# Flashcards

Flashcards 16 Flashcards 1 Students English Primary School 09.02.2020 / 23.02.2020 Not defined

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):

$$-t+2>5\Rightarrow t>-3\\ t+1>5\Rightarrow t>4$$