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© 2009 Pearson Education Inc., Upper Saddle River, NJ. All rights reserved. Information Sources and Signals Asst. Prof. Chaiporn Jaikaeo, Ph.D. Computer Engineering Department Kasetsart University, Bangkok, Thailand Adapted from the notes by Lami Kaya,

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2 Analog vs. Digital Data Analog data Data take on continuous values E.g., human voice, your weights, temperature reading Numerical representation: real numbers Digital data Data take on discrete values E.g., number of students in class, text data Numerical representation: integers

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3 Analog vs. Digital Signals Analog signals have an infinite number of values in a range Digital signals Have a limited number of values To be transmitted, data must be transformed to electromagnetic signals

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4 Data and Signals Telephone Analog DataAnalog Signal Modem Digital DataAnalog Signal Codec Analog DataDigital Signal Digital Transmitter/ Line Coder Digital DataDigital Signal

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5 Periodic Signals A periodic signal completes a pattern within a timeframe, called a period A signal x(t) is periodic if and only if x(t) = x(t+T) - < t < value time period

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6 Simplest form of periodic signal General form: x(t) = A×sin(2 ft + ) period T = 1/f peak amplitude time signal strength Sine Waves phase / phase shift

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7 Sine Signal Characteristics Frequency ( f ): the number of oscillations per unit time (usually seconds) Amplitude ( A ): the difference between the maximum and minimum signal heights Phase ( ): how far the start of the sine wave is shifted from a reference time

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8 A = 1, f = 1, = 0A = 2, f = 1, = 0A = 1, f = 2, = 0A = 1, f = 1, = /4 Varying Sine Waves

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9 Sine Signal Characteristics The frequency can be calculated as the inverse of the time required for one cycle, which is known as the period Examples: period T = 1 seconds frequency is 1 / T or 1 Hertz period T = 0.5 seconds frequency is 2 Hertz

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10 Time and Frequency Units

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11 Composite Signals Consider the signal +=

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12 Composite Signals A mathematician named Fourier discovered that It is possible to decompose a composite signal into series of sine functions Each with different frequency, amplitude, and phase += Joseph Fourier ( )

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13 Time vs. Frequency Domains Frequency domain representation is much easier for analysis timesignal level signal levelfrequency Time Domain Representation plots amplitude as a function of time Frequency Domain Representation plots each sine wave’s peak amplitude against its frequency

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14 Bandwidth of Signal Bandwidth of a signal is the difference between the highest and lowest frequencies of the signal

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15 Digital Signals and Signal Levels Two-level signal Each level represents 1 bit Four-level signal Each level represents 2 bits

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16 Example How many different levels are required if we want each level to represent n bits?

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17 Baud and Bit Rate Baud How many times a signal changes per second Bit rate How many bits can be sent per time unit (usually per second) Bit rate is controlled by baud and number of signal levels 1 sec sec Baud = 10 Bit rate = 10 bps Baud = 10 Bit rate = 20 bps

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18 Baud and Bit Rate Relationship between baud, signal levels, and bit rate is: Example: What is the bit rate (in bps) of a 16-level signal transmitted at 20 baud

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19 Transmission Latency Composed of Propagation time Transmission time Queuing time Processing time Entire message transmission time propagation time

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20 Data bits Transmission Latency Time First bit leaves Last bit leaves First bit arrives Last bit arrives Sender Receiver Propagation time Transmission time

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21 Fourier Analysis of Digital Signals Digital signals consist of infinite set of sine waves What is the bandwidth? …

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22 Bandwidth of a Medium Transmission medium 1 (low-pass channel) gain freq tt 0 f0f0 3f03f0 5f05f0 f 0 f0f0 3f03f0 5f05f0 7f07f0... 9f09f0 f Most transmission media have bandwidth limit

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23 Line Coding The process of encoding digital data into digital signal Example: Manchester encoding (used in Ethernet LAN)

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24 Synchronization The electronics at both ends of a medium must have circuitry to measure time precisely Easy at low bit rate Much more difficult at high bit rate

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25 Synchronization Good line coding schemes allow receiver to synchronize its timing to match the sender's Bad Good

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26 Line Coding Schemes

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27 Converting Analog to Digital Common technique: Pulse Code Modulation (PCM)

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28 PCM: Sampling and Quantizing Sampling points quantizing (rounding to nearest integer)

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29 PCM: The Whole Picture *PAM: Pulse Amplitude Modulation *

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30 Minimum Sampling Rate Nyquist Theorem: t sampling interval Ex. Find the maximum sampling interval for recording human voice (freq. range 300Hz – 3000Hz)

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31 Nyquist’s Sampling Theorem See also: Wagon-wheel effect

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32 Example Calculate the minimum bit rate for recoding human voice, if each sample requires 60 levels of precision (Human voice has range of 300Hz – 3000Hz)

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33 Data Compression Data compression refers to a technique that reduces the number of bits required to represent data Lossy - some information is lost during compression (e.g, JPG, MP3) Lossless - all information is retained in the compressed version (e.g., PNG, PCM)

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34 Summary Data and signals Signal as series of sine waves Fourier analysis Bandwidth Line coding Analog to digital conversion PCM Data compression

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