7. For each of the following, determine if the following systems are causal and if they are stable. Provide reasons for each answer.
7. For each of the following, determine if the following systems are causal and if they...
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...
Signal and Systems 8 + If Problem la (10 points) Find the inverse Laplace transform of: Fo(s) 12 the ROC is defined as: -12 <Re(s) <0 Identify terms as right sided or left sided. S+12 Re(s) < 0 Re(s) >-12 Х X -12 0 Problem 1b (2 points) Circle one: The function f(t) Is: causal anti-causal not causal Explain why:
2. Circle the causal BIBO stable ROC below. a) 1.1<\리<1.2 b) Izk1/201zP1/2 d) 0.5<Izl<0.9 e) none above 3. A linear time-invariant IIR system is always BIBO stable a) True b) False 4. If a fiter has z-transform H(z)05, then the fiter s ;z>0.5, then the filter is zz-0.5z a) Nonlinear b)FIR )R d) two-sided e) none above 5. The discrete-time frequency o in rad/ sample of the sinusoid hin] below is d) T2 e) none above hIn] -1
Laplace Transform 3. If the ROC for a Laplace Transform pair x(t) <-> X(s) contains the entire w . axis, which of the following two statements are true: The Fourier Transform for x(t) does not exist. The Fourier Transform for x(t) exists. The Fourier Transform for x(t) exists provided that x(t) is absolutely integrable, if not then it does not exist. The system is unstable. The system is stable. There is not enough information to determine existence or non-existence of...
for each of the systems shown below check all of the following statement that always true. Statement The system is stable. The system is unstable. system is causal The system is non-causal If the system is causal, it is stable. If the system is not causal, it is stable. If the system is stable, it is causal. If the system is not stable, it is causal. The causal. The system is FIR The system is IIR b) Im/z) c) Imfa)...
Linear Time Invariant Systems 4] For each of the following continuous-time systems xt) is a real input. Determine whether the system is (1) stable, (2) causal, (3) linear and (4) time invariant (5% each): (a) T(x(t)] = sin(2π) x(t + 2%)-cos(2π) x(t-ro), where τ。> (b)T(x(t)] = x(4) (c) T(x(t)]Ξ14- AxzQ A is a complex constant.
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)
12 Problem la (10 points) Find the inverse Laplace transform of: Fo(s) the ROC is defined as: -12 < Re(s) <0 Identify terms as right sided or left sided. 8 +- If S S+12 Re(s)< 0 Re(s) >-12 X X -12 0 Problem lb (2 points) Circle one: The function f(t) Is: causal anti-causal not causal Explain why: Given the unilateral Laplace transform of the impulse response for a causal system H(S) = Determine h(t) the impulse response? Hint synthetic...
Question 1: (25marks) Determine whether each of the following represents a BIBO (Binary Input/Binary Output) stable system: H(z) (z-7)(z2+1/9), causal b. H(z) (z-7)(z2+1/9), anticausal H(z) z/[(z-0.7) (2+z+1)], mixed d. H(z)-(z+1)(2-1), causal a. C. For each case in which the system is determined the ROC. Question 1: (25marks) Determine whether each of the following represents a BIBO (Binary Input/Binary Output) stable system: H(z) (z-7)(z2+1/9), causal b. H(z) (z-7)(z2+1/9), anticausal H(z) z/[(z-0.7) (2+z+1)], mixed d. H(z)-(z+1)(2-1), causal a. C. For each case...
please show steps 4. (25 points) Laplace and LCCDE Systems Consider an LTI system with input-output relation described by the LCCDE: -2y(t) - y0) + 3x(t) + deco (O) = (a) (5 pts) Find the transfer function H(s) and write it in factored form. (b) (5 pt) Sketch the ROC corresponding to H(s) if it is known the system is causal. Mark the poles and zeros. (c) (5 pts) Sketch the ROC corresponding to H(s) if it is known the...