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Erstellt / Aktualisiert 09.02.2020 / 23.02.2020
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0 Exakte Antworten 16 Text Antworten 0 Multiple Choice Antworten
Fenster schliessen

Determine the value of \(P_\infty\) and \(E_\infty\) for a signal \(x(t)\).

\(E_\infty=\int_{-\infty}^\infty|x(t)|^2dt\)

\(P_\infty=\displaystyle{\lim_{T \to \infty}}\frac{1}{2T}\int_{-T}^T|x(t)|^2dt\)

Fenster schliessen

What is the unit step function, \(u(t)\).

\(u(t)=\begin{cases} 0, t<0\\1,t\ge0\end{cases}\)

Fenster schliessen

Determine the value of \(P_\infty\) and \(E_\infty\) for a discrete signal \(x[n]\).

\(E_\infty=\displaystyle{\sum_{n=-\infty}^{\infty}|x[n]|^2}\)

\(P_\infty=\displaystyle{\lim_{N \to \infty}}\frac{1}{2N+1}\sum_{n=-N}^{N}|x[n]|^2\)

Fenster schliessen

Determine the value of \(P\) and \(E\) for a discrete signal \(x[n] \) over the timer priod \(t_1< t< t_2\).

\(N_0=|n_1|+|n_2|\)

\(E=\displaystyle{\sum_{n=n_1}^{n_2}|x[n]|^2}\)

\(P=\displaystyle{\frac{1}{N_0+1} \sum_{n=n_1}^{n_2}|x[n]|^2}\)

Fenster schliessen

Determine the value of \(P\) and \(E\) for a continuos time signal \(x(t) \) for the time period \(t_1 < t < t_2\).

\(T_0=|t_1|+|t_2|\) get the time between \(t_1\) and \(t_2\).

\(E=\int_{-\frac{T_0}{2}}^{\frac{T_0}{2}}|x(t)|^2dt\)

\(P=\displaystyle{\frac{1}{T_0}\int_{-\frac{T_0}{2}}^{\frac{T_0}{2}}|x(t)|^2dt}\)

Fenster schliessen

What is the magnitude of \(\alpha e^{j\omega+\theta}\)?

\(|\alpha e^{j\omega+\theta}|\rightarrow\\\text{[Re]}=\alpha cos({j\omega+\theta}),\\\text{[Im]}=\alpha sin({j\omega+\theta}),\\\sqrt{[Re]^2+[Im]^2}\rightarrow\\\\\\\\sqrt{\alpha cos^2({j\omega+\theta})+\alpha sin^2({j\omega+\theta})}=\alpha \)

Fenster schliessen

What are the following summation formulas?

\(\displaystyle{\sum_{n=1}^A}\ 1\\\displaystyle{\sum_{n=1}^A}\ n\)

\(\displaystyle{\sum_{n=1}^A}\ 1=A\\\displaystyle{\sum_{n=1}^A}\ n=\frac{n(n+1)}{2}\)

Fenster schliessen

Let x(t) be a signal with x(t) = 0 for t > 5.

For what range will x(t) be equal to 0.

x(-t)

x(t + 1)

x(t + 2) + x(t - 2)

x(-t + 2)x(t + 1)

x(-t):

\(-t>5\Rightarrow t>-5\)

 

x(t + 1):

 

\(t+1>5\Rightarrow t>4\)

 

x(t + 2) + x(t - 2):

\(t+2>5\Rightarrow t>3\\ t-2>5\Rightarrow t>7\)

 

x(-t + 2)x(t + 1):

\(-t+2>5\Rightarrow t>-3\\ t+1>5\Rightarrow t>4\)