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Signals and Noise. Jan 29, 2002. Announcement. Homework-Chapter 2, Problems 2, 6, 8, 12, 16, 18 Recommended Problems: 13, 15, 23 Email: ebonilla@gmu.edu TA: Alexe Lue, aleu@gmu.edu http://teal.gmu.edu/ececourses/tcom500/spring2002/ Change in schedule. Class Objectives. Review
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Signals and Noise Jan 29, 2002
Announcement • Homework-Chapter 2, Problems 2, 6, 8, 12, 16, 18 • Recommended Problems: 13, 15, 23 • Email: ebonilla@gmu.edu • TA: Alexe Lue, aleu@gmu.edu • http://teal.gmu.edu/ececourses/tcom500/spring2002/ • Change in schedule
Class Objectives • Review • Fundamentals of Signals • Mathematical concepts • Signal-to-Noise Ratio • Noise Figure • Bit Error Rate • Channel Capacity
Fundamentals of Electric Signals • Electrical signals are created by the flow of electrons • Electrons flow from high charge potential to lower charge potential (EMF) • Circuits are conductive paths that direct the flow of electrons
Frequency • The number of complete cycles of sinusoidal variation per unit time • 1 Cycle per second = 1 Hertz = 1 Hz • 1000 cycles per second = 1000 Hz = 1kHz • 1,000,000 cycles per second = 1 MHz • 1,000,000,000 Hz = 1 GHz
Sine Wave • Peak Amplitude (A) • maximum strength of signal • volts • Frequency (f) • Rate of change of signal • Hertz (Hz) or cycles per second • Period = time for one repetition (T) • T = 1/f • Phase () • Relative position in time
Frequencies • Acoustic frequencies: • human speech: 100 Hz to 7 kHz • Music: up to 20 kHz • ultrasounds: above 20 Khz to 1 MHz • Electromagnetic carrier frequencies: • AM radio broadcast (example) 710 kHz • FM broadcast 89 MHz- 108 MHz • TV broadcasting 150 MHz- 900 MHz • Cellular telephony ~ 1 GHz
Frequency Domain Concepts • Signal can be made up of many frequencies • Components are sine waves • Frequency domain functions can be plotted • Changes in the time domain affects the signal in the frequency domain
Spectrum & Bandwidth • Spectrum • range of frequencies contained in signal • Absolute bandwidth • width of spectrum • Effective bandwidth • Often just bandwidth • Narrow band of frequencies containing most of the energy • DC Component • Component of zero frequency
Data Rate and Bandwidth • All transmission systems have a limited band of frequencies • Data Rate: the amount of data that is transmitted in a unit time (one second) • Limited bandwidth results in limited data rate
Analog and Digital Data Transmission • Data • Entities that convey meaning • Signals • Electric or electromagnetic representations of data • Transmission • Communication of data by propagation and processing of signals
Data • Analog • Continuous values within some interval • e.g. sound, video • Digital • Discrete values • e.g. text, integers
Signals • Means by which data are propagated • Analog • Continuously variable • Various media • wire, fiber optic, space • Speech bandwidth 100Hz to 7kHz • Telephone bandwidth 300Hz to 3400Hz • Video bandwidth 4MHz • Digital • Use discrete components (mostly two DC components)
Data and Signals • Past: digital signals for digital data and analog signals for analog data • Present: digital signals for both digital and analog data • Can use analog signal to carry digital data • Phone Modem • Can use digital signal to carry analog data • Compact Disc audio
Analog Transmission Characteristics • Analog signal transmitted without regard to content • Vulnerable to noise • Attenuated over distance • Use amplifiers to boost signal (& noise)
Digital Transmission Characteristics • Content sensitive • Integrity endangered by noise, attenuation etc. • Repeaters are used to regenerate signal • Extracts bit pattern • Retransmits • Attenuation is overcome • Noise is not amplified
Advantages of Digital Transmission • Digital technology • Low cost LSI/VLSI technology • Data integrity • Longer distances are possible • Error correction • Capacity utilization • High bandwidth links economical due to efficiency • High degree of multiplexing easier with digital techniques • Security & Privacy • Encryption • Integration • Can treat analog and digital data similarly
Transmission Impairments • Transmitted signal must be compatible with receiver • Analog - degradation of signal quality • Digital - bit errors • Signal degradation causes include: • Attenuation and attenuation distortion • Delay distortion • Noise • Interference
Attenuation • Signal strength falls off with distance • Depends on medium • Attenuation is an increasing function of frequency • Received signal strength: • must be enough to be detected • must be sufficiently higher than noise to be received without error
Attenuation & Delay Distortion • Attenuation varies with frequency • Certain frequencies are attenuated more than others • Propagation velocity varies with frequency • Some frequencies arrive earlier than others, results in modifying the phase
Noise & Interference • Unwanted signals inserted between transmitter and receiver • Thermal • Due to thermal agitation of electrons • Uniformly distributed (White noise) • Intermodulation • Signals that are the sum and difference of original frequencies sharing a medium • Interference • Identifiable, man-made noise
Noise & Interference • Crosstalk • A signal from one line is picked up by another • Impulse • Irregular pulses or spikes • e.g. External electromagnetic interference • Short duration • High amplitude
Topics – 2nd Half • Decibels • Signals and Noise • Signal-to-noise ratio • BER, Channel capacity • Noise types
On-line resources for basic concepts of Electricity Electric circuits http://www.fclabs.com.au/onlinesamples/ec/elect01/els01dx.htm Animation of Ohm's law http://www.phy.ntnu.edu.tw/java/rc/rc.html Animation of an RLC circuit with AC currents http://www.phy.ntnu.edu.tw/java/rlc/rlc.html Animation of a clipping circuit http://www.phy.ntnu.edu.tw/java/electronics/clip_e.html Animation of Fourier synthesis of oscillatory signals http://www.phy.ntnu.edu.tw/java/sound/sound.html Propagation of Electromagnetic Wave http://www.phy.ntnu.edu.tw/java/emWave/emWave.html
Electric Power If an electric current flows through a resistance R thenthe power dissipated is rms = root-mean-square value If voltage V varies in time, then the average power dissipated is proportional to its rms value
Signal Power Gain/Loss Quantity of interest: (Output Signal Power)/(Input signal power)
Decibels • Decibel, dB, is a measure of a relative amplitude (or power) of a signal, be it acoustic or electric • The term “relative” means that we are measuring the ratio of the given amplitude to another amplitude, for example the ratio of the amplitude (Volts) at the end of the phone line to the amplitude (Volts) at the beginning of the phone line • In acoustics, the decibel is a measure of the relative level of sound or noise compared to some standardized level of sound or noise. One decibel (0.1 bel) equals 10 times the logarithm of the power ratio of the given sound to the power of the sound barely perceptible by human ear.
