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Question 29017

posted 1 years ago

5 Use Parseval's identity to compute the following integrals.
\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 {. }

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Question 29015

posted 1 years ago

2. Let s be a periodic signal with period To = 2 and
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.

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Question 29016

posted 1 years ago

4 Find and sketch the Fourier transforms for the following signals.
\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)

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Question 29014

posted 1 years ago

1. (30 pts) For each of the following systems, determine whether it is linear and whether it is time-invariant. Justify your answers. If it is LTI, find the impulse response function h(t). Each system is specified by the output y that is produced from an input r.
\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.

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Question 29973

posted 1 years ago

Consider the circuit shown below. Find using circuit analysis techniques,
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.

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Question 14431

posted 1 years ago

1.Consider the coupled acoustic-mechanical system. The velocity of the masses are given by u and applied force by the variable f. The variables k represent the mechanical stiffness, M the mass and b the damping coefficient. The closed open pipe is filled with a fluid having mass density Po, sound speed c,cross sectional area A , length L.
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).

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Question 14433

posted 1 years ago

3. Given the signal flow graph below determine the transfer matrix A where Aij = Yi/Xj.
\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

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Question 14434

posted 1 years ago

4. Given the system equations
\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.

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Question 14432

posted 1 years ago

2. Given the block diagram shown below
а.Determine its signal flow graph realization.
b. Using Mason's gain formula determine Y (s)/X(s).

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Question 14822

posted 1 years ago

Consider the following linear program:
\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?

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