5. For each of the following h[n] and x[n], characterize the output of the LTI system...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
1. An LTI digital system with impulse response h[n] = 2(1/4)"u[n] produces an output y[n] = (-3)"u[n]. Determine the corresponding input x[n] using Z-transform. (30 points)
1. An LTI system has impulse response defined by h (n )={2 ,2 ,−1,−1 ,−1,−1}first 2 zero . Determine the outputs when the input x(n) is (a) u(n ) ; (b) u(n−4 ) 2. Let the rectangle pulse x ( n )=u ( n ) −u (n −10 ) be an input to an LTI system with impulse response h (n )=(0.9 )n u (n ) . Determine the output y ( n ) . (Hint: You need to consider muliple...
Q2. The block diagram of an LTI system is given below. x[n] - h[n] = a[n+ 2] - a[n - 2] h2[n] = 8[n - 1] y[n] a) Represent the overall impulse response h[n] in terms of hi[n] and h2[n]. b) If the input is x[n] = 8[n], sketch y[n]. c) If the input is x[n] = u(n + 1] - u[n -2], sketch y[n].
Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation 3y[n] – 7y[n – 1] + 2y[n – 2] = 3x[n] – 3x[n – 1] (2.1) The fact that sequences x[ ] and y[ ] are in input-output relation and satisfy (2.1) does not yet determine which LTI system. a) We assume each possible input sequence to this system has its Z-transform and that the impulse response of this system also has its Z-transform. Express the...
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]. When the input signal x[n] = (6)" is applied to the system, the output signal is y[n] = 0 for all n When the input signal xn] (3)" u[n] is applied to the system, the output signal is y[n] = A 8[n] + 2 (5)" u[n] for all n, where A is a constant number a) Find A. b) Find the impulse response of...
3. Consider the following system LTI LTI System 2 h2ln] System 1 x [n] hiln) wIn] yIn] with h(n) (0.2)" un),h(n) is the impulse response of 2y(n)-4y(n-1) 2w(n), and x(n) (0.6"u(n). (a) Determine h2(n) (b) Determine the overall impulse response hn) (c) Determine w(n) e Demine e gu x n ) (a) velw mine hrCn) (b) Peke a jin
1. (20 p) Compute and sketch the output y(t) of the continuous-time LTI system with impulse response h(t) = el-tuſt - 1)for an input signal x(t) = u(t) - ut - 3). 2. (20p) Consider an input x[n] and an unit impulse response h[n] given by n-2 x[n] = (4)”- u[n – 2] h[n] = u(n + 2] Determine and plot the output y[n] = x[n] *h[n].
1. For each of the LTI systems below find the system output y, where h is the system impulse response and x is the system input:
1- Compute and plot the output for LTI systems with an input x[n] and unit impulse response of h[n] given by: n a) xn] = () uln], h[n] = u[n + 2] (1, 0sn<8 b) xn= (0, Otherwise ln] : 2, 0sns4 l0, Otherwise