COE 341: Data & Computer Communications (T081) Dr. Marwan Abu-Amara. Chapter 3: Data Transmission. Agenda. Concepts & Terminology Decibels and Signal Strength Fourier Analysis Analog & Digital Data Transmission Transmission Impairments Channel Capacity. Terminology (1). Transmitter

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COE 341: Data & Computer Communications (T081) Dr. Marwan Abu-Amara

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Agenda • Concepts & Terminology • Decibels and Signal Strength • Fourier Analysis • Analog & Digital Data Transmission • Transmission Impairments • Channel Capacity COE 341 – Dr. Marwan Abu-Amara

Terminology (1) • Transmitter • Receiver • Medium • Guided medium • e.g. twisted pair, optical fiber • Unguided medium • e.g. air, water, vacuum COE 341 – Dr. Marwan Abu-Amara

Terminology (2) • Direct link • No intermediate devices • Point-to-point • Direct link • Only 2 devices share link • Multi-point • More than two devices share the link COE 341 – Dr. Marwan Abu-Amara

Terminology (3) • Simplex • One direction • e.g. Television • Half duplex • Either direction, but only one way at a time • e.g. police radio • Full duplex • Both directions at the same time • e.g. telephone COE 341 – Dr. Marwan Abu-Amara

Frequency, Spectrum and Bandwidth • Time domain concepts • Analog signal • Varies in a smooth way over time • Digital signal • Maintains a constant level then changes to another constant level • Periodic signal • Pattern repeated over time • Aperiodic signal • Pattern not repeated over time COE 341 – Dr. Marwan Abu-Amara

T PeriodicSignals Temporal Period S (t+nT) = S (t); Where: t is time T is the waveform period n is an integer COE 341 – Dr. Marwan Abu-Amara

Sine Wave – s(t) = A sin(2ft +) • Peak Amplitude (A) • maximum strength of signal • unit: volts • Frequency (f) • rate of change of signal • unit: Hertz (Hz) or cycles per second • Period = time for one repetition (T) = 1/f • Phase () • relative position in time • unit: radians • Angular Frequency (w) • w = 2 /T = 2 f • unit: radians per second COE 341 – Dr. Marwan Abu-Amara

Wavelength () • Distance occupied by one cycle • Distance between two points of corresponding phase in two consecutive cycles • Assuming signal velocity v • = vT • f = v • For an electromagnetic wave, v = speed of light in the medium • In free space, v = c = 3*108 m/sec COE 341 – Dr. Marwan Abu-Amara

Frequency Domain Concepts • Signal usually made up of many frequencies • Components are sine waves • Can be shown (Fourier analysis) that any signal is made up of component sine waves • Can plot frequency domain functions COE 341 – Dr. Marwan Abu-Amara

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 COE 341 – Dr. Marwan Abu-Amara

Bandwidth and Data Rate • Any transmission system supports only a limitedband of frequencies for satisfactory transmission • “system” includes: TX, RX, and Medium • Limitation is dictated by considerations of cost, number of channels, etc. • This limitedbandwidth degrades the transmitted signals, making it difficult to interpret them at RX • For a given bandwidth: Higher data rates More degradation • This limits the data rate that can be used withgiven signal and noise levels, receiver type, and error performance • More about this later!!! COE 341 – Dr. Marwan Abu-Amara

Bandwidth Requirements 1,3 Larger BW needed for better representation BW = 2f More difficult reception with more limited BW f 3f 1 1,3,5 BW = 4f 5f f 3f 2 1,3,5,7 BW = 6f 7f 5f f 3f 3 … BW = 1,3,5,7 ,9,… COE 341 – Dr. Marwan Abu-Amara …… 7f 5f f 3f 4 Fourier Series for a Square Wave

Decibels and Signal Strength • Decibel is a measure of ratio between two signal levels • NdB= number of decibels • P1 = input power level • P2 = output power level • Example: • A signal with power level of 10mW inserted onto a transmission line • Measured power some distance away is 5mW • Loss expressed as NdB =10log(5/10)=10(-0.3)=-3 dB COE 341 – Dr. Marwan Abu-Amara

Decibels and Signal Strength • Decibel is a measure of relative, not absolute, difference • A loss from 1000 mW to 500 mW is a loss of 3dB • A loss of 3 dB halves the power • A gain of 3 dB doubles the power • Example: • Input to transmission system at power level of 4 mW • First element is transmission line with a 12 dB loss • Second element is amplifier with 35 dB gain • Third element is transmission line with 10 dB loss • Output power P2 • (-12+35-10)=13 dB = 10 log (P2 / 4mW) • P2 = 4 x 101.3 mW = 79.8 mW COE 341 – Dr. Marwan Abu-Amara

