Causal System Definition ::
In control theory, a causal system (also known as a physical or non-anticipative system) is a system where the output depends on past and current inputs but not future inputs i.e., the output y(t0) depends on only the input x(t0) for values of t < t0.
Solutions ::
(a) y[n] = 0.5*u[n] + 2.5*u[n-2] , n >= 0
Ans :: Given y[n] is only depends on present and previous Inputs Signals . So this is a causal system
(b) y[n] = 0.25*u[n] + 0.5*u[n+1] - 0.4*y[n-1] , n>=0
Ans :: Given y[n] is depends not only on present and previous Inputs Signals but also with future input signals . So this is a non-causal system
3) Determine whether the systems : a) y En] = 0.5 a[n] + 2.5 u [n-2],...
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)
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) For each of the following systems with input xfin] and output y/nl, determine whether it is linear, time invariant, causal, and/or stable. lineax - time-varient
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)]
determine whether 20 total pts] For each of the following systems described by their input-output behavior, or not the system is (1) linear,(2) time-invariant, (3) causal. For each case, make sure that you explain why. a. (5 pts] y[n] Axn] +B where A and B are nonzero constants d. 5 pts] y[n] x[n cos(0.25n)
3. Determine whether the series a permintulude demise en ligne conventionate camere consist on n-1169/2 -n+1 converges absolutely, converges conditionally, or 71+1 ns diverges. 4. Use the Ratio Test to determine the convergence or divergence of the series. n=1
The impulse response of some LTI systems are given below. Determine which ones are stable and/or causal? e. hn] (-0.5)"u[n] (1.02)"u[1-n] ht)2u(t 2) -2t t h, h(t)-sin()
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)
Dasi 1. For each of the following systems, determine whether the system is (1) stable, (2) causal, (3) linear, (4) time invariant, and (5) memoryless: (a) 7(x[n]) = g[n]X[n] with g[n] given (b) (x[n]) = x=no x[k] n20 (c) 7(x[n]) = (d) T(x[n]) = x[n - nol + x[k] (e) T(x[n]) = ex[n] (f) T(x[n]) = ax[n] + b (g) T(x[n]) = x[-n] (h) T(x[n]) = x[n] + 3u[n + 1).
- A causal system has input x[n] and output y[n]. Use the transfer function to determine the impulse response of this system. (a) x[n] = [[n]+} \n - 1]- 38[n – 20, x[n] = [[n] - [n – 1] (b) x[n] = (-3)" u[n], y[n] = 4(2)"u[n] – (7)" u[n]