**CONCEPT OF EYE PATTERN **

**Basic concept**

** **Eye pattern is a pattern displayed on the screen of a cathode ray oscilloscope (C.R.O.). The shape of this pattern resembles with the shape of human eye. Therefore, it is called as eye pattern. Eye pattern is a practical way to study the intersymbol interference (ISI) and its effects on a PCM or data communication system. The eye pattern is obtained on the C.R.O. by applying the received signal to vertical deflection plates (Y-plates) of the C.R.O. and a sawtooth wave at the transmission symbol rate i.e., (1/T_{b}) to the horizontal deflection plates (X-plates) as shown in figure 6.50(c). The received digital signal and the corresponding oscilloscope display are as shown in figure 6.36(α) and (c) respectively. The resulting oscilloscope display shown in figure 6.50(c) is called as the eye pattern. This is due to its resemblance to the human eye.

The interior region of the eye pattern is called as the eye opening. The eye pattern provides a great deal of information about the performance of the system. The information obtainable is as follows (Figure 6.51)

**DIAGRAM**

**FIGURE 6.50** *obtaining eye pattern.*

**DIAGRAM**

**FIGURE 6.51** *Interpretation of eye pattern.*

**Information Obtained from Eye Pattern**

(i) The width of the eye opening defines the time interval over which the received wave can be sampled, without an error due to ISI. The best time for sampling is when the eye is open widest.

(ii) The sensitivity of the system to the timing error is determined by the rate of closure of the eye as the sampling rate is varied.

(iii) The height of eye opening at a specified sampling time defines the margin over noise.

(iv) When the effect of ISI is severe, the eye is completely closed and it is impossible to avoid errors due to the combined presence of ISI and noise in the system.

**EXAMPLE 6.24 Show that (a pulse-shape, function) h(t), with Fourier transform given by H(****), that satisfies the criterion**

**EQUATION**

has h (nT) which is given by

**EQUATION**

*(GATE Examination-1999)*

**Solution:** The criterion given in equation (i) is known as Nyquist’s pulse-shaping criterion.

Taking the inverse Fourier transform of H(), we have

**EQUATION**

The range of integration in the above equation can be divided into segments of length 2/T as under:

**EQUATION**

and we can write h(nT) as

**equation**

Changing variable u = – 2(5/T), equation (iii) becomes

**equation**

Assuming that the integration and summation can be interchanged, we have

**equation**

Finally, if equation (i) is satisfied, then we have

**equation**

which verifies h(t) with a Fourier transform H() satisfying criterion in equation (i) produces zero ISI. **Ans.**

**EXAMPLE 6.25 A communication channel of bandwidth 75 kHz is required to transmit binary data at a rate of 0.1 Mb/s using raised-consine pulses. Determine the Roll-off factor α.**

**Solution :** We have

or f_{B} = 75 kHz = 75 (10^{3}) Hz

We know that 1 + α = 2 f_{B}T_{b} = 2(75) (10^{3})(10^{-5}) = 1.5

Hence, we obtain α = 0.5 **Ans.**

**EXAMPLE 6.26. In a certain telemetry system, eight message signals having 2 kHz bandwidth each are time-division multiplexed using a binary PCM technique. The error in sampling amplitude cannot be greater than 1 per cent of the peak amplitude. Determine the minimum transmission bandwidth required if raised-consine pulses with roll-off factor α = 0.2 are used. The sampling rate must be at least 25 per cent above the Nyquist rate. **

**Solution:** We know that the maximum quantizing error must satisfy.

Hence, q ≥ 100, and we choose q = 128 = 2^{7}. The number of bits per sample required is 7. Since the Nyquist sampling rate is 2 f_{m} = 4000 samples/s, the sampling rate for each signal is

f_{s} = 1.25(4000) = 5000 samples/s

There are eight time-division multiplexed signals, requiring a total of

8(5000) = 40,000 samples/s

Now, since each sample is encoded by 7 bits, therefore, the resultant bit rate will be

(40,000) = 280 kb/s

Further, we know that the minimum transmission bandwidth required is

f_{B} = (280) = 168 kHz **Ans.**

**EXAMPLE 6.27. Let X _{α}(f) be the raised cosine spectrum with a roll-off factor α. **

**Show that**

**(f) df = 1**

**Solution:**Earlier, we have derived the expression for X

_{α}(f) i.e., P(f). The raised cosine spectrum for different value of a is shown in figure 6.52.

