The Laplace transform of the output of the below LTI system is calculated as: 10(52 +...
A continuous-time LTI system has unit impulse response h(t). The Laplace transform of h(t), also called the “transfer function” of the LTI system, is . For each of the following cases, determine the region of convergence (ROC) for H(s) and the corresponding h(t), and determine whether the Fourier transform of h(t) exists. (a) The LTI system is causal but not stable. (b) The LTI system is stable but not causal. (c) The LTI system is neither stable nor causal 8...
Consider the LTI system with input ??(??) = ?? ?????(??) and the impulse response ?(??) = ?? ?2????(??). A. (3 points) Determine ??(??) and ??(??) and the ROCs B. (3 points) Using the convolutional property of the Laplace transform, determine ??(??), the Laplace transform of the output, ??(??) C. (3 points) From the answer of part B, find ??(??) 9 points) Consider the LTI system with input x(t)eu(t) and the impulse response h(t)-e-2u(t) A. 3 points) Determine X(s) and H(s)...
In a continuous-time system, the laplace transform of the input X(s) and the output Y(s) are related by Y(s) = 2 (s+2)2 +10 a) If x(t) = u(t), find the zero-state response of the system, yzs(1). yzs() = b) Find the zero-input response of the system, yzi(t). Yzi(t) = c) Find the steady-state solution of the system, yss(t). Yss(t) =
Calculated i(t) from circuit is : apply the Laplace transform to the time-domain expression for the current i(t) to determine I(s). - R (+) Biological Tissue IDEAL JODA APPROX 100AA + Mathematical expression for current ilt) = 10,000 @ tato, 100MA lons @tato, 100uA ult-10ns) i for current ilt): ilt) = 10,000+ ult) - 10,000tult - 10x10-9) +100x10 bult-10x10 -9)
Determine the inverse Laplace transform of the function below 6s 52 + 25 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. e 6s L-1 s2 + 25 >(t) =
10. Explain using only the Laplace transform formulas developed in class. a) Find the Laplace transform of uſt - 3) sin (htt) b) Find the inverse Laplace transform of the function using convolution F(s)G(s) = f(t) *g(t) 1 s? (s2 + 1)
Determine the inverse Laplace transform of the function below. Se -45 s2 + 10s + 50 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 4s Se 2-1 s2 (t) = + 10s + 50 (Use parentheses to clearly denote the argument of each function.)
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...
3. (l’+2° +1²=4') Topic: Laplace transform, CT system described by differential equations, LTI system properties. Consider a differential equation system for which the input x(t) and output y(t) are related by the differential equation d’y(t) dy(t) -6y(t) = 5x(t). dt dt Assume that the system is initially at rest. a) Determine the transfer function. b) Specify the ROC of H(s) and justify it. c) Determine the system impulse response h(t).
The transfer function of a system is Use Inverse Laplace Transform to determine y(t) when r(t) =b u(t). “b” is a constant. Y(s) R(S) 10s + 2) 52 +8s + 15