10.19 Determine which of the following pair of impulse responses correspond to inverse systems:
QUESTIONS 1. Determine whether or not the LTI systems with the following impulse responses are causal and stable. Note that simply writing causal /noncausal, or stable /unstable is not enough, the verification of your answers are required to gain points from this question (15 puan) a. hon)-(0.5 u(n) +(1.01) u(n-1) b. h(n)-(0.5) u(n)+(1.01) u(1-n)
Four systems have the following impulse responses. For each one sketch its impulse response, then draw its pole-zero plot and region of convergence. For each one also determine whether the system is causal and whether it is stable. (a) h1(t) e u(t) (b) h2(t) eu-t)
please solve it
10.19. (a) Find the responses for systems described by the following difference equations with the initial conditions given: (i) y[n] - Sy[n – 1] = 2"u[n], y[- 1] = 0 (ii) y[n] - 0.7y[n - 1] = { "u[n], y[-1] = 0 (iii) y[n] + 3y[n – 1] + 2y[n – 2] = 3u[n], y[-1] = 0, y[-2] = 0 (iv) y[n] – 0.7y[n – 1] = cos(n)u[n], y[- 1] = -1 (b) Verify that your response...
Problem 1. Determine if the LTI systems with impulse responses as given below are sta ble/unstable and causal/non-causal Note: u(t)/ ulnl represents unit-step. δ(1)/ δ[n] represents unit impulse. I. hl (t) = δ(t + 4)-5(5-t) 2. h2(l) e"cos(nt)u(-)
The following functions have impulse responses from discrete and continuous LTI systems. Determine whether each system is causal and convergent a) h[n] = 2n u[3 - n] b) h(t) = u(1 – t) – 1/2e-t u(t) c) h[n] = [1 – (0.99)n ]u[n] d) h(t) = e15t [u(t – 1) – u(t – 100)]
The system shown below is formed by connecting two systems in parallel. The impulse responses of the systems are given by: t h, (t) = € 2€ u(t) , h (t) = 2e fu(t) 1) Find the impulse response h(t) of the overall system. 2) Is the overall system stable? h,(t) x vo h(t)
Problem 5. (20 points) Topic: System interconnections. Given two systems with the impulse responses h:(0) = e (l) and hz(t) = u(t) - ufl-1) (rectangular pulse of duration 1). Find the impulse response h(t) of a new system which is a series interconnection of two mentioned systems. Present mathematical and graphical solution Total 100 points (1) =
Problem 1. (10 points) The unit impulse responses of two linear time-invariant systems are hi(t) = 400me-200t u(t) h (t) = 4007e-200nt cos(20,000nt u(t). a) Find the magnitude responses of these systems. b) Determine the filter type and 3 dB cut-off frequency of the first system hi(t). c) How about the second system hz(t)?
5- Determine whether or not each of the following LTI systems with the given impulse response are memoryless: a) h(t) = 56(t- 1) b) h(t) = eT u(t) e) h[n] sinEn) d) h[n] = 26[n] 6- Determine whether or not each of the following LTI systems with the given impulse response are stable: a) h(t) = 2 b) h(t) = e2tu(t - 1) c) h[n] = 3"u[n] d) h[n] = cos(Tm)u[n] 7- Determine whether or not each of the following...
3.5 Determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t): 11) X (İİİ) x(1) = 11(1)-211(1-1) + 11(1-2), h(1) = 11(1 + 1)-11(t-1); Part lI Continuous-time signals and systems (iv) x(t) - e2"u(-t), h(t)-eu(); (v) x(t)-sin(2tt)(u(t _ 2) _ 11(1-5)), h (t) = 11(1) _ II(ț-2); (vi) x(t) = e-圳, h(t) = e-51,1. (vii) x(1)= sin(t)11(1), h(1) = cos(t)11(1).
3.5 Determine the output y(t) for the following pairs of input signals x(t) and...