posted 1 years ago

\text { a) } \int_{-\infty}^{\infty} \operatorname{sinc}^{2}(2 r) d t \text {, }

\text { (b) } \int_{0}^{\infty} \operatorname{sinc}(t) \operatorname{sinc}(2 t) d t \text {. }

posted 1 years ago

s(t)=\left\{\begin{array}{ll} -t(t-1) & 0 \leq t<1 \\ (t-1)(t-2) & 1 \leq t<2 \end{array}\right.

) Find the first, second, and third derivatives r = Ds, u= D²s, and v = D³s.

s) Find the Fourier coefficients of each of the four signals: §, î, û, and û.

:) (12 pts) For each of the four signals, compute the power with a time domain calculation and compute the power in frequencies ±1/2 (the positive and negative fundamental frequencies) with a frequency domain calculation. What fraction of the power is in the positive and negative fundamental frequencies? Express all answers both symbolically and with an approximate decimal representation.

posted 1 years ago

\text { (c) } s(t)=v(t) \cos (200 \pi t) \text {. }

v(t)=\operatorname{sinc}(2 t) \operatorname{sinc}(4 t) \text {. }

(d) Classify cach of the signals in (a) (c) as baseband or passband.

u(t)=(1-|t|) I_{[-1,1]}(t)

posted 1 years ago

\text { (a) } y(t)=x(t+7)

\text { (b) } y(t)=x(3 t)

\text { (c) } y(t)=|x(10)|

y(t)=\int_{-\infty}^{\infty} I_{[0,+\infty)}(t-\tau) \exp (\tau-t) x(\tau) d \tau

y(t)=\int_{-\infty}^{\infty} \frac{1}{1+\tau^{2}} x(\tau-t) d \tau

y(t)=\int_{-1}^{0}(\tau-1) x(t+\tau) d \tau

y(t)=\min (1, \max (-1, x(t-4)))

n) Let (a1,. , ak) be a vector of k nonnegative reals and let (T1,.., Tk) E R*.

y(t)=\underset{x \in \mathbb{R}}{\operatorname{argmin}} \sum_{i=1}^{k} a_{j}\left(z-x\left(t-\tau_{i}\right)\right)^{2}

The argmin, is the value of z (the argument) that minimizes the expression.

posted 1 years ago

Vab, the voltage across the terminals a and b,

PRL, the power dissipated by the load resistor, RL,

The power delivered to the load resistor by the voltage source, V1, and

The The venin equivalent circuit presented to the load resistor, RL.

Validate all of your answers with Multisim circuit analysis. Submit both sowing they produce the same result.

posted 1 years ago

а. Using mobility analogy where the velocity as the "across" variable, determine the an equivalent circuit for the system.

b. Determine the equations of motion in the Laplace-domain.

c. Determine the equations of motion in the time-domain.

d. Find the transfer function U2(s)/Uo(s).

posted 1 years ago

\left.\left[\begin{array}{l} Y_{1} \\ Y_{2} \end{array}\right]=\left[\begin{array}{ll} A_{11} & A_{12} \\ A_{21} & A_{22} \end{array}\right] \begin{array}{l} X_{1} \\ X_{2} \end{array}\right]

Note that Aij = Yi/Xj given that all other inputs equal to zero.are

posted 1 years ago

\frac{d x_{1}}{d t}=x_{1}+5 x_{2}

\frac{d x_{2}}{d t}=2 x_{1}+u

a. Using only amplifiers and integrators draw a signal-flow graph representation of the system where U(s) is the input and X2(s) is the output. You may assume zero initial conditions.

b. Find the transfer function X2(s)/U(s) using Mason's Gain formula. Check your result using an algebraic approach.

posted 1 years ago

а.Determine its signal flow graph realization.

b. Using Mason's gain formula determine Y (s)/X(s).

posted 1 years ago

\begin{array}{l} \max x_{1}+x_{2} \\ \text { s.t.: } \\ \text { Cl } 3 x_{1}+2 x_{2} \leq 12 \\ \text { C2 } 2 x_{1}+3 x_{2} \leq 12 \\ \text { C3 } 2 x_{1}+2 x_{2} \leq 9 \\ \text { C4 } 2 x_{1}+2 x_{2} \geq 3 \\ \text { CS } \quad x_{1}, x_{2} \geq 0 \end{array}

a) (5 points) Graph the feasible region of the LP. Is the feasible region unbounded?

b) (35 points) Solve this problem using Simplex algorithm. Make sure to indicate:

* Whether or not you need to perform Phase

* Show the BV and NBV for each iteration of Simplex

* Show the steps of the algorithm in the graph from point a)

* Is this a unique or multiple solution?