Signals and Noise Sept 5, 2002

Announcements Homework-Chapter 2, Problems 2, 6, 8, 12, 16, 18 Recommended Problems: 13, 15, 23 TA: Mahdu Rangarajan, Course URL Reading Assignment for next week: Chapter 3 Chapter 4, Sections

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

Frequencies 1Hz, 2, 10, 20 Hz

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

Periodic Signals

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

Acoustic Spectrum

Continuous & Discrete Signals

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

Addition of Frequency Components

Time-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

Signal with DC Component

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)

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 (cont) 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

Effects of Noise on a Signal

Gaussian Noise Distribution

Crosstalk

Break

Topics – 2 nd Half Decibels Signals and Noise Signal-to-noise ratio BER, Channel capacity Noise types

Electric circuits Animation of Ohm's law Animation of an RLC circuit with AC currents Animation of a clipping circuit Animation of Fourier synthesis of oscillatory signals Propagation of Electromagnetic Wave On-line resources for basic concepts of Electricity Courtesy of Dr. Manitius

Electric Power Power can be expressed in several ways: P = VI = I 2 R = V 2 /R If an electric current flows through a resistance R then the power, expressed as I 2 R, is dissipated (loss) as heat. rms = root-mean-square value If voltage V varies in time, then the average power dissipated is proportional to its rms value.

Quantity of Interest: Power Gain/Loss = A p A p = (Output Signal Power)/(Input signal power) Signal Power Gain/Loss Signal InputSignal Output Amplifier

Relative Power Gain P input = P i = Input Power P output = P 0 = Output Power A p = Relative Power Gain = P 0 /P i

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.

Decibels in Acoustics

Log Base x = y For a given number y (y>0), x is the exponent of 10 that makes 10 x equal to y For example: 10 2 = 100 means that 2 is log 10 (100) 10 3 = 1000 means that 3 is log 10 (1000) 10 4 = 1000 means that 4 is log 10 (10000) = 0.01 means that -2 is log 10 (0.01) = means that -3 is log 10 (0.001)

Linear vs. Logarithmic

Decibels – Power Gain/Loss

Power Gain/Loss Examples Let’s do Example 2.1 and others.

Decibels - Voltage

dB value = 10 log (Output power/Input Power) dB value = 20 log (Output voltage/ Input Voltage) e.g. power gain = 2 implies dB value = 10 log 2 = dB e.g. Attenuators can have a fixed values (10, 20, 30 dB) e.g. Wire AWG 24 produces loss of dB/km or 2.16 dB/mile Decibels

. dBm - Absolute Power Gain

dBm Examples Lets do Examples 2.7 and 2.8 with different values.

Key dB Values

Miliwatts and dBm

Linear vs. Logarithmic

SNR Signal-to-Noise Ratio Every receiver has a SNR requirement that must be met for error free reception Quantifies the “quality” of the received signal SNR = 10 log(Signal Power/Noise Power) SNR = 20 log(Signal Voltage/Noise Voltage)

SNR Example A sinusoid signal has a peak-to-peak amplitude of 3 V There is noise which has a rms value of 640 mV What is the SNR? Let us try to visualize what is going on with the signal and noise. (solve problem and view next 5 slides)

If SNR is positive, it means the desired signal has greater power than noise. This is good. If SNR is negative, it means the desired signal has smaller power than noise. This is bad. SNR = 0 means signal and noise have equal power. Not good. The higher the SNR, the better for communications. Different systems have different minimum SNR requirements in order to work properly. For example a typical residential phone line has SNR 24 dB to 30dB Important SNR Concepts

Noise Factor Noise Factor: a measure of how noisy a device is Ratio of SNR at the input to SNR at the output If the device does not add noise to the signal, then the ratio is 1 Noise Figure is Noise Factor in dB

Noise Sources Thermal –Due to thermal agitation of electrons –Uniformly distributed, white noise From other signals (Interference) –Signals that are combinations of original frequencies sharing a medium

Noise Sources (cont) Cross-talk –A signal from one line is picked up by another Impulse disturbance or impulse noise –Irregular pulses or spikes of short duration and high amplitude –electromagnetic interference

BER = Bit Error Rate BER = fraction of bits that are in error (incorrectly transmitted)

BER & Reliability BER = 1 – Reliability

Characterizations of Channel Capacity Data rate –Bps, In bits per second –Sps - In bauds: symbols per second Bandwidth –In cycles per second or Hertz –Bandwidth is limited by electronics and medium

Shannon’s Law C = BW log 2 (1+ S/N) (bps) BW = bandwidth (Hz) S/N = Signal-to-Noise Ratio (SNR) (not in dB) C = channel capacity (bps) The underlying assumption is that the noise is Gaussian.

Example Textbook Example 2.13 plus additional exercise Note: Most calculators work with log 10 instead of log 2 which is used in Shannon’s Law. To get the correct answer you can multiply your calculator’s answer by a conversion factor of 3.32 and this will give you the log 2 answer.

Discussion Exercise "How many pairs of people can hold conversations simultaneously in a closed room before the background noise becomes too great"? Explain the key variables that are involved in determining a solution. How would you estimate a solution based on these variables? Suggestion: Use Signal-to-Noise as your starting point.