3. (20 points) Find the impulse responses of the subsystems (h[n] and h2[n]) shown in figure...
2. Find the overall impulse response h in terms of the impulse responses of the subsystems. Your answer should not contain x. X(t)
Problem 3. See the cascaded LTI system given in Fig. 3. w in Figure 3: Cascaded LTI system Let the z-transform of the impulse response of the first block be (z - a)(z -b)(z - c) H1(2) a) Find the impulse response of the first block, hi[n in terms of a, b, c, d. Is this an FIR and IIR system? Explain your reasoning b) Find a, b, c, so that the first block nullifies the input signal c) Let...
Find the impulse response of the system shown in Figure 1. Assume that h(n) = h (n) = /1n un) h3(n) = u(n) 11n haln) = (3) "un) mon) - mm hi(n) h2(n) x(n) y(n) ☺ - Helm von h₃ (n) han) Figure 1. The system.
Problem 5.3 (20 Points) A discrete-time, linear time-invariant system H is formed by ar- ranging three individual LTI systems as shown below. LTI LII System 1 System 2 n] > >yn] ATI System 3 Figure 2: The cascaded LTI system H. The frequency response of the individual system H, is as follows: H2 : H el) = -1 + 2e- ja The impulse response of the other individual systems are as follows: Huhn = 0[n] - [n - 1] +...
l(20 points) (1) Linear convolution: In a linca response h(n) impulse response h(n) f 2 -1). Use the direct linear convolution method to find the output y(n). r system, let input x(n) (n 2), 0s n s 1, and impulse
3.(10 points) Two linear time invariant (L TI) systems with impulse response hy(k) and h2(k) are connected in cascade as shown in Figure 1. Let x(k) be the input, yı(k) be the output of the first LTI, and yz(k) be the output of the second LTI. Let h;(k) = k(0.5)* u(k), hz(k)= ku(k), and x(k) = (0.7)* u(k). Use z-transform to (a) find yı(k). (b) find y2(k). x(k) yi(k) h;(k) h2(k) ya(k)
3. (10 points) Two linear time invariant (LTI) systems with impulse response hi(k) and h2(k) are connected in cascade as shown in Figure 1. Let x(k) be the input, yı(k) be the output of the first LTI, and y2(k) be the output of the second LTI. Let hi(k) = k(0.7)k u(k), h2(k) = ku(k), and x(k) = (0.3)k u(k). Use z-transform to (a) find yı(k). (b) find y2(k). x(k) yi(k) y2(k) hi(k) h2(k)
Given to the system with the impulse responses h1(t) and the h2 (t) cos π t, 0 < t < ∞ Find the impulse response h(t) of a new system which is a series interconnection of two mentioned system using the convolutional integral. Present mathematical and graphical solution.
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n] = 2e-n + sin(nn)- 2, -co <n< 0o. 7. (20 pts.) Determine the response of the system described by the difference equation 1 1 y(n)y(n1)n2)x(n 8 7 for input signal x(n) u(n) under the following initial conditions 1, y(-2) 0.5 y(-1) (20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input...
H1(2) y[n] Xn] 1 H3(2) H2(2) Figure 2: Consider the system shown in Figure 2. Suppose that Hi(z) = -1,-1 and H2(z) = 1-1,-1. Determine the impulse response h3[n] ++ H3(z) such that when x[n] = 8[n – 1], the output is y[n] = $[n – 1] +38[n – 3]. Using MATLAB, generate the signal x[n] and propagate it through the system to verify that the output y[n] is as desired.