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**Information Sources and Signals**

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

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**Analog vs. Digital Data Analog data Digital 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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**Analog vs. Digital Signals**

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

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**Data and Signals Analog Data Analog Signal Digital Data Analog Signal**

Telephone Analog Data Analog Signal Modem Digital Data Analog Signal Codec Analog Data Digital Signal Digital Transmitter/ Line Coder Digital Data Digital Signal

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**x(t) = x(t+T) - < t < **

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 period time

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**Sine Waves Simplest form of periodic signal**

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

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**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 7

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**Varying Sine Waves A = 1, f = 1, = 0 A = 2, f = 1, = 0**

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**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 9

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**Time and Frequency Units**

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Composite Signals Consider the signal + =

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**Composite Signals A mathematician named Fourier discovered that**

Joseph Fourier ( ) 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 = +

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**Time vs. Frequency Domains**

1 -1 2 4 time signal level 1 -1 2 4 signal level frequency Time Domain Representation plots amplitude as a function of time Frequency Domain Representation plots each sine wave’s peak amplitude against its frequency Frequency domain representation is much easier for analysis

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

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**Digital Signals and Signal Levels**

Two-level signal Each level represents 1 bit Four-level signal Each level represents 2 bits 15

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

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**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 1 00 11 10 01 1 sec Baud = 10 Bit rate = 10 bps Baud = 10 Bit rate = 20 bps

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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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**Transmission Latency Composed of Propagation time Transmission time**

Queuing time Processing time Entire message propagation time transmission time

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**Transmission Latency Sender Receiver First bit leaves Data bits**

Propagation time First bit arrives Transmission time Last bit leaves Last bit arrives Time Time

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**Fourier Analysis of Digital Signals**

Digital signals consist of infinite set of sine waves What is the bandwidth? + + + + …

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**Bandwidth of a Medium Most transmission media have bandwidth limit f f**

1 (low-pass channel) gain freq f0 3f0 5f0 7f0 ... 9f0 f f0 3f0 5f0 f Transmission medium t t

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**Line Coding The process of encoding digital data into digital signal**

Example: Manchester encoding (used in Ethernet LAN)

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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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Synchronization Good line coding schemes allow receiver to synchronize its timing to match the sender's 1 1 1 1 1 1 1 Bad Good

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Line Coding Schemes

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**Converting Analog to Digital**

Common technique: Pulse Code Modulation (PCM)

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**PCM: Sampling and Quantizing**

quantizing (rounding to nearest integer) Sampling points

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

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**Minimum Sampling Rate Nyquist Theorem:**

Ex. Find the maximum sampling interval for recording human voice (freq. range 300Hz – 3000Hz) t sampling interval

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**Nyquist’s Sampling Theorem**

See also: Wagon-wheel effect

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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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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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**Summary Data and signals Signal as series of sine waves Bandwidth**

Fourier analysis Bandwidth Line coding Analog to digital conversion PCM Data compression

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