A system with input x(t) and output y(t) is described by y(t) = 5 sin(x(t)). Identify the properties of the given system. Select one: a. Non-linear, time invariant, BIBO stable, memoryless, and causal b. Non-linear, time invariant, unstable, memoryless, and non-causal c. Linear, time varying, unstable, not memoryless, and non-causal d. Linear, time invariant, BIBO stable, not memoryless, and non-causal e. Linear, time invariant, BIBO stable, memoryless, and non-causal 0
3. Let y(t) (2+2sint)x(t) Determine if the system above has the following properties: a) Memoryless b) Linear c) Time-Invarient d) Stable
1) Determine if the discrete-time system,y[k] =x[k] +r·y[k−1]is linear / time-invariant / causal / memoryless. Show your work and explain each property. Start by assuming,x1[k]→y1[k], x2[k]→y2[k]. 2) Determine if the discrete-time system,y[k] =x[k] +rk·y[k−1]is linear / time-invariant / causal / memoryless. Show your work and explain each property. 3) For the system in part 1), if x[k] = 100·u[k−1] and y[k] = 0 for k<0, what is the range of values for r that makes this system BIBO stable? Show...
Q1. True / False Memoryless Causal Stable Time-invariant Linear y(t) = x(2t) – 1 rt-1 J-00 y(t) = Sx() dt y[n] = 2 x[m] m =0
Determine which of these properties (Memoryless, Time invariant, Linear, Causal, and Stable) hold and which do not hold for each of the continuous-time system, y[n] = x [4n + 1]. Justify your answers. y(t) denotes the system output and x(t) is the system input
Determine whether the system described byy(t) = cos[x(t – 1)] is a) Memoryless b) Causal c) Linear d) Time Invariant
A system is given by: yt=5xt+1-3 Is the system BIBO stable? Justify Is the system memoryless? Explain Is the system causal? Explain Is the system time invariant? Justify Is the system linear? Justify What is the impulse response h(t) of the system? Is the system internally stable? If you could not figure out h(t) from part f, use the h(t) from the problem below. ht=5e-tut-u(t-4)
(c) Let X have an exponential density with parameter λ > 0, Prove the "memoryless" property: P(X > t + s|X > s) = P(X > t) for t>0 and s 0. For example, the probability that the conversation lasts at least t more minutes is the same as the probability of it lasting at least t minutes in the first place.
2 2 0 0 3" (12%) Solve the linear system x"(t) AX(t) with A 0 0 4 4 a) (406) Write down the characteristic equation of the coefficient matrix λ and solve its eigenvalues, . b) (8%) Find the four independent solutions of the system.
Problem 3 Determine whether each of the following system is memoryless, stable. Justify your answer time-invariant, linear, causal or (a) y(t)r(t -2)+x(-t2) b) y(t) cos(3t)(t) (c) y(t) =ar(r)dT d) y(t)t/3) (e) y(t) =