Consider the following circuits connected in series. The input is the voltage x(t), the output to...
5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F, C2-1F. Identify the natural and forced response of the system a) Find the zero input response. b) Unit impulse response. c) zero state response. d) The total response. e Identify the natural and forced response of the system. 5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F,...
The input-output relationship for a system is ¨y(t) + ˙y(t) = x(t). (a) Find the impulse response of the system. (b) Find the zero-state response when the input is a unit step. (c) Find the zero-state response when the input is x(t) = 1.6u(t) − 0.6u(t − 1).
1. For a system described in Figure 1. x(t) - input voltage, y(t) - output voltage. (a) Determine Continuous Time (C.T.) "Math Model" when R = 1/3 121, L = 1/2 [F], and C = 1 [F]. (b) Fine "Zero Input Response". y zit. for the C.T.system. when y(0) = 1 [V], y'(0) = 2 IV (c) Draw "Zero Input Response". y_zi(t) with respect to time 1 (2-D graph) (d) Find impulse response, h(!). of the Continuous Time (C.T.) system....
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) + ay(t) = x(t) dt where a is a constant. (a) Find y(t) with the condition y(0) = yo and x(t) = Ke-bu(t) (b) Express y(t) in terms of the zero-input and zero-state responses. 2. Consider the system in Problem 1. (a) Show that the system is not linear if y(0) = yo 70. (b) Show that the system is linear if y(0) = 0....
Determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t): iv) x(t) = exp(2t)u(−t), h(t) = exp(−3t)u(t);
Determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t) USING CONVOLUTION THEOREM ONLY: iv) x(t) = exp(2t)u(−t), h(t) = exp(−3t)u(t);
determine the output y(t) for the following pairs of input signals x(t) and impulse responses h(t): (1) x(t) = u(t), h(t) = u(t) (2) x(t) = exp(2t)u(-t), h(t) = exp(-3t)u(t)
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)
(a) LTI Systems. Consider two LTI subsystems that are connected in series, where system Tl has step response s1(t)=u(t-1)-u(t-5) and system T2 has impulse response h2t = e-3tu(t). Find the overall impulse response h(t). Hint: you will need to find h1(t) first (b)Fourier Series. The input signal r(t) and impulse response h(t) of an LTI system are as follows:x(t) = sin(2t)cos(t)-ej3t +2 and h(t) = sin(2t)/t Use the Fourier Series method to find the output y(t) (c)Parseval's Identity and Theorem. Consider the system in the...