Homework Answers
Add Answer to:
Consider the linear system described by x(t)= A(t)x(t), x(f,)= x0 Show that the following relation is...
For a continuous time linear time-invariant system, the input-output relation is the following (x(t) the input, y(t) the...
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
() At)x()B(f)u() Consider the following time-varying system y(t) C(f)x(t) where x) R", u(t)E R R 1...
() At)x()B(f)u() Consider the following time-varying system y(t) C(f)x(t) where x) R", u(t)E R R 1 1) Derive the state transition matrix D(t,r) when A(f) = 0 0 sint 2) Assume that x(to) = x0 is given and u(f) is known in the interval [to, 4] Based on these assumptions, derive the complete solution by using the state transition matrix D(f, r). Also show that the solution is unique in the interval [to, 4]. 3) Let x(1) 0 and u(f)...
f) Use the definition of a linear system to show if the following system is linear:...
f) Use the definition of a linear system to show if the following system is linear: 3dy0)-2)-). t)-xt). dt g) Use the definition of a linear system to show if the following system is linear: 3t yle)-2x(). h) Use the definition of a linear system to show if the following system is linear: 24 3)1). dy(t) dt
Consider a causal, linear and time-invariant system of continuous time, with an input-output relation that obeys...
Consider a causal, linear and time-invariant system of continuous time, with an input-output relation that obeys the following linear differential equation: y(t) + 2y(t) = x(t), where x(t) and y(t) stand for the input and output signals of the system, respectively, and the dot symbol over a signal denotes its first-order derivative with respect to time t. Use the Laplace transform to compute the output y(t) of the system, given the initial condition y(0-) = V2 and the input signal...
Q2. Consider the system described by the following differential equation x(t) Ax(t) where and x(0) -
Q2. Consider the system described by the following differential equation x(t) Ax(t) where and x(0) -
(d) [5] The input-output relation for DT system is described by following system equation y[n] =...
(d) [5] The input-output relation for DT system is described by following system equation y[n] = 31[] State if the system possesses the following properties: Linear BIBO-Stable Casual Memoryless Time-Invariance
Let a linear system with input x(t) and output y(t) be described by the differential equation...
Let a linear system with input x(t) and output y(t) be described
by the differential equation .
(a) Compute the simplest math function form of the impulse
response h(t) for this system. HINT: Remember that with zero
initial conditions, the following Laplace transform pairs hold:
Let the time-domain function p(t) be given by p(t) = g(3 − 0.5
t). (a) Compute the simplest piecewise math form for p(t).
(b) Plot p(t) over the range 0 ≤ t ≤ 10 ....
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww +...
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
The input signal x(1) of the LTI system is given by the following relation x(t) =...
The input signal x(1) of the LTI system is given by the following relation x(t) = xo(1–17), where ,1)= 1 3/4 +2,05151 / and it is passed through a filter with frequency response given below: (-;,O< f 54 H(S)= ,-45 f<0 (0, otherwise Determine the power of the signal x. (t)
Consider the LTI system described by the following information X(s) = 2. S-2 where x(t) =...
Consider the LTI system described by the following information X(s) = 2. S-2 where x(t) = 0 for t > 0, and y(t) = -e2'u(-t) + e-t u(t). 3 Determine H(s), and its region of convergence. (5 points). Determine h(t). (5 points). a. b. Using the system function found in part(a), determine the output y(t) if the - o <t < + o. ( 10 points). c. input is given by: est,
For a continuous time linear time-invariant system, the
input-output relation is the following (x(t) the input, y(t)
the
output):
, where h(t) is the impulse response function of the
system.
Please explain why a signal like e/“* is always an eigenvector
of
this linear map for any w. Also, if ¥(w),X(w),and H(w) are
the
Fourier transforms of y(t),x(t),and h(t), respectively.
Please
derive in detail the relation between Y(w),X(w),and H(w),
which means to reproduce the proof of the basic convolution
property...
() At)x()B(f)u() Consider the following time-varying system y(t) C(f)x(t) where x) R", u(t)E R R 1 1) Derive the state transition matrix D(t,r) when A(f) = 0 0 sint 2) Assume that x(to) = x0 is given and u(f) is known in the interval [to, 4] Based on these assumptions, derive the complete solution by using the state transition matrix D(f, r). Also show that the solution is unique in the interval [to, 4]. 3) Let x(1) 0 and u(f)...
f) Use the definition of a linear system to show if the following system is linear: 3dy0)-2)-). t)-xt). dt g) Use the definition of a linear system to show if the following system is linear: 3t yle)-2x(). h) Use the definition of a linear system to show if the following system is linear: 24 3)1). dy(t) dt
Consider a causal, linear and time-invariant system of continuous time, with an input-output relation that obeys the following linear differential equation: y(t) + 2y(t) = x(t), where x(t) and y(t) stand for the input and output signals of the system, respectively, and the dot symbol over a signal denotes its first-order derivative with respect to time t. Use the Laplace transform to compute the output y(t) of the system, given the initial condition y(0-) = V2 and the input signal...
Q2. Consider the system described by the following differential equation x(t) Ax(t) where and x(0) -
(d) [5] The input-output relation for DT system is described by following system equation y[n] = 31[] State if the system possesses the following properties: Linear BIBO-Stable Casual Memoryless Time-Invariance
Let a linear system with input x(t) and output y(t) be described
by the differential equation .
(a) Compute the simplest math function form of the impulse
response h(t) for this system. HINT: Remember that with zero
initial conditions, the following Laplace transform pairs hold:
Let the time-domain function p(t) be given by p(t) = g(3 − 0.5
t). (a) Compute the simplest piecewise math form for p(t).
(b) Plot p(t) over the range 0 ≤ t ≤ 10 ....
3. Consider a linear time invariant system described by the differential equation dy(t) dt RCww + y(t)-x(t) where yt) is the system's output, x(t) ?s the system's input, and R and C are both positive real constants. a) Determine both the magnitude and phase of the system's frequency response. b) Determine the frequency spectrum of c) Determine the spectrum of the system's output, y(r), when d) Determine the system's steady state output response x()-1+cos(t) xu)+cost)
The input signal x(1) of the LTI system is given by the following relation x(t) = xo(1–17), where ,1)= 1 3/4 +2,05151 / and it is passed through a filter with frequency response given below: (-;,O< f 54 H(S)= ,-45 f<0 (0, otherwise Determine the power of the signal x. (t)
Consider the LTI system described by the following information X(s) = 2. S-2 where x(t) = 0 for t > 0, and y(t) = -e2'u(-t) + e-t u(t). 3 Determine H(s), and its region of convergence. (5 points). Determine h(t). (5 points). a. b. Using the system function found in part(a), determine the output y(t) if the - o <t < + o. ( 10 points). c. input is given by: est,
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago