Although the actual bandwidth ofa digital signal is infinite, the effective bandwidth is finite in Software

Generation Code 39 in Software Although the actual bandwidth ofa digital signal is infinite, the effective bandwidth is finite

Although the actual bandwidth ofa digital signal is infinite, the effective bandwidth is finite
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We can say that the baud rate, not the bit rate, determines the required bandwidth for a digital signal If we use the transpOltation analogy, the number of vehicles affects the traffic, not the number of people being carried More changes in the signal mean injecting more frequencies into the signal (Recall that frequency means change and change means frequency) The bandwidth reflects the range of frequencies we need There is a relationship between the baud rate (signal rate) and the bandwidth Bandwidth is a complex idea When we talk about the bandwidth, we normally define a range of frequencies We need to know where this range is located as well as the values of the lowest and the highest frequencies In addition, the amplitude (if not the phase) of each component is an impOltant issue In other words, we need more information about the bandwidth than just its value; we need a diagram of the bandwidth We will show the bandwidth for most schemes we discuss in the chapter For the moment, we can say that the bandwidth (range of frequencies) is proportional to the signal rate (baud rate) The minimum bandwidth can be given as
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1 B min =: c >< N >< -
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We can solve for the maximum data rate if the bandwidth of the channel is given
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N max = - xBxr c
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Example 42
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The maximum data rate of a channel (see 3) is N max = 2 >< B >< log2L (defined by the Nyquist formula) Does this agree with the previous formula for N max
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A signal with L levels actually can carry log2 L bits per level If each level corresponds to one signal element and we assume the average case (c = ~), then we have
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Baseline Wandering In decoding a digital signal, the receiver calculates a running average of the received signal power This average is called the baseline The incoming signal power is evaluated against this baseline to determine the value of the data element A long string of Os or 1s can cause a drift in the baseline (baseline wandering) and make it difficult for the receiver to decode correctly A good line coding scheme needs to prevent baseline wandering
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SECTION 41
DIGITAL-TO-DIGITAL CONVERSION
DC Components When the voltage level in a digital signal is constant for a while, the spectrum creates very low frequencies (results of Fourier analysis) These frequencies around zero, called DC (direct-current) components, present problems for a system that cannot pass low frequencies or a system that uses electrical coupling (via a transformer) For example, a telephone line cannot pass frequencies below 200 Hz Also a long-distance link may use one or more transformers to isolate different parts of the line electrically For these systems, we need a scheme with no DC component Self-synchronization To correctly interpret the signals received from the sender, the receiver's bit intervals must correspond exactly to the sender's bit intervals If the receiver clock is faster or slower, the bit intervals are not matched and the receiver might misinterpret the signals Figure 43 shows a situation in which the receiver has a shorter bit duration The sender sends 10110001, while the receiver receives 110111 000011
Effect of lack ofsynchronization
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A self-synchronizing digital signal includes timing information in the data being transmitted This can be achieved if there are transitions in the signal that alert the receiver to the beginning, middle, or end of the pulse If the receiver's clock is out of synchronization, these points can reset the clock
Example 43
In a digital transmission, the receiver clock is 01 percent faster than the sender clock How many extra bits per second does the receiver receive if the data rate is 1 kbps How many if the data rate is 1 Mbps
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