(4 points) Consider a system H that takes a signal x(t) as input
and returns the even part of x(t) as output, i.e., xe(t) = H(x(t))
where xe(t) is the even part of x(t). Is it time invariant? Is it
stable? (c) (5 points) Consider the following three systems:
S1 : w(t) = x(t/2) S2 : z(t) =Zt −∞ w(τ)dτ S3 : y(t) = S3(z(t)) The
three systems are connected in series as illustrated here:
Choose the third system S3, such that overall system is equivalent
to the following system: y(t) =Zt−1 −∞ x(τ)dτ
Homework Answers
Add Answer to:
(4 points) Consider a system H that takes a signal x(t) as input
and returns the...
2. (a) For each sample of a discrete time signal x[n] as input, a system S...
2. (a) For each sample of a discrete time signal x[n] as input, a system S outputs the value y[n- . Determine whether the system S is i. linear ii. time-invariant 1ll. causal iv. stable Each of your answers should be supported by justification. In other words, show your reasoning (b) Consider a stable linear time-invariant (LTI) system with transfer function H(z). It is required to design a LTI compensator system G(z) that is in cascade with H(z) such that...
Consider the following AM system x(t) z(t) y(t) H(a) 10ω -10 othwise 2cos (100t) Ifthe input signal x(t), the has a spectrum function, X(w), shown above, a) Write the expressions of r(w) and Z(w)...
Consider the following AM system x(t) z(t) y(t) H(a) 10ω -10 othwise 2cos (100t) Ifthe input signal x(t), the has a spectrum function, X(w), shown above, a) Write the expressions of r(w) and Z(w) in terms of X(w). b) Sketch the spectrums, x(ω), and r(a)Jdentify the LSE and USB components on the graphs? 14] 131 lain the type of AM modulation is the output z(03
Consider the following AM system x(t) z(t) y(t) H(a) 10ω -10 othwise 2cos (100t) Ifthe...
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...
Question # 4 Let x(t) u(t) be a signal, let h(t) = e -5tu(t) be a...
Question # 4 Let x(t) u(t) be a signal, let h(t) = e -5tu(t) be a linear time invariant system (a) Sketch x(t) and h(t) (b) Find the mathematival expression of output of the system y(t) by using convolution. (c) Sketch y(t)
Q2 (a) Given the signal x(t) and system h(t) as presented in Figure Q2(a). Determine the...
Q2 (a) Given the signal x(t) and system h(t) as presented in Figure Q2(a). Determine the output y(t) using the graphical representation of convolution integral. (7 marks) x(1) h(t) 1 e-'u(t) e-2 (1) 0 Figure Q2(a) Q2 (b) Consider a system as shown in Figure Q2(b). t2 - 1 x(t) y(t) Advance by 1 second Х Figure Q2(b) Find the input-output relation between x(t) and y(t). (i) (1 mark) Examine whether the system is time variant or time invariant. (5...
Consider three systems with the following input-output relationships 6. Consider three systems with the following input-output...
Consider three systems with the following input-output
relationships
6. Consider three systems with the following input-output relationships: { 4 0, odd System 1: y[n n even r[n] 10ar(n 2]3r[n - 1 System 2: yn + + System 3: yn x[3n] The interconnection diagram is at follows: System 1 System 2 System 3 Find the input-output relationship of the interconnected system. State the properties of the system (linear, stable, time invariant, memoryless, and causal).
6. Consider three systems with the following...
QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to...
QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to a Linear Time Invariant system of which the impulse response h(t) is shown as h(t) = { .. 12, -osts-2 elsewhere Compute the output y(t) of the system above using convolution in time domain for all values of time t. [8 marks) (b) The impulse response h[n] of an LTI system is given as a[n] = 4(0.6)”u[n] Determine if the system is stable. [3...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
If of the input signal X(t) and output signal yl to a continuous - time linear...
If of the input signal X(t) and output signal yl to a continuous - time linear time - invariant system - Y(t) = 5 to xc ej elt- el de o find the impluse response of the system hat) o If the input signal is x (t) = f(t) - f (t-1) find the output signal y ct) o Find the impulse response of the system hit) @ If the input signal Is x (t) = f(t)-f(t-1) find the -...
Signal system 8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the...
Signal system
8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the Fourier series coefficients for this signal. (4 points). b. If this signal passes through a LTI system with the impulse response h(t)=e* u(t), particularly, would the output signal also be a periodic signal ? If so, what would be the Fourier coefficients of the output signal ? (4 points). c. Give the mathematical expression for the output signal y(t). (2 points).
2. (a) For each sample of a discrete time signal x[n] as input, a system S outputs the value y[n- . Determine whether the system S is i. linear ii. time-invariant 1ll. causal iv. stable Each of your answers should be supported by justification. In other words, show your reasoning (b) Consider a stable linear time-invariant (LTI) system with transfer function H(z). It is required to design a LTI compensator system G(z) that is in cascade with H(z) such that...
Consider the following AM system x(t) z(t) y(t) H(a) 10ω -10 othwise 2cos (100t) Ifthe input signal x(t), the has a spectrum function, X(w), shown above, a) Write the expressions of r(w) and Z(w) in terms of X(w). b) Sketch the spectrums, x(ω), and r(a)Jdentify the LSE and USB components on the graphs? 14] 131 lain the type of AM modulation is the output z(03
Consider the following AM system x(t) z(t) y(t) H(a) 10ω -10 othwise 2cos (100t) Ifthe...
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...
Question # 4 Let x(t) u(t) be a signal, let h(t) = e -5tu(t) be a linear time invariant system (a) Sketch x(t) and h(t) (b) Find the mathematival expression of output of the system y(t) by using convolution. (c) Sketch y(t)
Q2 (a) Given the signal x(t) and system h(t) as presented in Figure Q2(a). Determine the output y(t) using the graphical representation of convolution integral. (7 marks) x(1) h(t) 1 e-'u(t) e-2 (1) 0 Figure Q2(a) Q2 (b) Consider a system as shown in Figure Q2(b). t2 - 1 x(t) y(t) Advance by 1 second Х Figure Q2(b) Find the input-output relation between x(t) and y(t). (i) (1 mark) Examine whether the system is time variant or time invariant. (5...
Consider three systems with the following input-output
relationships
6. Consider three systems with the following input-output relationships: { 4 0, odd System 1: y[n n even r[n] 10ar(n 2]3r[n - 1 System 2: yn + + System 3: yn x[3n] The interconnection diagram is at follows: System 1 System 2 System 3 Find the input-output relationship of the interconnected system. State the properties of the system (linear, stable, time invariant, memoryless, and causal).
6. Consider three systems with the following...
QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to a Linear Time Invariant system of which the impulse response h(t) is shown as h(t) = { .. 12, -osts-2 elsewhere Compute the output y(t) of the system above using convolution in time domain for all values of time t. [8 marks) (b) The impulse response h[n] of an LTI system is given as a[n] = 4(0.6)”u[n] Determine if the system is stable. [3...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
If of the input signal X(t) and output signal yl to a continuous - time linear time - invariant system - Y(t) = 5 to xc ej elt- el de o find the impluse response of the system hat) o If the input signal is x (t) = f(t) - f (t-1) find the output signal y ct) o Find the impulse response of the system hit) @ If the input signal Is x (t) = f(t)-f(t-1) find the -...
Signal system
8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the Fourier series coefficients for this signal. (4 points). b. If this signal passes through a LTI system with the impulse response h(t)=e* u(t), particularly, would the output signal also be a periodic signal ? If so, what would be the Fourier coefficients of the output signal ? (4 points). c. Give the mathematical expression for the output signal y(t). (2 points).
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