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diff --git a/tex/lti.tex b/tex/lti.tex index b01a31f..316bef1 100644 --- a/tex/lti.tex +++ b/tex/lti.tex @@ -4,9 +4,9 @@ Let \(\mathcal{S}\) denote a system. \begin{table}[H] \begin{tabularx}{\linewidth}{p{.3\linewidth} X} - \toprule - \bfseries Property & \bfseries Meaning \\ - \midrule + \toprule + \bfseries Property & \bfseries Meaning \\ + \midrule static \(\leftrightarrow\)\newline dynamic & Static means that it is memoryless (in the statistical sense), whereas dynamic has memory. Static systems depend only on the input \(u\), dynamic systems on \(du/dt\) or \(\int u\,dt\). \\ causal \(\leftrightarrow\)\newline acausal & Causal systems use only informations from the past, i.e. \(h(t < 0) = 0\). Real systems are always causal. \\ linear \(\leftrightarrow\)\newline nonlinear & The output of a linear system does not have new frequency that were not in the input. For linear system the superposition principle is valid: \(\mathcal{S}(\alpha_1 x_1 + \alpha_2 x_2) = \alpha_1 \mathcal{S} x_1 + \alpha_2 \mathcal{S} x_2\). \\ @@ -14,8 +14,8 @@ Let \(\mathcal{S}\) denote a system. \midrule SISO, MIMO & Single input single output, multiple input multiple output. \\ BIBO & Bounded input bounded output, i.e. there are some \(A\), \(B\) such that \(|x| < A\) and \(|y| < B\) for all \(t\), equivalently \(\int_\mathbb{R} |h|\,dt < \infty\).\\ - \bottomrule - \end{tabularx} + \bottomrule + \end{tabularx} \end{table} \subsection{Impulse response} |