(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when...
Consider a causal LTI system with frequency response H(jw) = 1 2 + jw For a particular input x(t) this system is observed to produce the output y(t) = e-ºut) - e-stutt) i) Determine x(t). ii) Is this system stable? Explain your reasoning. iii) Plot the magnitude and phase responses of H (jw).
5. Fourier Transform and System Response (12 pts) A signal æ(t) = (e-t-e-3t)u(t) is input to an LTI system T with impulse response h(t) and the output has frequency content Y(jw) = 3;w – 4w2 - jw3 (a) (10 pts) Find the Fourier transform H(jw) = F{h(t)}, i.e., the frequency response of the system. (b) (2 pts) What operation does the system T perform on the input signal x(t)?
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
3. Consider an LTI system with the impulse response h(t)e Find the Fourier series representation for the output y(t) for each of the inputs below: b ra(t) in Figure 2. Figure 2: a2(t)
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)] =...
2. Linearity Consider a system given with the following impulse response: (5%) h[n] 4u[1 a) Is the system LTI? b) Is it causal? c) Is it stable? 2. Linearity Consider a system given with the following impulse response: (5%) h[n] 4u[1 a) Is the system LTI? b) Is it causal? c) Is it stable?
Problem 3. The input and the output of a stable and causal LTI system are related by the differential equation dy ) + 64x2 + 8y(t) = 2x(t) dt2 dt i) Find the frequency response of the system H(jw) [2 marks] ii) Using your result in (i) find the impulse response of the system h(t). [3 marks] iii) Find the transfer function of the system H(s), i.e. the Laplace transform of the impulse response [2 marks] iv) Sketch the pole-zero...
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
A causal LTI system yields the following input output relationship. Find h(t), the impulse response of the system. (Hint: Try first to determine the output when the input is u(t)) a(t) y(t) LTT →t 2 2 Figure 1: An input-output pair
Using parsevals theorem and FT to find y(t) and its power (b) (4 pts) Fourier Series The input signal r(t) and impulse response h(t) of an LTI system are as follows: z(t) = sin(2t)cos(t)-e131 + 2 and h(t) = sin(21) Use the Fourier Series method to find the output y(t) (c) (4 pts) Parseval's Identity and Theorem. Consider the system in the previous problem. Use Parseval's Identity to compute the power P of the output y(t). Use Parseval's Theorem to...