Determine the output response y[n] of a causal LTI digital system with an impulse response h[n]=2(0.2)n μ[n] for an input sequence x[n] = 4(0.3)n μ[n]
Determine the output response y[n] of a causal LTI digital system with an impulse response
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)
Problem 2: Find the impulse response h(n) of a causal LTI system if the input x(n) and the output y(n) are given as follows 72 42)un-1) y(n)-G)na(n) xnun)
A causal LTI system yields the following input output relationship. Find h(t), the impulse response of the system. (Hint: Try first to determine the output when the input is u(t)) a(t) y(t) LTT →t 2 2 Figure 1: An input-output pair
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...
Problem 6 (20 pts) Suppose that the impulse response of a causal LTI system has a Laplace transform which is given by 5+1 H(3) and that the input to this system is x(t) = ell! $+ 25 +2 a) Determine the Laplace transform of the output y(t), along with its associated region of convergence. (12 pts) b) Determine the output y(t). (8 pts)
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution determine yin, 1f XIn = 1 un.(6 marks Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution...
A causal LTI system is characterized by : y[n] - 3/4 y[n-1] + 1/8 y[n-2] =2x[n]. (a) Find the impulse response h[n] of this system (b) Find the response of the system to input x[n] = (1/4)^n * u[n]
A causal and stable LTI system has the property that: 〖(4/5)〗^n u(n) →n 〖(4/5)〗^n u(n) Determine the frequency response H(e^jω) for the system. Determine a difference equation relating any input x(n) and the corresponding output y(n). Question 3:[4 Marks] A causal and stable LTI system has the property that: 4 4 a) Determine the frequency response H(e/ø) for the system. b) Determine a difference equation relating any input x(n) and the corresponding output y(n)
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
Consider an LTI system whose input x[n] and output y[n] are related by the difference equation y[n – 1] + 3 y[n] + $y[n + 1] = x[n]. Determine the three possible choices for the impulse response that makes this system 1) causal, 2) two-sided and 3) anti-causal. Then for each case, determine if the system is stable or not. Causality Impulse Response Stability Causal Unstable v two-sided Unstable anti-Causal Unstable y In your answers, enter z(n) for a discrete-time...