5:
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Practical Sampling Rates Speech
- Telephone quality speech has a bandwidth of 4 kHz(actually 300 to 3300Hz)
- Most digital telephone systems are sampled at 8000samples/sec
Audio:- The highest frequency the human ear can hear is
approximately 15kHz
- CD quality audio are sampled at rate of 44,000
samples/sec Video
- The human eye requires samples at a rate of at least 20frames/sec to achieve smooth motion
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Pulse Code Modulation PCM)
Pulse Code Modulation refers to a digital baseband signal that isgenerated directly from the quantizer output
Sometimes the term PCM is used interchangeably with quantization
Other methods
PWM (Pulse Width Modulation) PPM (Pulse Position Modulation)
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Advantages of PCM:
Relatively inexpensive
Easily multiplexed: PCM waveforms from different
sources can be transmitted over a common digital
channel (TDM)
Easily regenerated: useful for long-distance
communication, e.g. telephone
Better noise performance than analog system
Signals may be stored and time-scaled efficiently (e.g.,
satellite communication)
Efficient codes are readily available
Disadvantage:
Requires wider bandwidth than analog signals
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2.5 Sources of Corruption in the sampled,quantized and transmitted pulses Sampling and Quantizat ion Effects
Quantization (Granularity) Noise:Results whenquantization levels are not finely spaced apart enoughto accurately approximate input signal resulting intruncation or rounding error.
Quantizer Saturation or Overload Noise:Results wheninput signal is larger in magnitude than highestquantization level resulting in clipping of the signal.
Timing Jitter:Error caused by a shift in the sampler
position. Can be isolated with stable clock reference.
Channel Effects
Channel Noise
Intersymbol Interference (ISI)
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The level of quantization noise is dependent on how close anyparticular sample is to one of the L levels in the converter
For a speech input, this quantization error resembles a noise-like disturbance at the output of a DAC converter
Signal to Quantization Noise Ratio
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Uniform Quantization A quantizer with equal quantization level is a Uniform Quantizer
Each sample is approximated within a quantile interval Uniform quantizers are optimal when the input distribution is
uniform
i.e. when all values within the range are equally likely
Most ADCs are implemented using uniform quantizers
Error of a uniform quantizer is bounded by
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Quantization Levels
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The mean-squared value (noise variance) of the quantization error isgiven by:
2/
2/
2)(2/
2/
2/
2/
112)()(2)(2 q
q
deeq
q
q
q qdeqedeepe
12
22/
2/3
31 qq
q
eq
Signal to Quantization Noise Ratio
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The peak power of the analog signal can be expressed as:
Therefore the Signal to Quatization Noise Ratio is given by:
)4
22()
2
2(2 qLVV ppp
23LSNRq
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where L = 2nis the number of quantization levels for the converter.
(n is the number of bits).
Since L = 2n, SNR = 22nor in decibels
LppV
q
dBnn
dBN
S 6)22(
10
log10
If q is the step size, then the maximum quantization error that canoccur in the sampled output of an A/D converter is q
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Nonuniform Quantization Nonuni form quant izershave unequally spaced levels
The spacing can be chosen to optimize the Signal-to-Noise Ratiofor a particular type of signal
It is characterized by:
Variable step size
Quantizer size depend on signal size
Sometimes non-uniform spacing is preferred to uniform spacing
Many signals such as speech have a nonuniform distribution
More amplitude is close to zero than a high level (see Fig. 2.17)
Basic principleis to use more levels at regions with large
probability density function (pdf) Concentrate quantization levels in areas of largest pdf
Or use fine quantization (small step size) for weak signals and
coarse quantization (large step size) for strong signals
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Companding Companding is a method of reducing the number of bits required in
ADC while achieving an equivalent dynamic range or SQNR
In order to improve the resolution of weak signals within a converter,
and hence enhance the SQNR, the weak signals need to be
enlarged, or the qu ant izat ion s tep size decreased, but only for the
weak signals
But strong signals can potentially be reduced without significantly
degrading the SQNR or alternatively increasing quantization step size The compression process at the transmitter must be matched with an
equivalent expansion process at the receiver
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Input/Output Relationship of Compander
Logarithmic expression Y = log X is the most commonly usedcompander
Taking the log of Y = log X reduces the dynamic range sinceloge(1+x) x if x 0
This is effective in speech and music which often have smallabsolute values
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Types of Companding-Law Companding Standard (North & South
America, and Japan)
where
x and y represent the input and output voltages
is a constant number determined by experiment
In the U.S., telephone lines uses companding with = 255
Samples 4 kHz speech waveform at 8,000 sample/sec
Encodes each sample with 8 bits, L = 256 quantizer levels
Hence data rate R = 64 kbit/sec
= 0 corresponds to uniform quantization
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A-Law Companding Standard (Europe, China, Russia,
Asia, Africa)
where
x and y represent the input and output voltages
A = 87.6
A is a constant number determined by experiment
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Pulse Modulation Recall that analog signals can be represented by a sequence of discrete
samples (output of sampler)
APM results when some characteristic of the pulse (amplitude, width orposition) is varied in correspondence with the data signal
Can be obtained either by Natural or Flat top Sampling
Two Types:
Pulse Amplitude Modulation (PAM)
The amplitude of the periodic pulse train is varied in proportion to thesample values of the analog signal
Pulse Time Modulation
Encodes the sample values into the time axis of the digital signal
