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Physical LayerPhysical LayerContinue LectureContinue Lecture

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Chapter 3 of Data Communication & Networks

Author by Behrouz A. Forouzan

Fundamental ofSignals

Continue Lecture

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3.3 Digital Signals3.3 Digital Signals

Bit Interval and Bit RateAs a Composite Analog Signal

Through Wide-Bandwidth MediumThrough Band-Limited Medium

Versus Analog BandwidthHigher Bit Rate

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Figure 3.16 A digital signal

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Example 6Example 6

A digital signal has a bit rate of 2000 bps. What is the

duration of each bit (bit interval)

SolutionSolution

The bit interval is the inverse of the bit rate.

Bit interval = 1/ 2000 s = 0.000500 s

= 0.000500 x 106

s = 500 s

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Figure 3.17 Bit rate and bit interval

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Figure 3.18 Digital versus analog

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A digital signal is a composite signalA digital signal is a composite signal

with an infinite bandwidth.with an infinite bandwidth.

Note:Note:

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Table 3.12 Bandwidth RequirementTable 3.12 Bandwidth RequirementBit

Rate

Harmonic

1

Harmonics

1, 3

Harmonics

1, 3, 5

Harmonics

1, 3, 5, 7

1 Kbps 500 Hz 2 KHz 4.5 KHz 8 KHz

10 Kbps 5 KHz 20 KHz 45 KHz 80 KHz

100 Kbps 50 KHz 200 KHz 450 KHz 800 KHz

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The bit rate and the bandwidth areThe bit rate and the bandwidth are

proportional to each other.proportional to each other.

Note:Note:

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3.4 Analog versus Digital3.4 Analog versus Digital

Low-pass versus Band-pass

Digital Transmission

Analog Transmission

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Figure 3.19 Low-pass and band-pass

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The analog bandwidth of a medium isThe analog bandwidth of a medium is

expressed in hertz; the digitalexpressed in hertz; the digitalbandwidth, in bits per second.bandwidth, in bits per second.

Note:Note:

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Digital transmission needs aDigital transmission needs a

low-pass channel.low-pass channel.

Note:Note:

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Analog transmission can use a band-Analog transmission can use a band-

pass channel.pass channel.

Note:Note:

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3.5 Data Rate Limit3.5 Data Rate Limit

Noiseless Channel: Nyquist Bit Rate

Noisy Channel: Shannon Capacity

Using Both Limits

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Example 7Example 7

Consider a noiseless channel with a bandwidth of 3000 Hz

transmitting a signal with two signal levels. The maximumbit rate can be calculated as

BitBit Rate = 2Rate = 2 30003000 loglog22 2 = 6000 bps2 = 6000 bps

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Example 8Example 8

Consider the same noiseless channel, transmitting a signal

with four signal levels (for each level, we send two bits).The maximum bit rate can be calculated as:

Bit Rate = 2 x 3000 x logBit Rate = 2 x 3000 x log22 4 = 12,000 bps4 = 12,000 bps

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Example 9Example 9

Consider an extremely noisy channel in which the value of

the signal-to-noise ratio is almost zero. In other words, thenoise is so strong that the signal is faint. For this channel

the capacity is calculated as

C = B logC = B log22 (1 + SNR) = B log(1 + SNR) = B log22 (1 + 0)(1 + 0)

= B log= B log22 (1) = B(1) = B 0 = 00 = 0

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Example 10Example 10

We can calculate the theoretical highest bit rate of a

regular telephone line. A telephone line normally has abandwidth of 3000 Hz (300 Hz to 3300 Hz). The signal-to-

noise ratio is usually 3162. For this channel the capacity is

calculated as

C = B logC = B log22 (1 + SNR) = 3000 log(1 + SNR) = 3000 log22 (1 + 3162)(1 + 3162)

= 3000 log= 3000 log22 (3163)(3163)C = 3000C = 3000 11.62 = 34,860 bps11.62 = 34,860 bps

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Example 11Example 11

We have a channel with a 1 MHz bandwidth. The SNR for

this channel is 63; what is the appropriate bit rate andsignal level?

SolutionSolution

C = B logC = B log22

(1 + SNR) = 10(1 + SNR) = 1066 loglog22

(1 + 63) = 10(1 + 63) = 1066 loglog22

(64) = 6 Mbps(64) = 6 Mbps

Then we use the Nyquist formula to find thenumber of signal levels.

4 Mbps = 24 Mbps = 2 1 MHz1 MHz loglog22LL L = 4L = 4

First, we use the Shannon formula to find our upper limit.First, we use the Shannon formula to find our upper limit.

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3.6 Transmission Impairment3.6 Transmission Impairment

Attenuation (The gradual loss of intensity of any kind of flux) (

Distortion (is the alteration of the original shape )

Noise (a random fluctuation in an electrical signal)

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Figure 3.20 Impairment types

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Figure 3.21 Attenuation