ECE155ALecture3

# ECE155ALecture3 - Computer Networks Lecture 3 Professor...

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1 Computer Networks Lecture 3 Professor Louise E. Moser Winter 2010

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2 Hybrid Model The hybrid reference model (network architecture) used in the textbook and this course
3 The Physical Layer Theoretical Basis for Data Communication Data rate, baud rate, bandwidth Maximum data rate of channel Fourier analysis

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4 Baud Rate data rate = rate at which the data are sent, i.e., bits/sec baud rate = rate at which the signal changes its value, i.e., number of changes/sec Not necessarily bits/sec, because each signal value can convey several bits EX: signal value v = 0, 1, 2, …, 7=2 3 -1 (each signal value conveys 3 bits) T = time to send 1 signal value (3 bits), baud rate = 1 / T, data rate = 3 x baud rate data rate = b bits/sec, baud rate = b / 3 signals/sec, T = 1/(baud rate) = 3 / b sec to send 3 bits (1 signal value) baud rate is the rate at which signals are sent data rate is the rate at which bits are sent
5 Bandwidth bandwidth = highest frequency that can be transmitted Voice line bandwidth (cut off frequency) = 3000 Hz The bandwidth determines the max data rate Nyquist’s Theorem for a noiseless channel Shannon’s Theorem for a noisy channel Generally, the data rate for a noisy channel is less than the data rate for a noiseless channel

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6 Maximum Data Rate of a Channel THM ( Nyquist 1924) Noiseless Channels If an arbitrary signal is run through a low-pass filter of bandwidth H , the filtered signal can be completely reconstructed by taking only 2 H samples per second Max data rate = 2 H log 2 V bits/sec, where there are V values (levels) of the signal and log 2 V bits per sample EX: H = 3000 Hz, V = 2 values (0 and 2 1 -1=1) Max data rate = 2 (3000) log 2 2 = 6000 bits/sec EX: H = 3000 Hz, V = 2 6 = 64 values (0,1,2,3,…,2 6 -1=63) Max data rate = 2 (3000) log 2 64 = 36000 bits/sec
7 Maximum Data Rate of a Channel THM ( Shannon 1948) Noisy Channels Amount of thermal noise = signal to noise ratio = signal power/noise power = S/N Max data rate = H log 2 (1+ S/N ) bits/sec EX: H = 3000 Hz, S/N = 30dB = 10xlog 10 10 3 dB = 1000 Max data rate = 3000 log 2 (1+1000) = 30000 bits/sec Upper bound is hard to reach 9600 bits/sec is good

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8 Fourier Approximation Information is transmitted by varying voltage or current Let v(t) be the voltage, or c(t) the current, at time t Any well-behaved periodic function g(t) with period T can be represented by a Fourier series where the fundamental frequency f = 1/T, the frequency of the nth harmonic (term) is nf, and a n and b n are the sine and cosine amplitudes of the nth harmonic The amplitudes and constant are given by
9 Fourier Approximation Example Binary signal x = 01100010 Root-mean-square (rms) of amplitudes Successive approximations to

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## This note was uploaded on 05/20/2010 for the course ECE 155a taught by Professor Louisee.moser during the Winter '09 term at UCSB.

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ECE155ALecture3 - Computer Networks Lecture 3 Professor...

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