ECEN 314 - Exam I
Exam 1
Exam 1
Kartei Details
| Karten | 16 |
|---|---|
| Sprache | English |
| Kategorie | Elektrotechnik |
| Stufe | Grundschule |
| Erstellt / Aktualisiert | 09.02.2020 / 23.02.2020 |
| Lizenzierung | Keine Angabe |
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Determine the value of \(P_\infty\) and \(E_\infty\) for a signal \(x(t)\).
\(E_\infty=\int_{-\infty}^\infty|x(t)|^2dt\)
\(P_\infty=\displaystyle{\lim_{T \to \infty}}\frac{1}{2T}\int_{-T}^T|x(t)|^2dt\)
What is the unit step function, \(u(t)\).
\(u(t)=\begin{cases} 0, t<0\\1,t\ge0\end{cases}\)
Determine the value of \(P_\infty\) and \(E_\infty\) for a discrete signal \(x[n]\).
\(E_\infty=\displaystyle{\sum_{n=-\infty}^{\infty}|x[n]|^2}\)
\(P_\infty=\displaystyle{\lim_{N \to \infty}}\frac{1}{2N+1}\sum_{n=-N}^{N}|x[n]|^2\)
Determine the value of \(P\) and \(E\) for a discrete signal \(x[n] \) over the timer priod \(t_1< t< t_2\).
\(N_0=|n_1|+|n_2|\)
\(E=\displaystyle{\sum_{n=n_1}^{n_2}|x[n]|^2}\)
\(P=\displaystyle{\frac{1}{N_0+1} \sum_{n=n_1}^{n_2}|x[n]|^2}\)
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 \(t_2\).
\(E=\int_{-\frac{T_0}{2}}^{\frac{T_0}{2}}|x(t)|^2dt\)
\(P=\displaystyle{\frac{1}{T_0}\int_{-\frac{T_0}{2}}^{\frac{T_0}{2}}|x(t)|^2dt}\)
What is the magnitude of \(\alpha e^{j\omega+\theta}\)?
\(|\alpha e^{j\omega+\theta}|\rightarrow\\\text{[Re]}=\alpha cos({j\omega+\theta}),\\\text{[Im]}=\alpha sin({j\omega+\theta}),\\\sqrt{[Re]^2+[Im]^2}\rightarrow\\\\\\\\sqrt{\alpha cos^2({j\omega+\theta})+\alpha sin^2({j\omega+\theta})}=\alpha \)
What are the following summation formulas?
\(\displaystyle{\sum_{n=1}^A}\ 1\\\displaystyle{\sum_{n=1}^A}\ n\)
\(\displaystyle{\sum_{n=1}^A}\ 1=A\\\displaystyle{\sum_{n=1}^A}\ n=\frac{n(n+1)}{2}\)
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):
\(-t+2>5\Rightarrow t>-3\\ t+1>5\Rightarrow t>4\)
