1 intro digital communication
TRANSCRIPT
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Digital Communication
Introduction
By- D. Sarma
Asst. Prof., Dept. Of ECE,DBCET
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Why Digital Communication
Easy to regenerate. Less subject to distortion- Since in two
operated in either on or off . Digital circuits are more reliable and of lower
cost. Provides encryption and privacy. Finally signal processing.
Non Graceful Degradation
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Basic Flow of Digital Communication
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Some milestones in the history of electrical communications
Versi on
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Milestones in the history of electrical communicationscontd .
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Electromagnetic bands with typical applications
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Electromagnetic bands contd..
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A few important frequency bands
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Some Carrier frequency values and nominal bandwidth that may be
available at the carrier frequency
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Typical power losses duringtransmission through a few media
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The PCM system
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Introduction Two basic operations in the conversion of analog signal
into the digital.Time discretization
Amplitude discretization.In the context of PCM, The first is accomplished with the sampling operation The second by means of quantization. PCM involves another step,
Conversion of quantized amplitudes into a sequence of simpler pulse patterns (usually binary) - code words.
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Block Diagram
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m(t ) is the information bearing messagesignal that is to be transmitted digitally.
m(t ) is first sampled and then quantized. The quantizer converts each sample to one of
the values that is closest to it from among apre-selected set of discrete amplitudes.
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4.15
Sampling Analog signal is sampled every T S secs. Ts is referred to as the sampling interval. f s = 1/Ts is called the sampling rate or sampling
frequency.
According to the Nyquist theorem, thesampling rate must be
at least 2 times the highest frequencycontained in the signal.
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Let a signal x (t ) be band limited to W Hz; that
is, X (f ) = 0 for f > W . Let X(nTs ) = X(t ) t=nTs , - < n < represent
the samples of x (t ) at uniform intervals of Ts
seconds. If Ts 1/ 2W , than it is is possible to
reconstruct x (t ) exactly from the set of
samples, {X (n Ts )} .
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Types of sampling There are 3 sampling methods:
Ideal - an impulse at each sampling instant Natural - a pulse of short width with varying amplitude Flattop - sample and hold, like natural but with single
amplitude value The process is referred to as pulse amplitude
modulation PAM and the outcome is a signal withanalog (non integer) values
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Ideal impulse sampling
Consider an arbitrary low pass signal x (t )shown in Fig 3 . Let
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where ( t ) is the unit impulse function of Xs (t) , shown in red in Fig 3. consists of a
sequence of impulses; the weight of the impulse at t = nTs is equal to
x (nTs ) . X s (t ) is zero between two adjacent impulses.
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Fig 3:
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It is very easy to show in the frequencydomain that Xs (t ) preserves the completeinformation of x (t ).
X s (t ) is the product of x (t ) and (t n Ts)hence the corresponding Fourier relation isconvolution.
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That is,
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we see that Xs (f ) is a superposition of X (f )and its shifted versions (shifted by multiples of fs , the sampling frequency) scaled by 1/ Ts
Let X (f ) be a triangular spectrum as shown inFig. 4(a).
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Fig 4:
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it is obvious that we can recover x (t ) from Xs(t ) by passing Xs (t ) through an ideal low
pass filter with gain Ts and bandwidth W asshown bellow.
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Of course, with respect to Fig. 4(b), whichrepresents the over-sampled case,
reconstruction filter can have some transitionband which can fit into the gap between f = W and f = (fs W) .
when fs < 2W , (under-sampled case) we seethat spectral lobes overlap resulting in signaldistortion, called aliasing distortion. In this
case, exact signal recovery is not possible
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Sampling with a rectangular pulsetrain
Let yp (t ) represent the periodic rectangularpulse train as shown in Fig.5(b).
Let Xs (t ) =[ x (t )] yp (t ) Then, Xs (f ) = X (f ) Yp (f ) Therefore
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4.30
Figure : Three different sampling methods for PCM
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4.31
Quantization Sampling results in a series of pulses of varying
amplitude values ranging between two limits: amin and a max.
The amplitude values are infinite between thetwo limits.
We need to map the infinite amplitude valuesonto a finite set of known values.
This is achieved by dividing the distance betweenmin and max into L zones , each of height= (max - min)/L
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4.32
Quantization Levels
The midpoint of each zone is assigned avalue from 0 to L-1 (resulting in L values)
Each sample falling in a zone is thenapproximated to the value of the midpoint.
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4.33
Quantization Error When a signal is quantized, we introduce an error
- the coded signal is an approximation of theactual amplitude value.
The difference between actual and coded value(midpoint) is referred to as the quantization error.
The more zones, the smaller which results insmaller errors.
BUT, the more zones the more bits required toencode the samples -> higher bit rate
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4.34
Quantization Error and SN Q R Signals with lower amplitude values will suffer
more from quantization error as the error range:/2, is fixed for all signal levels.
Non linear quantization is used to alleviate thisproblem. Goal is to keep SN Q R fixed for all samplevalues.
Two approaches: The quantization levels follow a logarithmic curve.
Smaller s at lower amplitudes and larger s at higheramplitudes.
Companding: The sample values are compressed at thesender into logarithmic zones, and then expanded atthe receiver. The zones are fixed in height.
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4.35
Bit rate and bandwidth requirements of
PCM The bit rate of a PCM signal can be calculated form the
number of bits per sample x the sampling rate
Bit rate = n b x f s The bandwidth required to transmit this signal depends
on the type of line encoding used. Refer to previoussection for discussion and formulas.
A digitized signal will always need more bandwidth thanthe original analog signal. Price we pay for robustness andother features of digital transmission.
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4.36
We want to digitize the human voice. What is the bit rate, assuming 8 bits per sample?
SolutionThe human voice normally contains frequencies from 0to 4000 Hz. So the sampling rate and bit rate arecalculated as follows:
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4.37
PCM Decoder
To recover an analog signal from a digitized signalwe follow the following steps:
We use a hold circuit that holds the amplitude value of a pulse till the next pulse arrives. We pass this signal through a low pass filter with a
cutoff frequency that is equal to the highest frequencyin the pre-sampled signal.
The higher the value of L, the less distorted asignal is recovered.
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4.38
We have a low-pass analog signal of 4 kHz. If we send theanalog signal, we need a channel with a minimumbandwidth of 4 kHz. If we digitize the signal and send 8 bits per sample, we need a channel with a minimum
bandwidth of 8 4 kHz = 32 kHz.
A brief aside about ADCs
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39
0000
1111
1110
1101
1100
1011
1010
1001
0001
0010
0011
0100
0101
0110
0111
A brief aside about ADCs
0000 0110 0111 0011 1100 1001 1011
Numbers passed from ADC to computer to represent analogue voltage
ADCs are used to convert an analogue input voltage into a number that can beinterpreted as a physical parameter by a computer.
Resolution= 1 part in 2 n
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THANK YOU