Decibel-Watt (dBW) • Absolute level of power in decibels • Value of 1 W is a reference defined to be 0 dBW • Example: • Power of 1000 W is 30 dBW • Power of 1 mW is –30 dBW COE 341 – Dr. Marwan Abu-Amara

Decibel & Difference in Voltage • Decibel is used to measure difference in voltage. • Power P=V2/R • Decibel-millivolt (dBmV) is an absolute unit with 0 dBmV equivalent to 1mV. • Used in cable TV and broadband LAN COE 341 – Dr. Marwan Abu-Amara

Fourier Analysis Signals Aperiodic Periodic (fo) Discrete Continuous Discrete Continuous DFS FS FT Finite time Infinite time DTFT DFT FT : Fourier Transform DFT : Discrete Fourier Transform DTFT : Discrete Time Fourier Transform FS : Fourier Series DFS : Discrete Fourier Series COE 341 – Dr. Marwan Abu-Amara

Fourier Series (Appendix B) • Any periodic signal of period T (f0 = 1/T) can be represented as sum of sinusoids, known as Fourier Series fundamental frequency DC Component If A0 is not 0, x(t) has a DC component COE 341 – Dr. Marwan Abu-Amara

Fourier Series • Amplitude-phase representation COE 341 – Dr. Marwan Abu-Amara

Another Example x(t) x1(t) 1 -2 -1 1 2 -1 T Note that x1(-t)= -x1(t) x(t) is an odd function Also, x1(t)=x(t-1/2) COE 341 – Dr. Marwan Abu-Amara

Another Example Sine is an odd function Where: COE 341 – Dr. Marwan Abu-Amara

Fourier Transform • For a periodic signal, spectrum consists of discrete frequency components at fundamental frequency & its harmonics. • For an aperiodic signal, spectrum consists of a continuum of frequencies (non-discrete components). • Spectrum can be defined by Fourier Transform • For a signal x(t) with spectrum X(f), the following relations hold COE 341 – Dr. Marwan Abu-Amara

A t f 1/ Fourier Transform Example Sin (x) / x “sinc” function COE 341 – Dr. Marwan Abu-Amara Study the effect of the pulse width

The narrower a function is in one domain, the wider its transform is in the other domain The Extreme Cases COE 341 – Dr. Marwan Abu-Amara

Power Spectral Density & Bandwidth • Absolute bandwidth of any time-limited signal is infinite • However, most of the signal power will be concentrated in a finite band of frequencies • Effective bandwidth is the width of the spectrum portion containing most of the signal power. • Power spectral density (PSD) describes the distribution of the power content of a signal as a function of frequency COE 341 – Dr. Marwan Abu-Amara

Signal Power • A function x(t) specifies a signal in terms of either voltage or current • Assuming R = 1 W, Instantaneous signal power = V2 = i2 = |x(t)|2 • Instantaneous power of a signal is related to average power of a time-limited signal, and is defined as • For a periodic signal, the averaging is taken over one period to give the total signal power COE 341 – Dr. Marwan Abu-Amara

Power Spectral Density & Bandwidth • For a periodic signal, power spectral density is where (f) is Cn is as defined before on slide 27, and f0 being the fundamental frequency COE 341 – Dr. Marwan Abu-Amara

Power Spectral Density & Bandwidth • For a continuous valued function S(f), power contained in a band of frequencies f1 < f < f2 • For a periodic waveform, the power through the first j harmonics is COE 341 – Dr. Marwan Abu-Amara

Fourier Analysis Example • Consider the half-wave rectified cosine signal from Figure B.1 on page 793: • Write a mathematical expression for s(t) • Compute the Fourier series for s(t) • Write an expression for the power spectral density function for s(t) • Find the total power of s(t) from the time domain • Find a value of n such that Fourier series for s(t) contains 95% of the total power in the original signal • Determine the corresponding effective bandwidth for the signal COE 341 – Dr. Marwan Abu-Amara

+3T/4 +T/4 -3T/4 -T/4 Example (Cont.) • Mathematical expression for s(t): Where f0 is the fundamental frequency, f0 = (1/T) COE 341 – Dr. Marwan Abu-Amara

Example (Cont.) f0 = (1/T) • Fourier Analysis: COE 341 – Dr. Marwan Abu-Amara

Example (Cont.) f0 = (1/T) • Fourier Analysis (cont.): COE 341 – Dr. Marwan Abu-Amara

Example (Cont.) • Fourier Analysis (cont.): COE 341 – Dr. Marwan Abu-Amara

Example (Cont.) • Fourier Analysis (cont.): Note: cos2q = ½(1 + cos 2q) COE 341 – Dr. Marwan Abu-Amara

Example (Cont.) • Fourier Analysis (cont.): COE 341 – Dr. Marwan Abu-Amara