8In reality,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.
10Digital 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 0Two levels: 1 bit
11Digital Signal LevelsSome 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
12Digital Signal LevelsMore signal levels a system has, more bits need to be sent out per unit time.
13Bits and Signal Levels Often we use bits to describe signal levels How many bits can we represent using 4 levels?-5, -2, 2, 5How many bits can we represent using 8 levels?How many levels do we need to represent n bits?
14More 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.
15What’s the bandwidth of digital signals? Fourier Analysis:=Time Domain RepresentationFrequency Domain Representation
16Digital 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 impracticalEngineers adopt a compromise:generate analog waves that closely approximate the digital signalapproximation involves building a composite signal from only a few sine wavesthe quality of approximation depends on the channel bandwidth1616
18Speed/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.The number of signal levelsHow many bits at each level?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
19Baud Baud rate is confined by hardware. Some numbers (theoretical) Dial-in (v.90): 56kISDN: 128kDSL: 300k – 1,500k (1.5M)Cable: 300k – 6,000k (6M) (could go higher)T1: 1.5MT3: 44M100Base-T: 100MBaud rates on real connections may be lower.1919
20Bit RateIf 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 levels2020
21Synchronization 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
23Synchronization and Agreement about Signals HandshakingAt slow speeds, easyAt high speeds, many challengesif one end transmits a signal with 109 elements per second, the other end must expect exactly 109 elements per second (not 109-1, not 109+1)1… 0Um, how many zeros was that?
24Manchester EncodingFor computers, detecting a transition in signal level is much easier than measuring the signal levelA transition from 0V to +5V logical 1A transition from +5V to 0V logical 0Transitions occur in the middle of each time slot
25Converting an Analog Signal to Digital Pulse code modulation
26Converting an Analog Signal to Digital The three steps used PCMSampling an analog signal.Quantizing the sampled value.Encoding the quantized value.18.104.22.16826
27How many samples do we need? too few samples: may only give a crude approximation of the original signaltoo many samples: more digital data will be generated, which uses extra bandwidth
28The Nyquist Theorem and Sampling Rate A mathematician named Nyquist discovered exactly how much sampling is required:fmax : the highest frequency in the composite signal.Sample a signal at least twice as fast as the highest frequency that must be preserved.
29Q: At what rate should we sample the following signal?
30Example: Bit Rate of Telephone System Audio bandwidthAcceptable quality: preserving frequency up to 4kSampling rate (baud) = 2*4K = 8KQuantization:Reasonable quality reproduction: 8 bits / 256 levels
31Digital Audio Audio frequency Sampling frequency 20 Hz – 20k Varied from individual to individualTeenbuzz:Sampling frequencyMP3: 44.1kHzDVD-audio: 48 kHz
32Encoding and Data Compression Data compression refers to a technique that reduces the number of bits required to represent dataData compression is relevant to a communication systembecause reducing the number of bits used to represent data reduces the time required for transmissiona communication system can be optimized by compressing dataChapter 29 discusses compression in multimedia applicationsThere are two types of compression:Lossy - some information is lost during compressionLossless - all information is retained in the compressed version
33Encoding and Data Compression Lossy compression is generally used with data that a human consumes, such as an image, video/audioThe key idea is that the compression only needs to preserve details to the level of human perceptiona change is acceptable if humans cannot detect the changeJPEG (used for images) compression or MPEG-3 (abbreviated MP3 and used for audio recordings) employ lossy compressionLossless compression preserves the original data without missing anythinglossless compression can be used for documents or in any situation where data must be preserved exactlywhen used for communication, a sender compresses the data before transmission and the receiver decompresses the resultarbitrary data can be compressed by a sender and decompressed by a receiver to recover an exact copy of the original3333
34Friday Group research assignment 1 due at 11:59pm Use class time to work on it