data and signals

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IT209IT209

Data and SignalsData and Signals

Winter 2010Winter 2010

M.SudhaM.SudhaVITVIT UniversityUniversity--Vellore IndiaVellore India

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Topics:Topics:•• Analog and digital signalAnalog and digital signal•• Bandwidth of a signalBandwidth of a signal•• Transmission of digital signalTransmission of digital signal

Baseband transmissionBaseband transmission•• LowLow--pass channel with wide bandwidthpass channel with wide bandwidth•• LowLow--pass channel with limited bandwidthpass channel with limited bandwidth

Broadband transmissionBroadband transmission

•• Data rate limitsData rate limitsNoiseless Channel: Nyquist bit rateNoiseless Channel: Nyquist bit rateNoisy Channel: Shannon capacityNoisy Channel: Shannon capacity

•• PerformancePerformanceBandwidth, throughput, delayBandwidth, throughput, delay

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Figure 3.1 Comparison of analog and digital signals

From Figure 3.1 of Data Communications and Networking by Forouzan, 4th

3.1 Analog and Digital3.1 Analog and Digital

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3.2 Periodic Analog Signals3.2 Periodic Analog SignalsSine WaveSine Wave•• S(t) =A*sin(2S(t) =A*sin(2ππft + ft + θθ

))•• Peak Amplitude (A)Peak Amplitude (A)•• Period/Frequency (f)Period/Frequency (f)•• Phase (Phase (θθ

))ExamplesExamples•• S(t) = 5 sin(2S(t) = 5 sin(2ππ4000t + 0)4000t + 0)•• S(t) = 10sin(2S(t) = 10sin(2ππ8000t + 0)8000t + 0)•• S(t) = 5 sin(2S(t) = 5 sin(2ππ2000t + 2000t + ππ/4)/4)


A sine wave

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3.2 Periodic Analog Signals 3.2 Periodic Analog Signals (cont.)(cont.)

Time and Frequency DomainsTime and Frequency Domains•• Time Domain PlotTime Domain Plot•• Frequency DomainFrequency Domain

PlotPlot


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Composite SignalsComposite Signals•• A combination of many sine A combination of many sine

waves with different waves with different frequencies, amplitudes, frequencies, amplitudes, and phasesand phases

Fourier AnalysisFourier Analysiss(ts(t) = A) = A11

sin(2sin(2ππff11

++θθ11

) + ) + AA22

sin(2sin(2ππff22

++θθ22

) + ) + AA33

sin(2sin(2ππff33

++θθ33

) + ) + ……

3.2 Periodic Analog Signals 3.2 Periodic Analog Signals (cont.)(cont.)


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3.2 Periodic Analog Signals3.2 Periodic Analog Signals

For a For a periodicperiodic composite signalcomposite signal•• The decomposition gives a series of signals with The decomposition gives a series of signals with

discretediscrete

frequenciesfrequenciesFor a For a nonperiodicnonperiodic composite signalcomposite signal•• The decomposition gives a combination of sine The decomposition gives a combination of sine

waves with waves with continuouscontinuous

frequenciesfrequenciesBandwidth of a composite signalBandwidth of a composite signal•• The difference between the highest and the lowest The difference between the highest and the lowest

frequencies contained in that signalfrequencies contained in that signal

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Figure 3.10 Decomposition of a composite periodic signal in the time and frequency domains


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Figure 3.11 The time and frequency domains of a nonperiodic signal


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Figure 3.12 The bandwidth of periodic and nonperiodic composite signals


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If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is its bandwidth? Draw the spectrum, assuming all components have a maximum amplitude of 10 V.

Example 3.10

A periodic signal has a bandwidth of 20 Hz. The highest frequency is 60 Hz. What is the lowest frequency? Draw the spectrum if the signal contains all frequencies of the same amplitude.

Example 3.11

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Two digital signals: one with two signal levels and the other with four signal leve�ɠ

3.3 Digital Signals3.3 Digital Signals


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Example:1) A digital signal has eight levels. How

many bits are needed per level? We calculate the number of bits from the formula

2) A digital signal has nine levels. How many bits are needed per level?

In general, if a signal has L levels, each level needs log2 L bits.

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Bit Rate Bit Rate –– number of bits sent in 1s, bpsnumber of bits sent in 1s, bpsDigital SignalDigital Signal•• A composite signal having an A composite signal having an infiniteinfinite

number number

of frequencies or harmonicsof frequencies or harmonics•• Bandwidth (Bandwidth (∞∞))•• PeriodicPeriodic

digital signal digital signal ––

discretediscrete

frequenciesfrequencies

•• NonperiodicNonperiodic

digital signal digital signal ––

continuouscontinuous frequenciesfrequencies

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A digitized voice channel, as we will see in Chapter 4, is made by digitizing a 4-kHz bandwidth analog voice signal. We need to sample the signal at twice the highest frequency (two samples per hertz). We assume that each sample requires 8 bits. What is the required bit rate?

Example 3.19

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The time and frequency domains of periodic and nonperiodic digital signals


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3.3 Digital Signals 3.3 Digital Signals (cont.)(cont.)

Transmission of Digital SignalsTransmission of Digital Signals•• A digital signal is a composite analog signal A digital signal is a composite analog signal

with an infinite bandwidth.with an infinite bandwidth.•• Baseband Transmission Baseband Transmission ––

lowlow--pass channelpass channel


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Bandwidths of two low-pass channels


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Baseband transmission using a dedicated medium


Case 1: Low-Pass Channel with Wide Bandwidth

Baseband transmission of a digital signal that preserves the shape of the digital signal is possible only if we have a low-passChannel with an infinite or very wide bandwidth.

• Example: dedicated links in LAN

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Case 2: Low-Pass Channel with Limited BandwidthRough approximation of a digital signal using the first harmonic

for worst case – Required bandwidth = N/2 – 0 = N/2


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Simulating a digital signal with first three harmonics


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In baseband transmission, the required bandwidth is proportional to the bit rates; if we need to send bits faster, we need more bandwidth.

Bandwidth Requirements

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Example:What is the required bandwidth of a low-pass channel if we need to send 1 Mbps by using baseband transmission?

SolutionThe answer depends on the accuracy desired.a. The minimum bandwidth, is B = bit rate /2, or 500 kHz.

b. A better solution is to use the first and the third harmonics with B = 3 × 500 kHz = 1.5 MHz.

c. Still a better solution is to use the first, third, and fifth harmonics with B = 5 × 500 kHz = 2.5 MHz.

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Transmission of Digital SignalsTransmission of Digital Signals•• Broadband Transmission (using modulation) Broadband Transmission (using modulation) –– bandpassbandpass

channelchannel•• BandpassBandpass channel channel –– a channel with a bandwidth that a channel with a bandwidth that

does not start from zero.does not start from zero.Bandwidth of a Bandwidth of a bandpassbandpass

channelchannel


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Transmission of Digital SignalsTransmission of Digital Signals•• Broadband Transmission (using modulation) Broadband Transmission (using modulation) –– bandpassbandpass

channelchannelBandpassBandpass channel is more available than a lowchannel is more available than a low--pass channelpass channelDigital signal can not be directly sent by Digital signal can not be directly sent by bandpassbandpass channel. channel. Digital signal needs to be changed to an analog signal before Digital signal needs to be changed to an analog signal before transmission using transmission using bandpassbandpass channel channel -- modulationmodulation..

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Modulation of a digital signal for transmission on a bandpass channel


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