Homework Answers
For finding out whether a function is linear or not we have to see whether the system follows the principle of superposition and homogeneity. A system is only linear if it follows both these principles.
Here both the given function are not linear.
The explanation is as follows.
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For the systems (H) described by the equations below, with ult) as the input and ylt)...
it is Linear Systems Analysis class 1.7-8 For the systems described by the equations below, with...
it is Linear Systems Analysis class
1.7-8 For the systems described by the equations below, with the input (1) and output y(t), determine which of the systems are invertible and which are noninvertible. For the invertible systems, find the input-output relationship of the inverse system (a) y(t) = [ f(t)dr (b) y(t) = f(3-6) (c) y(t) = {"(t) n, integer (d) y(t) = cos(/(t))
1.7-1 For the systems described by the equations below, with the input f(t) and output v(t),...
1.7-1 For the systems described by the equations below, with the input f(t) and output v(t), determine which of the systems are linear and which are nonlinear. dy dt (a) + 2y(t)-f(t) (b) +3y() -se) (e) ( ) +2y(t)-f(t) (d) +92(t) = f(t) (c) 3y(t) + 2 = f(t) (f) + (sin t)y(t)-2 + 2/(t) dt dt (h) v(t)f(r)dr dt
1) Linearity: In order for a system to be linear it must satisfy the following equation: In other...
need solution and code for this signal and system
problem
1) Linearity: In order for a system to be linear it must satisfy the following equation: In other words, the response of a linear system to an input that is a linear combination of two signals is the linear combination of the responses of the system to each one of these signals. Let xi)- u(t) -u(t-1) and x2t) u- u(t-2) be input signals to the systems described by the i/o...
1.2 [12 points] Determine the transfer functions for the following systems. (a) A system described by...
1.2 [12 points] Determine the transfer functions for the following systems. (a) A system described by the signal flow graph below: -1 Figure 2 (b) A second-order system with input u and output y described by the state variable model below: i- Ax + Bu y -2x, 01 where x- A-TT
Determine if the systems described by the following input and output equation are linear or non-linear...
Determine if the systems described by the following input and output equation are linear or non-linear 1) Y(n) = nX(n) .(2) Y(n) = X(n2) (3) Y(n) = X2(n) (4) Y(n) = Ax(n) + B. (5) Y(n) = ex(n)
Find the frqeuncy response and impulse response of the system with the output y(t) for the next input x(t) Please, Solve (a) and (c) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x...
Find the frqeuncy response and impulse response of the
system with the output y(t) for the next input x(t)
Please, Solve (a) and (c)
x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult)
x)e u(t), ()eu(te ult)
x)e u(t), ()eu(te ult)
x)e u(t), ()eu(te ult)
x)e u(t), ()eu(te ult)
x)e u(t), ()eu(te ult)
Question 1.. Detemine if the following systems are linear or not (a) (5 points) y(t) =...
Question 1.. Detemine if the following systems are linear or not (a) (5 points) y(t) = tx(t (b) (5 points) y(t) = 2(t (c) (5 points) y(t) = 2.r(t) +3 15 points Question 2 Determine if the following systems are time-invariant or not 10 points (a) (5 points) y(t) = x(2t) (b) (5 points) y(t) =r(t)u(t) 5 points Question 3 Determine if the following systems are causal or not (a) (5 points) y(t) = r(-t) 20 points Question 4 Consider...
determine whether 20 total pts] For each of the following systems described by their input-output behavior,...
determine whether 20 total pts] For each of the following systems described by their input-output behavior, or not the system is (1) linear,(2) time-invariant, (3) causal. For each case, make sure that you explain why. a. (5 pts] y[n] Axn] +B where A and B are nonzero constants d. 5 pts] y[n] x[n cos(0.25n)
Problem 1 (25 points): Consider a system described by the differential equation: +0)-at)y(t) = 3ú(1); where...
Problem 1 (25 points): Consider a system described by the differential equation: +0)-at)y(t) = 3ú(1); where y) is the system output, u) is the system input, and a(t)is a function of time t. o) (10 points): Is the system linear? Why? P(15 points): Ifa(t) 2, find the state space equations?
SIGNALS and SYSTEMS HOMEWORK-IV 1. Let X(t) be the input to an LTI system with unit...
SIGNALS and SYSTEMS HOMEWORK-IV 1. Let X(t) be the input to an LTI system with unit impulse response h(t), where x(t) = e-tu(t) h(t) = u(t -3). Determine and plot the output y(t) = x(t) *h(t). Both analytically and graphical method. (25 p)
it is Linear Systems Analysis class
1.7-8 For the systems described by the equations below, with the input (1) and output y(t), determine which of the systems are invertible and which are noninvertible. For the invertible systems, find the input-output relationship of the inverse system (a) y(t) = [ f(t)dr (b) y(t) = f(3-6) (c) y(t) = {"(t) n, integer (d) y(t) = cos(/(t))
1.7-1 For the systems described by the equations below, with the input f(t) and output v(t), determine which of the systems are linear and which are nonlinear. dy dt (a) + 2y(t)-f(t) (b) +3y() -se) (e) ( ) +2y(t)-f(t) (d) +92(t) = f(t) (c) 3y(t) + 2 = f(t) (f) + (sin t)y(t)-2 + 2/(t) dt dt (h) v(t)f(r)dr dt
need solution and code for this signal and system
problem
1) Linearity: In order for a system to be linear it must satisfy the following equation: In other words, the response of a linear system to an input that is a linear combination of two signals is the linear combination of the responses of the system to each one of these signals. Let xi)- u(t) -u(t-1) and x2t) u- u(t-2) be input signals to the systems described by the i/o...
1.2 [12 points] Determine the transfer functions for the following systems. (a) A system described by the signal flow graph below: -1 Figure 2 (b) A second-order system with input u and output y described by the state variable model below: i- Ax + Bu y -2x, 01 where x- A-TT
Find the frqeuncy response and impulse response of the
system with the output y(t) for the next input x(t)
Please, Solve (a) and (c)
x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult) x)e u(t), ()eu(te ult)
x)e u(t), ()eu(te ult)
x)e u(t), ()eu(te ult)
x)e u(t), ()eu(te ult)
x)e u(t), ()eu(te ult)
x)e u(t), ()eu(te ult)
Question 1.. Detemine if the following systems are linear or not (a) (5 points) y(t) = tx(t (b) (5 points) y(t) = 2(t (c) (5 points) y(t) = 2.r(t) +3 15 points Question 2 Determine if the following systems are time-invariant or not 10 points (a) (5 points) y(t) = x(2t) (b) (5 points) y(t) =r(t)u(t) 5 points Question 3 Determine if the following systems are causal or not (a) (5 points) y(t) = r(-t) 20 points Question 4 Consider...
determine whether 20 total pts] For each of the following systems described by their input-output behavior, or not the system is (1) linear,(2) time-invariant, (3) causal. For each case, make sure that you explain why. a. (5 pts] y[n] Axn] +B where A and B are nonzero constants d. 5 pts] y[n] x[n cos(0.25n)
Problem 1 (25 points): Consider a system described by the differential equation: +0)-at)y(t) = 3ú(1); where y) is the system output, u) is the system input, and a(t)is a function of time t. o) (10 points): Is the system linear? Why? P(15 points): Ifa(t) 2, find the state space equations?
SIGNALS and SYSTEMS HOMEWORK-IV 1. Let X(t) be the input to an LTI system with unit impulse response h(t), where x(t) = e-tu(t) h(t) = u(t -3). Determine and plot the output y(t) = x(t) *h(t). Both analytically and graphical method. (25 p)
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