**DIAGRAM**

**FIGURE 6.52**

*Raised cosine spectrum*

Let us consider the spectrum corresponding to α = 0. This means that

**equation**

The same can be proved for different values of α

**EXAMPLE 6.28. Given a bit sequence of 01011001, draw line codes in NRZ-L, NRZ-I and pseudoternary formats. Compare them on the basis of their bandwidth and clocking capability.**

*(U.P. Tech. Sem. Exam; 2005) (10 marks)***Solution:**

Bit sequence | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 |

** **

**DIAGRAM**

**FIGURE 6.53**

**EXAMPLE 6.29. For the binary sequence 1101011101, construct RZ, AMI and Manchester format. (U.P. Tech. Sem. Exam; 2000) (10 marks) **

**Solution:**We consider figure 6.54 for the solution.

Binary sequence RZ AMI | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |

**DIAGRAM**

**FIGURE 6.54*** Raised cosine spectrum*

**SUMMARY**

■ The pulse code modulation (PCM), Delta modulation (DM), Adaptive delta modulation (ADM) etc: are used to convert an analog signal to digital data. This digital data is the sequence of binary symbols.

■ The output of a multiplexer is coded into electrical pulses or waveforms for the purpose of transmission over the channel. This process is known as line coding or transmission coding.

■ There are several possible ways of assigning waveforms (i.e., pulses) to the digital data. In the binary case (two symbols), for example, conceptually the simplest line code is on-off, where a 1 is transmitted by a pulse p(t) and a 0 is transmitted by no pulse (i.e., zero signal.)

■ Another line code that in the past appeared promising is the duobinary (and modified duobinary) proposed by Lender. Although this code is better than the bipolar in terms of bandwidth efficiency, it has lost its appeal due to some practical problems and will not be discussed here.

■ Regenerative repeaters are used at regularly spaced intervals along a digital transmission line to detect the incoming digital and regenerate new clean pulses for further transmission along the line. This process periodically eliminates, and thereby combats, the accumulation of noise and signal distortion along the transmissions, path.

■ The timing signal (i.e., the resonant circuit output) is sensitive to the incoming bit pattern. In the on-off or bipolar case, a 0 is transmitted by “no pulse”. Hence, if there are too many 0’s in a sequence (no pulses), there is no signal at the input of the resonant circuit and the sinusoidal output of the resonant circuit starts decaying, thus causing error in the timing information.

■ The digital data may be transmitted by various transmission or line codes such as on-off, polar, bipolar and so on. This is called line-coding. Each type of line-code has its advantages and disadvantages.

■ For a line-code, the transmission bandwidth must be as small as possible.

■ For a given bandwidth and a specified detection error probability, the transmitted power for a line code should be as small as possible.

■ It must be possible to detect nod preferably correct detection errors. For example, in a bipolar case, a signal error will cause bipolar violation and thus can easily be detected.

■ It must be possible to extract timing or clock information from the signal.

■ It must be possible to transmit a digital signal correctly regardles of the pattern of 1 s and 0 s.

■ The use of an appropriate waveform for baseband representation of digital data is basic to its transmission from a source to a destination. This means that digital pulse modulation can be used for transmitting the output of a digital source.

■ In Unipolar Format, the waveform has a single polarity. The waveform can have +5 or +12 volts when high. The waveform is simple on-off. In the unipolar RZ form, the waveform has zero value when symbol ‘0’ is transmitted and waveform has ‘*A*‘ volts when ‘1’ is transmitted.

■ Since polar RZ and NRZ formats are bipolar, therefore, the average DC value is minimum in these waveforms. If probabilities of occurrence of symbols ‘1’ and ‘0’ are same, then average DC components of the waveform would be zero.

■ The primary advantage of this format is that irrespective of the probability of occurrence of symbol ‘1’ and ‘0’ the waveform has zero average value. Therefore by this mode, the power saving is quite more.

■ However, the drawback of this format is that it requires absolute sense of polarity at the receiver end.

■ In a polar quaternary NRZ type of coding, we combine two successive bits. In M-ary coding , we combine ‘k’ successive message bits.

■ In digital baseband transmission, Intersymbol interference arises due to the dispersive nature of a communication channel. Mostly discrete pulse amplitude modulation is used to transmit the baseband pulse signal.

■ The output would be completely error free in the abosence of noise and ISI. Noise and ISI combinely introduce errors in the output. Hence, the efforts are made to increase signal to noise ratio and minimize the effect of ISI.

■ When the sequence is transmitted over a baseband binary data transmission system, the signal obtained at the output i.e., y(1) will be a continuous time signal.

■ An analog signal is converted to digital or binary waveform by means of waveform coding techniques.

■ In the bandpass transmission system, the digital signal modulates high frequency sinusoidal carrier. We have analysed such techniques in seventh chapter. These are known as digital carrier modulation techniques. With the help of such techniques, it is possible to transmit data over long distances. However, in baseband transmission, the data is transmitted without modulation.

■ During the transmission of data over the channel, it is corrupted by noise. Hence, at the receiver, the noisy signal is received. Therefore correct detection of the transmitted signal is necessary.

■ The detection method must attenuate noise and amplify signal. This means that if it must improve signal to noise ratio of the received signal.

■ The detection method must check the received signal at the time instant in the bit interval when signal to noise ratio is maximum.

■ The detection must be performed with minimum error probability. Now we shall study some methods for detection of digital signals.