Pulse Width Modulation (PWM)
Constant amplitude, width varied in proportion to the signal Pulse Duration Modulation (PDM)
sample values of the analog waveform are used in determining
the width of the pulse signal
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PCM Waveform Types The output of the A/D converter is a set of binary bits
But binary bits are just abstract entities that have no physical
definition We use pulses to convey a bit of information, e.g.,
In order to transmit the bits over a physical channel they must betransformed into a physical waveform
A l ine coder or baseband binary transm itter transforms a streamof bits into a physical waveform suitable for transmission over a
channel Line coders use the terminology mark for 1 and space to mean 0
In baseband systems, binary data can be transmitted using manykinds of pulses
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There are many types of waveforms. Why? performance criteria! Each line code type have merits and demerits
The choice of waveform depends on operating characteristics of a
system such as
Modulation-demodulation requirements
Bandwidth requirement
Synchronization requirement
Receiver complexity, etc.,
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Goals of Line Coding (qualities to look for)
A line code is designed to meet one or more of the following goals:
Self-synchronization
The ability to recover timing from the signal itself
That is, self-clocking (self-synchronization) - ease of clock lock
or signal recovery for symbol synchronization
Long series of ones and zeros could cause a problem
Low probability of bit error Receiver needs to be able to distinguish the waveform associated
with a mark from the waveform associated with a space
BER performance
relative immunity to noise
Error detection capability
enhances low probability of error
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Spectrum Suitable for the channel
Spectrum matching of the channel
e.g. presence or absence of DC level
In some cases DC components should be avoided
The transmission bandwidth should be minimized
Power Spectral Density
Particularly its value at zero
PSD of code should be negligible at the frequency near zero Transmission Bandwidth
Should be as small as possible
Transparency
The property that any arbitrary symbol or bit pattern can be
transmitted and received, i.e., all possible data sequence should
be faithfully reproducible
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Line Coder The input to the line encoder is
the output of the A/D converter
or a sequence of values an
that is a function of the data bit
The output of the line encoder
is a waveform:
where f(t) is the pulse shape and Tbis the bit period (Tb=Ts/nfor n bit quantizer)
This means that each line code is described by a symbol mappingfunction anand pulse shape f(t)
Details of this operation are set by the type of line code that is beingused
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Summary of Major Line Codes Categories of Line Codes
Polar - Send pulse or negative of pulse
Unipolar - Send pulse or a 0
Bipolar (a.k.a. alternate mark inversion, pseudoternary)
Represent 1 by alternating signed pulses
Generalized Pulse Shapes
NRZ -Pulse lasts entire bit period
Polar NRZ
Bipolar NRZ
RZ - Return to Zero - pulse lasts just half of bit period
Polar RZ
Bipolar RZ Manchester Line Code
Send a 2- pulse for either 1 (highlow) or 0 (lowhigh)
Includes rising and falling edge in each pulse
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No DC component
HS ( Half Sine)
When the category and the generalized shapes are combined, we
have the following:
Polar NRZ:
Wireless, radio, and satellite applications primarily use Polar
NRZ because bandwidth is precious
Unipolar NRZ
Turn the pulse ON for a 1, leave the pulse OFF for a 0
Useful for noncoherent communication where receiver cant
decide the sign of a pulse
fiber optic communication often use this signaling format
Unipolar RZ RZ signaling has both a rising and falling edge of the pulse
This can be useful for timing and synchronization purposes
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Bipolar RZ
A unipolar line code, except now we alternate betweenpositive and negative pulses to send a 1
Alternating like this eliminates the DC component This is desirable for many channels that cannot transmit the
DC components
Generalized Grouping
Non-Return-to-Zero: NRZ-L, NRZ-M NRZ-S
Return-to-Zero: Unipolar, Bipolar, AMI Phase-Coded: bi-f-L, bi-f-M, bi-f-S, Miller, Delay Modulation
Multilevel Binary: dicode, doubinary
Note:There are many other variations of line codes (see Fig. 2.22,page 80 for more)
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Commonly Used Line Codes Polar line codes use the antipodal mapping
Polar NRZ uses NRZ pulse shape
Polar RZ uses RZ pulse shape
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Unipolar NRZ Line Code
Unipolar non-return-to-zero (NRZ) line code is defined by
unipolar mapping
In addition, the pulse shape for unipolar NRZ is:
where Tbis the bit period
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Bipolar Line Codes
With bipo lar l ine codes a space is mapped to zero and
a mark is alternately mapped to -A and +A
It is also called pseudoternarysignaling or alternate mark inversion(AMI)
Either RZ or NRZ pulse shape can be used
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Manchester Line Codes
Manchester line codes use the antipodal mappingand the following spl i t -phase pulse shape:
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Summary of Line Codes
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Comparison of Line Codes Self-synchronization
Manchester codes have built in timing information because theyalways have a zero crossing in the center of the pulse
Polar RZ codes tend to be good because the signal level always
goes to zero for the second half of the pulse
NRZ signals are not good for self-synchronization
Error probability
Polar codes perform better (are more energy efficient) than
Unipolar or Bipolar codes
Channel characteristics
We need to find the power spectral density (PSD) of the linecodes to compare the line codes in terms of the channel
characteristics
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Generation of Line Codes
The FIR filter realizes the different pulse shapes
Baseband modulation with arbitrary pulse shapes can bedetected by
correlation detector
matched filter detector (this is the most common detector)