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Information Sources And Signals

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2 Review: Composite Signals and Frequency Domain Representations Time Domain RepresentationFrequency Domain Representation

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3 Signal Bandwidth A Measure of Signal Frequency Range The difference between the highest and the lowest frequencies contained in a signal.

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4 What Is the Bandwidth of This Signal? = 1Hz

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If a signal is decomposed into three sine waves with frequencies of 300, 700, and 1200 Hz, what is its bandwidth? 5

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Why Should We Care about Bandwidth? We need to know the bandwidth of a signal to make sure the communication channel is wide enough to transmit it. 6

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An Analogy 7

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In reality, 8 The bandwidth of a signal is much larger than what is allowed by a communication channel. We need to chop off some frequency components of a signal so that it can be transmitted AND as much information as possible can be preserved.

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Digital Signals

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10 Digital Signals Use voltage to represent digital values – A positive voltage a logical one (1) – Zero or a negative voltage a logical zero (0) +5 volts is usually what we use in computer hardware. – +5 or 0 -> 1 or 0 – Two levels: 1 bit

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11 Digital Signal Levels Some physical mechanisms can support more than two signal levels. – For example, consider a system that uses four levels of voltage: – -5 volts, -2 volts, +2 volts, and +5 volts

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Digital Signal Levels More signal levels a system has, more bits need to be sent out per unit time.

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Bits and Signal Levels Often we use bits to describe signal levels How many bits can we represent using 4 levels? – -5, -2, 2, 5 How many bits can we represent using 8 levels? How many levels do we need to represent n bits? 13

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14 More Bits, Better? More bits a system can deliver at a given time period, more information it can transfer. Can we increase the signal levels as many as possible? – Mathematically, it is doable. – Practically, electronic systems cannot distinguish between signal levels (voltage levels) that differ by small amounts.

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What’s the bandwidth of digital signals? Frequency Domain RepresentationTime Domain Representation = Fourier Analysis:

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16 Digital Signals The bandwidth of a digital signal is infinite! – Accurate representation of a digital signal requires an infinite set of sine waves. – Transmitting/reproducing digital signals is impractical Engineers adopt a compromise: – generate analog waves that closely approximate the digital signal – approximation involves building a composite signal from only a few sine waves – the quality of approximation depends on the channel bandwidth

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Bandwidth-Limited Signals Having less bandwidth (harmonics) degrades the signal CN5E by Tanenbaum & Wetherall, © Pearson Education-Prentice Hall and D. Wetherall, sine waves 4 sine waves 2 sine waves Lost! Bandwidth Lost!

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18 Speed/Capacity of Data Transmittion We use bit rate (bits per second) to measure the speed/capacity of transmission. Two factors to consider when measuring the bit rate. 1.The number of signal levels How many bits at each level? 2.How long does a system have to stay at a given level? Should be long enough to guarantee the signal to be received. We use Baud to measure how many times the signal can change per second

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19 Baud Baud rate is confined by hardware. Some numbers (theoretical) – Dial-in (v.90): 56k – ISDN: 128k – DSL: 300k – 1,500k (1.5M) – Cable: 300k – 6,000k (6M) (could go higher) – T1: 1.5M – T3: 44M – 100Base-T: 100M Baud rates on real connections may be lower.

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20 Bit Rate If a system with two signal levels operates at 1000 baud, how many bits he system can transfer per second? How about a system that operates at 2000 baud and has four signal levels

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21 Synchronization and Agreement about Signals Diverse signals and systems means different signal levels and baud rates. – Different signal levels + Different baud rates Troubles! The systems at both ends must be able to measure time precisely. – if one end transmits a signal with 10 elements per second, the other end must expect exactly 10 elements per second

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22 Example of Synchronization Error

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23 Synchronization and Agreement about Signals Handshaking – – pictured.html pictured.html At slow speeds, easy At high speeds, many challenges – if one end transmits a signal with 10 9 elements per second, the other end must expect exactly 10 9 elements per second (not , not ) … 0 Um, how many zeros was that?

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Manchester Encoding For computers, detecting a transition in signal level is much easier than measuring the signal level – A transition from 0V to +5V logical 1 – A transition from +5V to 0V logical 0 – Transitions occur in the middle of each time slot

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25 Converting an Analog Signal to Digital Pulse code modulation

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26 Converting an Analog Signal to Digital The three steps used PCM 1.Sampling an analog signal. 2.Quantizing the sampled value. 3.Encoding the quantized value

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How many samples do we need? 27 too few samples: may only give a crude approximation of the original signal too many samples: more digital data will be generated, which uses extra bandwidth

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28 The Nyquist Theorem and Sampling Rate A mathematician named Nyquist discovered exactly how much sampling is required: – f max : the highest frequency in the composite signal. Sample a signal at least twice as fast as the highest frequency that must be preserved.

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Q: At what rate should we sample the following signal?

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30 Example: Bit Rate of Telephone System Audio bandwidth – Acceptable quality: preserving frequency up to 4k – Sampling rate (baud) = 2*4K = 8K Quantization: – Reasonable quality reproduction: 8 bits / 256 levels

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Digital Audio Audio frequency – 20 Hz – 20k – Varied from individual to individual Teenbuzz: mp3/atc/atc_teenbuzz.mp3http://download.npr.org/anon.npr- mp3/atc/atc_teenbuzz.mp3 Sampling frequency – MP3: 44.1kHz – DVD-audio: 48 kHz

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32 Encoding and Data Compression Data compression refers to a technique that reduces the number of bits required to represent data Data compression is relevant to a communication system – because reducing the number of bits used to represent data reduces the time required for transmission – a communication system can be optimized by compressing data Chapter 29 discusses compression in multimedia applications There are two types of compression: – Lossy - some information is lost during compression – Lossless - all information is retained in the compressed version

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33 Encoding and Data Compression Lossy compression is generally used with data that a human consumes, such as an image, video/audio The key idea is that the compression only needs to preserve details to the level of human perception – a change is acceptable if humans cannot detect the change – JPEG (used for images) compression or MPEG-3 (abbreviated MP3 and used for audio recordings) employ lossy compression Lossless compression preserves the original data without missing anything – lossless compression can be used for documents or in any situation where data must be preserved exactly – when used for communication, a sender compresses the data before transmission and the receiver decompresses the result – arbitrary data can be compressed by a sender and decompressed by a receiver to recover an exact copy of the original

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Friday Group research assignment 1 due at 11:59pm Use class time to work on it

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