formatting and baseband modulation

7/28/2019 Formatting and baseband Modulation

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REPORT CHAPTER 2:

FORMATTING AND BASEBAND MODULATION

2.1 Baseband Systems

In Formatting, sources of information are converted into the sequences of binary digits. The

sources of information consist of Digital information, Textual information and Analog

information (Fig 2.2):

- Data already in digital format would bypass the formatting function.- Data in text is transformed into binary digit- Analog information is formatted using 3 processes: Sampling, Quantization, and Coding.

Then these digits are to be transmitted through the Baseband channel, such as a pair of wires or a

coaxial cable, after they are transformed into the waveforms in a block labeled Pulse modulate

that are compatible with the channel. For baseband channel, the waveforms are pulses.

After transmission through the channel, pulses are demodulated, formatted to recover as the

sources of information.

2.2 Formatting textual data (Character coding):

Character coding is the step that transforms text into binary digits.

Character can be encode with one of several standard formats: the American Standard Code for

Information Interchange (ASCII), the Extended Binary Coded Decimal Interchange Code

(EBCDIC), Baudot, and Hollerith.

2.3 Messages, Characters, and Symbols:


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When digitally transmitted, the characters are first encoded into a sequence of bits, called a bit

stream orbaseband signal. Group of k bits forms new digits, or symbols, from a finite symbol

set or alphabet of M = 2k

such symbols.

2.3.1 Example of Messages, Characters, and Symbols.

The figure below is an example of encoding the word THINK by 6 bit ASCII charactercoding.

In figure 2.5a, M is chosen to be 8 (k = 3). This resulting 10 numbers represent 10 octal symbols

to be transmitted. The transmitter must have 8 types of waveform ( where i = 1, 2,...,8). Thisis similar to the way of coding in figure 2.5b but in this case, M = 32 (k = 5).2.4 Formatting analog information.

If the information is analog, it must first be transformed into a digital format.

2.4.1 The sampling theorem.


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2.4.1.2 Natural sampling.

Using thefrequency translation property of the Fourier transform, we solve forXs(f) as follows:

(2.14)

Similarly to the impulse sampling case, Xs(f) is a replication ofX(f), periodically repeated in

frequency everyfshertz (we choosefs = 2fmin this case so that the Nyquist is satisfied), as seen

in fig 2.8b and 2.8f). When the pulse width, T, approaches zero, cnapproaches 1/Tsfor all n, and

equation 2.14 converges to equation 2.8.

2.4.1.3 Sampleand-Hold operator.

The sample-and-hold operator can be described by the convolution of the sampled pulse train,

[x(t) x(t)], shown in Fig 2.6e, with a unity amplitude rectangular pulse p(t) of pulse width Ts.

This convolution results in theflattop(nh bng phng) sampled sequence:


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(2.15)

The Fourier transform,Xs(f) is expressed as:

[

] (2.16)

HereP(f) is of the form Tssinc f Ts.

The effect of this product operation results in a spectrum similar to the natural sampled example.The most obvious effect of hold operation is the significant attenuation of the higher-frequency

spectral replicates (compare Fig 2.8f to Fig 2.6f). A secondary effect of the hold operation is the

nonuniform spectral gainP(f) applied to the disired baseband spectrum shown in equation 2.16.

2.4.2 Aliasing.

As mentioned in section 2.4.1.1, aliasing is the result of undersampling. The aliasing spectral

components represent ambiguous data that appear in the frequency band between (fs - fm) andfm,

as shown in Fig 2.9


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Tri pha v rung pha (Wander v Jitter) l nhng bin i v pha ca tn hiu sthu c so vivtr l tng ca chng:

- Nhng bin i pha c tn shn hn hoc bng 10Hz gi l rung pha.

- Nhng bin i pha c tn s nhhn 10Hz gi l tri pha

If there is slightly jitter in the position of the sample, the sampling is no longer uniform;

therefore, reconstruction of the signal using the sampling theorem is not precise.

2.5.2 Channel effects

2.5.2.1 Channel noise

Thermal noise, interference from other users and interference from circuit switching transients

can cause errors the pulses carrying the digitized samples. Channel-induced errors can degrade

(gim) the reconstructed signal quality quite quickly. This rapid degradation is called a thresholdeffect. If the channel noise is small, there will be no problem detecting the presence of the

waveform. In this case, only quantization noise presents in the reconstruction.

2.5.2.2 Intersymbol Interference

The channel is always bandlimitted. A band limitted chanel disperses (phn tn) or spreads a

pulse waveform passing through it. When the channel bandwidth is close to the signal

bandwidth, the spreading will exceed a symbol duration and cause signal pulses to overlap. This

overlapping is called intersymbol interference (ISI). ISI causes system degradation (higher error

rates); it is a particularly insidious (m thm, khng nhn thy c) form of interferencebecause raising the signal power to overcome the interference will not always improve the error

performance.

