[translation] boolean expressions, some typos fixes
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@ -833,11 +833,11 @@ the statements but not both are true. There is no operator for XOR in
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Table~\ref{logicalrelationaloperators} show the logical and relational
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operators that are available in \matlab{}. The additional
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\code[Operator!logical!and2@\&\&]{\&\&} und
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\code[Operator!logical!and2@\&\&]{\&\&} and
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\code[Operator!logical!or2@{"|}{"|} {}]{||} operators are the so
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called `\enterm{shorrt-circuit} operators for the logical OR and
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AND. Short-circuit means that \matlab{} stopps to evaluate a Boolean
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expresssion as soon as it becomes clear that the whole expression
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called `\enterm{short-circuit} operators for the logical OR and
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AND. Short-circuit means that \matlab{} stops to evaluate a Boolean
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expression as soon as it becomes clear that the whole expression
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cannot become true. For example assume that the two statements A and B
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are joined using a AND. The whole expression can only be true if A is
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already true. This means, that there is no need to evaluate B if A is
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@ -865,7 +865,7 @@ this saves processing time.
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\varcode{$\sim=$} & unequal\\
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\varcode{$>$} & greater than \\
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\varcode{$<$} & less than \\
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\varcode{$>=$} & greateror equal \\
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\varcode{$>=$} & greater or equal \\
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\varcode{$<=$} & less or equal \\
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\hline
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\end{tabular}
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@ -881,12 +881,12 @@ this saves processing time.
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Previously we have introduced the data types for integer or floating
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point numbers and discussed that there are instances where it is more
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efficient to use a integer data type rather than storing floating
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poing numbers. The result of a Boolean expression can only assume two
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point numbers. The result of a Boolean expression can only assume two
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values (true or false). This implies that we need only a single bit to
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store this information as a 0 (false) and 1 (true). In \matlab{} knows
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a special data type (\codeterm{logical}) to store the result of a
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Boolean expresssion. Every variable can be evaluated to true or false
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by just onverting it to the logical data type. When doing so \matlab{}
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Boolean expression. Every variable can be evaluated to true or false
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by converting it to the logical data type. When doing so \matlab{}
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interprets all values different form zero to be true. In
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listing~\ref{booleanexpressions} we show several examples for such
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operations. \matlab{} also knows the keywords \code{true} and
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@ -906,6 +906,8 @@ ans = 1
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ans = 0
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>> logical('test')
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ans = 1 1 1 1
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>> logical([1 2 3 4 0 0 10])
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and = 1 1 1 1 0 0 1
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>> 1 > 2
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ans = 0
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>> 1 < 2
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@ -919,83 +921,85 @@ ans = 1 0 1 1 0
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\end{lstlisting}
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\section{Logisches Indizieren}\label{logicalindexingsec}
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Einer der wichtigsten Einsatzorte f\"ur boolesche Ausdr\"ucke ist das
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logische Indizieren. Logisches Indizieren ist eines der
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Schl\"usselkonzepte in \matlab{}. Nur mit diesem k\"onnen
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Filteroperationen auf Vektoren und Matrizen effizient durchgef\"uhrt
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werden. Es ist sehr m\"achtig und, wenn es einmal verstanden wurde,
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sehr intuitiv zu benuzten.
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Das Grundkonzept hinter der logischen Indizierung ist, dass durch die
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Verwendung eines booleschen Ausdrucks auf z.B. einen Vektor ein
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logischer Vektor gleicher Gr\"o{\ss}e zur\"uckgegeben wird. Dieser
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wird benutzt um die Elemente des urspr\"unglichen Vektors
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auszuw\"ahlen, bei denen der logische Vektor \codeterm{wahr} ist
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(Listing \ref{logicalindexing1}). Zeile 14 kann wie
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folgt gelesen werden: Gib die Elemente von \varcode{x} an den
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Stellen, an denen \varcode{x < 0} wahr ist, zur\"uck.
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\begin{lstlisting}[caption={Beispiel logisches Indizieren.}, label=logicalindexing1]
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>> x = randn(1, 6) % Zeilenvektor mit 6 Zufallszahlen
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\section{Logical indexing}\label{logicalindexingsec}
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We have introduced how one can select certain element of a vector or
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matrix by addressing the respective elements by their index. This is
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fine when we know the range of elements we want t select. There are,
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however, many situations in which a selection based on the value of
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the stored element is desired. These situations is one of the major
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places where we need Boolean expressions. The selection based on the
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result of a Boolean expression is called \enterm{logical
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indexing}. With this approach we can easily filter based on the
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values stored in a vector or matrix. It is very powerful and, once
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understood, very intuitive.
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The basic concept is that applying a Boolean operation on a vector
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results in a \code{logical} vector of the same size (see
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listing~\ref{booleanexpressions}. This logical vector is then used to
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select only those values for which the logical vector is true. Line 14
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in listing~\ref{logicalindexing} can be read: ``Give me all those
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elements of \varcode{x} where the Boolean expression \varcode{x < 0}
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evaluates to true''.
