Chpt 3 Digital Baseband Modulation Techniques

Chpt 3 Digital Baseband Modulation Techniques - Chapter 3...

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1 Chapter 3 Digital Baseband Modulation Techniques
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2 A basic technique in a modern digital communication system is to use a pulse to represent a bit of information. For transmission systems, we are interested in generating the signal carrying information at the transmitter and recovering information at the receiver. The following issues are important for digital transmission systems. - Generation of the signal to carry information at the transmitter, - Bandwidth requirement, - Interference due to channel bandwidth, We will discuss these issues progressively. Goals and Problems
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3 Assume that we have a stream of binary signals: 101110110100. .. to transmit through a channel. We need to represent them by electronic signals, e.g., voltage waveforms. There are many ways to do this. The following is one. Here a negative pulse represents “0” and a positive pulse represents “1”. You can also use a negative to represent “1” and a positive pulse to represent “0”, which will make no difference. (Why?) Can we use other kinds of pulse or method for the same purpose? Binary Amplitude Pulse Modulation 1 0 1 1 1 0 1 1 0 1 0 0
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4 One Bit = Two Possibilities 01 Which scheme here can not be used to transmit one bit of information? Which scheme is more prone to error?
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5 A time domain signal s ( t ): The corresponding Fourier transform S ( f ): Spectrum Requirement 0 t τ /2 A - /2 s ( t ) τ sin( ) () s i n c ( ) f Sf A A f f π τπ πτ =⋅ = f A 1/ τ -1/ τ 2/ τ -2/ τ S ( f )
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6 The Impact of Pulse Width What is your observation of the above two signals? What is the consequence if we want to transmit a very narrow pulse? What is the relationship between the time domain speed and frequency domain spectrum? t τ /2 - /2 s ( t ) S ( f ) /2 - /2 s ( t ) f 1/ τ -1/ τ 2/ τ -2 τ f 1/ τ -1/ τ 2/ τ -2/ τ S ( f )
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7 Spectrum Requirement A narrow pulse has a wide spectrum. Next we will see that to transmit a sequence of pulses, the required spectrum is roughly the same as transmitting a single pulse. If we want to transmit many very narrow pulses, then we need to occupy a large range of spectrum. This is a fundamental problem for digital communication systems. s ( t ) τ f A 1/ τ -1/ τ 2/ τ -2/ τ S ( f )
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8 The Shift Property T t T+ τ /2 A T - /2 x ( t ) Time Shift : s ( t- Τ ) S ( f ) exp( -j 2 π f ) Example: Find the Fourier transform of the following function. Solution: Note that x ( t )= s ( t - T ) where s( t ) is given in the previous slide. For example, when x ( T )= s ( T - T )=s(0). Therefore using the shift property, X ( f ) = S ( f ) exp( -j2 fT ) 1/ τ -1/ τ 2/ τ -2/ τ f |X ( f )| = |S ( f )|
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9 Verification T t T+ τ /2 A T - /2 x ( t ) 2 2 2( / 2 ) / 2 ) 2 2 () ( ) /2 2 sin( ) ( ) jf t t T T T T Xf x te d t tT A e ee A f eA f eS f π πτ −∞ −+ −− = =+ = =− = =⋅
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10 The Linearity Property Let s ( t ) S ( f ). Then from the shift property and linearity X ( f ) = S ( f ) - exp( -j2 π f τ ) S ( f ) + exp( -j2 f 2 ) S ( f ) = S ( f ) [1 - exp(
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This note was uploaded on 01/11/2011 for the course EE 3008 taught by Professor Pingli during the Fall '08 term at City University of Hong Kong.

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Chpt 3 Digital Baseband Modulation Techniques - Chapter 3...

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