2.5.3 Signal-to-noise ratio for Quantized pulses.

Fig 2.15 illustrates an L-level linear quantizer for an analog signal; the step size between

quantization levels, called the quantile interval, is denoted q volts. When the quantization levels

are uniformly distributed over the full range, the quantizer is called a uniform orlinear quantizer.

The degradation of the signal due to quantization is limmited to half a quantile interval q/2

volts.

The quantizer error variance is found to be

(2.18a)

(2.18b)


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Where p(e) = 1/q is the uniform probability density function of the quantization. The variance 2corresponds to the average quantization noise power.

The peak power of the analog signal (normalized to 1) can be expressed as

( ) ( )

(2.19)Equation 2.18 and equantion 2.19 combined yield the ratio ofpeak signal power to average

quantization noise power, assuming that there are no errors due to ISI or channel noise:

() (2.20)In the limit, as L , the signal approches the PAM format (without quantization), and thesignal-to-quantization noise ratio is infinite.

2.6 Pulse code modulation.

Pulse code modulation (PCM) is the name given to the class of baseband signals obtained from

the quantized PAM signals by encoding each quantized sample into a digital word.

Assume that an analog signal x(t) is limited in its excursions to the range -4 to +4V. The stepsize between quantization levels is 1V. Thus, eight quantization levels are employed; these are

located at -3.5, -2.5, . . . , +3.5V. We assign the code number 0 to the level at -3.5V, 1 at -2.5V,

and so on until 7 is assigned to the level at 3.5V. Each code number has its representation in

binary arithmetic, ranging from 000 to 111 (Fig 2.16 for L = 8). The choice of voltage levels is

guided by two constraints:

- The quantile interval between the levels should be equal


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- Convenient for the levels to be symmetrical about zero.

If we increase the number of levels, L, the quantization noise will reduced . In a real-time

communication system, the messages must not be delayed. Hence, the transmission time for each

sample must be the samle, regardless (cho d) how many bits represent the sample. Hence when

there are more bits per sample, the bits must move faste and data rate is that increased.

The difference between PCM and a PCM waveform is that the former represents a bit sequence,

and the latter represents a particular waveform coveyance of that sequence.

2.7 Uniform and nonuniform quantization.

From the equantion 2.18b, we see that the quantization noise quantization depends on the step

size (size of the quantile interval). When the step are uniform in size, the quantization is known

as uniforrm quantization. Such a system is watseful for weak signal (such as speech signal)

because many of the the quantizing steps would rarely be used. In the system using equally

spaced quantization levels, the quantization noise (SNR) is worse for low-level signals than for

high-level signals.

Nonuniform quantization can provide fine quantization of the weak signal and coarse (th, khngmn) quantization of the strong signals. Thus, in the case of nonuniform quantization,quantization noise can be made proportional to signal size. Nonuniform quantization can be used

to make the SNR a constant for all signals within the input range.

Fig 2.18 below compares the quantization of a strong versus a weak signal for uniform and

nonuniform quantization:


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2.7.1 Nonuniform Quantization.

We achive nonuniform quantization by using a nonuniform quantizer characteristic (Fig 2.19a)

or by distorting the original signal with a logarithmic compression characteristic (Fig 2.19b), and

then using a uniform quantizer. After compression, the distorted signal is used as the input to a

uniform quantizer characteristic, as shown in Fig 2.19c. At the receiver, an inverse compression,


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2.8 Baseband transmission.

2.8.1 Waveform representation of binary digits.

We will represent the binary digits with electrical pulse in order to transmit them through a

baseband channel (Fig 2.21).

Fig 2.21a shows the 4-bit codeword representation of each quantized sample. In Fig 2.21b, each

binary one is represented by a pulse and each binary zero is represented by the absence of pulse.

At the receiver, a determination must be made as to the presence or absence of a pulse in each bit

time slot. Detecting the presence of a pulse seems to be a function of the receiver pulse energy.

Thus there is an advantage in making the pulse width T in Fig 2.21b as wide as possible. When

the pulse width equal to the bit time T, we have the waveform as shown in Fig 2.21c with two

levels (upper voltage level represents binary one whereas lower voltage level represents binary

zero).

2.8.2 PCM waveform types


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(phn 2.8.2 em vn cha hiu v my dng sng trang 87 v cch din t bng li cho nhngdng sng trong trang 88)

2.8.3 Spectral Attributes (thuc tnh) of PCM waveforms.

Fig 2.23 shows the spectral characteristics of some of the most popular PCM waveforms. The

figure plots power spectral density in watts/herzt versus normalized bandwidth, WT (often

referred to as the time-bandwidth productof the signal). The units of normalized bandwidth are

herzt/(pulse/s) or herzt/(symbol/s)

(on sau em khng hiu)

2.9 Corelative coding.


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-

Sifting property

Attenuation N S nh bt, s yu i

AliasingPostfiltering

Ambiguous Adj Khng r rng, m h Fidelity N S chnh xcConstrue V St, gn gingQuantization noise

Quantizer saturation

Round-off N S lm trnCoarse Adj Th, khng mn

formatting and baseband modulation

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