# Information Sources and Signals

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Information Sources and Signals

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

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

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

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

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

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

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

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

Time and Frequency Units

Composite Signals Consider the signal + =

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 = +

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

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

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

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

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

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

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

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

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

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

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

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

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

Line Coding Schemes

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

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

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

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

Nyquist’s Sampling Theorem

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)

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)

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