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