117 lines
2.8 KiB
Plaintext
117 lines
2.8 KiB
Plaintext
#import "../template/lib.typ": *
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#set page(paper: "a4")
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#show: notes.with(
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title: [EE2T1],
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subtitle: [Telecommunication and Sensing],
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author: "Folkert Kevelam"
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)
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= Lecture 1 - Introduction
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== Information
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#definition[
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Information content:
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Information is related to probability: a less probable message contains
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more information
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$
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I_j = log_2(1/P_j) = - log_2(P_j) space "[bit]"
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$
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Information is additive:
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$
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I_(i j) &= log_2(1/(P_i P_J)) = -log_2(P_i)-log_2(P_j) \
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&= I_i + I_j
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$
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iff the messages are independent.
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]
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#definition[
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Source entropy, the average amount of information per message generated
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by a source:
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$
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H = sum_(j=1)^M P_j I_j = sum_(j=1)^M P_j log_2(1/P_j) space "[bit/symbol]"
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$
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In a binary system, the maximum source entropy will be when $P_1 = P_0 = 0.5$.
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The speed of a source:
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$
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R = H/T space "[bit/s]"
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$
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]
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#theorem[
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Shannon-Hartley theorem:
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$
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C = B dot log_2( 1 + S/N) space "[bit/s]"
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$
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- $C = "capacity [bit/s]"$
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- $B = "bandwidth [Hz]"$
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- $S/N = "ratio of signal power to the noise power"$
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]
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== Principles of range measurement
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#definition[
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The transmitter "fires" a signal and the receiver measures the time delay
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$tau$ between the moments of transmission and reception of the echo.
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$
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2R = c dot tau arrow R = (c dot tau) / 2
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$
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with $c$ being the speed of light.
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]
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#definition[
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The ability of a radar to resolve two targets with a range difference
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$delta R$ is called *range resolution*.
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$
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delta R = (c dot tau_p) / 2 approx c/(2 B) space "[m]"
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$
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]
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== Modulation
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#definition[
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Modulation: *manipulation of a signal waveform* to carry information, in
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order to transmit the signal at a specified frequency in the spectrum.
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$
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s(t) = R(t)cos(2 pi f_c t + phi(t))
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$
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with
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$
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R(t) = L{m(t)} space "linear modulation" \
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phi(t) = L{m(t)} space "angle modulation"
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$
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]
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== Practical signal waveforms
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+ DC-value, mean value: $ w_(D C) = <w(t)> = lim_(T arrow infinity) 1/T integral_(-T/2)^(T/2) w(t) d t $
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+ Instantaneous power: $ p(t) = v(t) dot i(t) $
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+ Average power: $ P=<p(t)> = <v(t) dot i(t)> $
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+ RMS-value: root-mean-square: $ w_(r m s) = sqrt(<w^2(t)>) $
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For a resistive load: $ P = v_(r m s) i_(r m s) = (<v^2(t)>)/R = <i^2(t)>R $
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+ Normalized power = power delivered to a $1 omega$ load.
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$ P = <w^2(t)> = lim_(T arrow infinity) 1/T integral_(-T/2)^(T/2) w^2(t) d t space "[W] = [J/s]" $
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$w(t)$ is a *power waveform* iff $0 < P < infinity$.
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+ Normalized energy = energy dissipated in a $1 omega$ load.
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$ E = lim_(T arrow infinity) integral_(-T/2)^(T/2) w^2(t) d t space "[J]" $
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$w(t)$ is an *energy waveform* iff $0 < E < infinity$.
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A signal waveform $w(t)$ cannot both be an *energy waveform* and a *power waveform*.
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Practical waveforms are always energy waveforms.
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