diff options
| -rw-r--r-- | chapter02/content_ch02.tex | 2 | ||||
| -rw-r--r-- | chapter03/content_ch03.tex | 2 | ||||
| -rw-r--r-- | chapter04/content_ch04.tex | 8 |
3 files changed, 6 insertions, 6 deletions
diff --git a/chapter02/content_ch02.tex b/chapter02/content_ch02.tex index dbcbf62..9996706 100644 --- a/chapter02/content_ch02.tex +++ b/chapter02/content_ch02.tex @@ -1105,7 +1105,7 @@ This equation resembles \eqref{eq:ch02:def_inv_fourier_transform}. An example for the duality is the convolution in time-domain. Due to the duality, it becomes a multiplication in the frequency domain. \begin{equation} - \mathcal{F}\left\{ \underline{f}(t) * \underline{f}(t) \right\} = \mathcal{F}\left\{\underline{f}(t)\right\} \cdot \mathcal{F}\left\{\underline{g}(t)\right\} + \mathcal{F}\left\{ \underline{f}(t) * \underline{g}(t) \right\} = \mathcal{F}\left\{\underline{f}(t)\right\} \cdot \mathcal{F}\left\{\underline{g}(t)\right\} \label{eq:ch02:op_conv} \end{equation} diff --git a/chapter03/content_ch03.tex b/chapter03/content_ch03.tex index 20e7e00..85c1561 100644 --- a/chapter03/content_ch03.tex +++ b/chapter03/content_ch03.tex @@ -229,7 +229,7 @@ The temporal mean is calculated as the arithmetic mean with following difference \begin{definition}{Temporal mean} The \index{temporal mean} \textbf{temporal mean} of time-domain signal $x_i(t)$ is: \begin{equation} - \overline{x_i} = \E\left\{x_i(t)\right\} = \lim\limits_{T \rightarrow \infty} \frac{1}{T} \int\limits_{-\frac{T}{2}}^{\frac{T}{2}} x_i{t} \; \mathrm{d} t + \overline{x_i} = \E\left\{x_i(t)\right\} = \lim\limits_{T \rightarrow \infty} \frac{1}{T} \int\limits_{-\frac{T}{2}}^{\frac{T}{2}} x_i(t) \; \mathrm{d} t \end{equation}% \nomenclature[Sx]{$\overline{x}$, $\E\left\{x_i(t)\right\}$}{Temporal mean of x} \end{definition} diff --git a/chapter04/content_ch04.tex b/chapter04/content_ch04.tex index a5fc3bd..187fedd 100644 --- a/chapter04/content_ch04.tex +++ b/chapter04/content_ch04.tex @@ -51,7 +51,7 @@ xticklabels={$0$, $T_S$, $2 T_S$, $3 T_S$, $4 T_S$, $5 T_S$, $6 T_S$}, ] \addplot[smooth, blue, dashed] coordinates {(0, 1.1) (1, 1.8) (2, 2.1) (3, 1.0) (4, 0.8) (5, 1.7) (6, 2.4)}; - \addlegendentry{$\underline{x}{t}$}; + \addlegendentry{$\underline{x}(t)$}; \addplot[red, thick] coordinates {(0, 0) (0, 1.1)}; \addplot[red, thick] coordinates {(1, 0) (1, 1.8)}; \addplot[red, thick] coordinates {(2, 0) (2, 2.1)}; @@ -60,7 +60,7 @@ \addplot[red, thick] coordinates {(5, 0) (5, 1.7)}; \addplot[red, thick] coordinates {(6, 0) (6, 2.4)}; \addplot[only marks, red, thick, mark=o] coordinates {(0, 1.1) (1, 1.8) (2, 2.1) (3, 1.0) (4, 0.8) (5, 1.7) (6, 2.4)}; - \addlegendentry{$\underline{x}_S{t}$}; + \addlegendentry{$\underline{x}_S(t)$}; \end{axis} \end{tikzpicture} \caption{Sampling of a time-continuous signal} @@ -169,10 +169,10 @@ The Dirac delta function is zero expect at $t = n T_S$. So, \eqref{eq:ch4:one_sa xticklabels={$0$, $T_S$, $2 T_S$, $3 T_S$, $4 T_S$, $5 T_S$, $6 T_S$}, ] \addplot[smooth, blue, dashed] coordinates {(0, 1.1) (1, 1.8) (2, 2.1) (3, 1.0) (4, 0.8) (5, 1.7) (6, 2.4)}; - \addlegendentry{$\underline{x}{t}$}; + \addlegendentry{$\underline{x}(t)$}; \addplot[red, thick] coordinates {(2, 0) (2, 2.1)}; \addplot[only marks, red, thick, mark=o] coordinates {(2, 2.1)}; - \addlegendentry{$\underline{x}_{S,n}{t}$}; + \addlegendentry{$\underline{x}_{S,n}(t)$}; \end{axis} \end{tikzpicture} \caption[Taking out exactly one sample out of $\underline{x}(t)$]{Taking out exactly one sample out of $\underline{x}(t)$ -- in this example $n = 2$.} |