1. Consider a continuous system whose input x(t) and output y(t) are related by dy(t) +...
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,...
Consider the following circuits connected in series. The input is the voltage x(t), the output to system Si is the voltage y(t), and the output of system S2 is the voltage y(t). The differential equation relating the input X(t) to the output yı(t) was found in Homework #3. S2 x(1) y(t) | X(t) 6+ R yce) .66) (1) + y(t) Let L = 0.01, C1 = 0.01, R = 100, C2 = 0.002, and R2 = 50. a) Find the...
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....
For a continuous time linear time-invariant system, the input-output relation is the following (x(t) the input, y(t) the output): , where h(t) is the impulse response function of the system. Please explain why a signal like e/“* is always an eigenvector of this linear map for any w. Also, if ¥(w),X(w),and H(w) are the Fourier transforms of y(t),x(t),and h(t), respectively. Please derive in detail the relation between Y(w),X(w),and H(w), which means to reproduce the proof of the basic convolution property...
Problem 4. Given the input/output system represented by t-1 y(t) = 2 ( x(y - 3) dy where x(t) is the input and y(t) is the output, a) Determine whether the system is linear or non-linear. b) Determine the impulse response h(t, to) of the system by setting x(t)= 8(t–to). c) Determine whether the system is time invariant or time variant. d) Determine whether the system is causal or non-causal.
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output y(t) are shown below: r(t) Page 1 of 2 Please go to next page... y(t) ? (a) Find the impulse response function h(t) of ? (b) Find the output of S when its input is e*, t<0, t2, t20
Problem 2 Consider a continuous-time LTI system whose frequency response is given by 2 sin(40 (a) Find the impulse response, h(t) of the system (b) Determine the outputy() =x(t)*h(t) of the system given an input x(f)--1, ț < 8 4 otherwise 0,
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).
Q4. An LTI continuous-time system is specified by dy(t).dyết + 4y(t) = f(t) dt2 *4 dt 4y(t) = f(t) a) Find its unit impulse response with the initial conditions yn (0) = 0, yn (0) = 1 where yn(t) is the zero input response and yn (0) = 1 is the 1st order derivative of yn(t). b) Please state the definition for stability, and then verify that whether this system is stable or not?
If of the input signal X(t) and output signal yl to a continuous - time linear time - invariant system - Y(t) = 5 to xc ej elt- el de o find the impluse response of the system hat) o If the input signal is x (t) = f(t) - f (t-1) find the output signal y ct) o Find the impulse response of the system hit) @ If the input signal Is x (t) = f(t)-f(t-1) find the -...