Problem 1 Let's consider an LTI system with intput and output relatex through the equation y(t)...
Problem 1. The input x(t) and output y(t) of an LTI system satisfy the differential equation d’y(t) + wốy(t)=r(t), where wo is a fixed real number. A) Find the right-going impulse response of the system. B) Find the left-going impulse response of the system.
Problem 4. Use the convolution integral to find the response y(t) of the LTI system with impulse response h(t) to input x(t) a) x(I)-2expl_2t)u(t) , h(1)-expl-t)u(t)
Consider a continuous-time LTI system S with impulse response h(t) = 2(u(t + 1)-u(t 1)). Determine the values of the amplitude scaling and the tme shifting that takes place when each of the following input signals is provided to the system S. Don't use the convolution integral, instead use the result about how LTI systems respond to complex exponential signals. (a) x(t) 2 (b) x(t) ej0.5Tt (c) x(t) = e-j0.5πt (d) x(t) = e-jmt (e) x(t) = cos (0.5t) (f)...
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...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
Problem #2 Consider a continuous-time LTI system given by: dy[ + 2y(t) = x(t). Using the Fourier transform, find the output y(t) to each of the following input signals: (a) x(t) = e-'u(t), and (b) x(t) = u(t).
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
1. Evaluate and sketch the convolution integral (the output y(t)) for a system with input x(t) and impulse response h(t), where x(t) = u(1-2) and h(t)= "u(t) u(t) is the unit step function. Please show clearly all the necessary steps of convolution. Determine the values of the output y(t) at 1 = 0,1 = 3,1 = 00. (3 pts)
Mouzey bighalsledsystems tionne 907 octet Acone s ona 27/0 y the 13. The input-output relationship of an LTI system is deseribed by the difference squation: n]+0.5y[n-1]-xn], Try to figure out two possible unit impulse responses for such a system. Then state which unit impulse response comresponding to tomer les modules com a stable system. 2, b) x,(2)=z" +62 452 | > 1 14) Find the inverse z-transform of the following signals a) X(E)(-2 XI-2) :-5 c) X2(E)-0.5:)1-0.5 )0. <2 15....
4. (5 pts) Consider a discrete-time LTI system T that generates an output y[n] according to a2 y[n] bx[n] – ay[n – 1] - *[n – 2] where a, b are non-negative real constants. (a) (2 pts) Find the poles of the z-transform of the impulse response h[n] of T. (b) (3 pts) Let H(ejl be the frequency response of T. Find a, b so that the system is causal and stable, |H(1)| = |H(ejº)] = 0.04, and |H(-1)] =...