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it is Linear Systems Analysis class 1.7-8 For the systems described by the equations below, with...
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...
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
For the systems (H) described by the equations below, with ult) as the input and ylt) as the output (y Hu, determine if the system is linear or not. (a) y(t)=u(t)+1
1.30. Determine if each of the following systems is invertible. If it is, construct the inverse system. If it is not, find two input signals to the system that have the same output. (a) ya)-x(t - 4) (c) y[n] nx[n] (b) y(t) = cos(x(t)] x[n - 11, n z 1 In], (e) yIn]-0, ns-1 (g) y[n] x[1 -n] G) y(t) dxt (1) V(f) = X(20) n 0 (k) vini =lx(n+1],
9. Determine whether the following systems are invertible. If so, find the inverse. If not, find 2 input signals that produce the same output. (a) y)-r (b) yn]-ewl, where a is a real number (c) yt)-vx(t) for real-valued signals x(t) (d) yIn] xIn] (complex conjugate) 10. In most of the book, we will be discussing ways to analyze linear time-invariant (LTI) systems. As we will explore in much more detail later, the response of an LTI system to a particular...
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)
Please answer # 22 and 24 hapter 1 Systems of Linear Equations and Matrices *21. Suppose that A is n × m and B is m × n so that AB is n × n. Show that AB is no invertible if n> m. [Hint: Show that there is a nonzero vector x such that AB then apply Theorem 6.] and 22.) Use the methods of this section to find the inverses of the following matrices complex entries: 1- 0...
Problem 1 (Linear Systems of Equations). (a) Determine the values of a for which the follow- ing system of equations have no solution, exactly one solution, infinitely many solutions (a + 2)y + (a2-4)2 = (0-2) (b) If A = 4-1 0 a 2b a a be the augmented matrix of a linear system of equations then evaluate the values of a and b for which the linear system has no solution? exactly one solution? one parameter solution? two parameter...
solve all 22. The input-output relationship for a linear, time-invariant system is described by differential equation y") +5y'()+6y(1)=2x'()+x(1) This system is excited from rest by a unit-strength impulse, i.e., X(t) = 8(t). Find the corresponding response y(t) using Fourier transform methods. 23. A signal x(1) = 2 + cos (215001)+cos (210001)+cos (2.15001). a) Sketch the Fourier transform X b) Signal x() is input to a filter with impulse response (1) given below. In each case, sketch the associated frequency response...
need help all those questions. 10. Solve the following systems of linear differential equations: 11. Determine the Laplace transform of each of the following functions: (a) fe)-2t+1, 0StcI , 21 (b) f(t) te (c) f(t) = cos t cos 2t (Hint: Examine cos(a ± b).) Determine the inverse Laplace transform of each function: 12. (a) F(s) = 52 +9 is Demin 13. Determine L{kt cos kt + sin kt). 0, t< a 14. Determine L(cos 2t)U(t-r), where U(t-a)={ 15. Use...