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\begin{lstlisting}[caption={Logical indexing.}, label=logicalindexing1]
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>> x = randn(1, 6) % a vector with 6 random numbers
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x =
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-1.4023 -1.4224 0.4882 -0.1774 -0.1961 1.4193
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>> % logisches Indizieren in zwei Schritten:
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>> x_smaller_zero = x < 0 % logischer Vektor
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>> % logical indexing in two steps
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>> x_smaller_zero = x < 0 % create the logical vector
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x_smaller_zero =
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1 1 0 1 1 0
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>> elements_smaller_zero = x(x_smaller_zero) % benutzen, um zuzugreifen
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>> elements_smaller_zero = x(x_smaller_zero) % use it to select
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elements_smaller_zero =
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-1.4023 -1.4224 -0.1774 -0.1961
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>> % logisches Indizieren in einem Schritten:
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>> % logical indexing with a single command
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>> elements_smaller_zero = x(x < 0)
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elements_smaller_zero =
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-1.4023 -1.4224 -0.1774 -0.1961
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\end{lstlisting}
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\begin{exercise}{logicalVector.m}{logicalVector.out}
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Erstelle einen Vektor \varcode{x} mit den Werten 0--10.
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Create a vector \varcode{x} containing the values 0--10.
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\begin{enumerate}
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\item F\"uhre aus: \varcode{y = x < 5}
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\item Gib den Inhalt von \varcode{y} auf dem Bildschirm aus.
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\item Was ist der Datentyp von \varcode{y}?
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\item Gibt alle Elemente aus \varcode{x} zur\"uck, die kleiner als 5 sind.
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\item Execute: \varcode{y = x < 5}
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\item Display the content of \varcode{y} in the command window.
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\item What is the data type of \varcode{y}?
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\item Return only those elements \varcode{x} that are less than 5.
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\end{enumerate}
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\pagebreak[4]
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\end{exercise}
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\begin{figure}[t]
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\includegraphics[width= 0.9\columnwidth]{logicalIndexingTime}
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\titlecaption{Beispiel f\"ur logisches Indizieren.}
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{Der rot markierte Abschnitt aus den Daten wurde indirekt
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mit logischem Indizieren auf dem Zeitvektor
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ausgew\"ahlt (\varcode{x(t > 5 \& t < 6)}).}\label{logicalindexingfig}
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\titlecaption{Example for logical indexing.} {The highlighted
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segment of the data was selected using logical indexing on
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the time vector: (\varcode{x(t > 5 \& t <
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6)}).}\label{logicalindexingfig}
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\end{figure}
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Logisches Indizieren wurde oben so benutzt, dass die Auswahl auf dem
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Inhalt desselben Vektors beruhte. Ein weiterer sehr h\"aufiger Fall
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ist jedoch, dass die Auswahl aus einem Vektor auf dem Inhalt eines
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zweiten Vektors basiert. Ein Beispiel ist, dass \"uber einen
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gewissen Zeitraum Daten aufgenommen werden und aus diesen die Daten eines
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bestimmten Zeitraums ausgew\"ahlt werden sollen (\figref{logicalindexingfig}).
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So far we have used logical indexing to select elements of a vector
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that match a certain condition. When analyzing data we are often
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faced with the problem that we want to select the elements of one
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vector for the case that the elements of a second vector assume a
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certain value. One example for such a use-case is the selection of a
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segment of data of a certain time span (the stimulus was on,
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\figref{logicalindexingfig}).
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\begin{exercise}{logicalIndexingTime.m}{}
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Angenommen es werden \"uber einen bestimmten Zeitraum Messwerte
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genommen. Bei solchen Messungen erh\"alt man einen Vektor, der die
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Zeitpunkte der Messung speichert und einen zweiten mit den
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jeweiligen Messwerten.
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Assume that measurements have been made for a certain time. Usually
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measured values and the time are stored in two vectors.
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\begin{itemize}
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\item Erstelle einen Vektor \varcode{t = 0:0.001:10;}, der die Zeit
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repr\"asentiert.
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\item Erstelle einen zweiten Vektor \varcode{x} mit Zufallszahlen, der
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die gleiche L\"ange hat wie \varcode{t}. Die Werte darin stellen
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Messungen zu den Zeitpunkten in \varcode{t} dar.
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\item Benutze logische Indizieren um die Messwerte
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auszuw\"ahlen, die dem zeitlichen Abschnitt 5--6\,s entsprechen.
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\item Create a vector that represents the recording time \varcode{t
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= 0:0.001:10;}.
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\item Create a second vector \varcode{x} filled with random number
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that has the same length as \varcode{t}. The values stored in
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\varcode{x} represent the measured data at the times in
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\varcode{t}.
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\item Use logical indexing to select those values that have been
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recorded in the time span form 5--6\,s.
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\end{itemize}
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\end{exercise}
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