Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: [[x(+) *...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)-u(t). [Hint: use Laplace Transform multiplication: C[x(t) * h(t)] = x(s)H(s). y(t) = tu(t)-(t - 2)u(t - 2) y(t) = tu(t)-(t + 2)u(t+2) y(t) = tu(t) + (t - 2)u(t - 2) y(t) = tu(t) + (t - 2)u(t + 2)
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
Need help asap. will rate Determine the system response y(t) for h(t)=u(t)tu(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: C[x(t) *h(t)) = X(s)H(s). y(t) = tu(t)-(t +2)u(t + 2) y(t) = tu(t) + (t - 2)u(t + 2) y(t) = tu(t) + (t - 2)u(t - 2) y(t) = tu(t)-(t - 2)u(t - 2) Question 8 (10 points) What is the Fourier Transform of f(t) = 55(t - 1)? ew 5e-sw 5e-510 را که م
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...
1. [5 pts] Unilateral Laplace Transform. Use the unilateral Laplace transform to determine the response of the system described by the following differential equation with the given inputs and initial conditions:LaTeX: \frac{\rm d}{ {\rm d} t } y(t) + \ 10y(t) = \ 10x(t), d d t y ( t ) + 10 y ( t ) = 10 x ( t ) , LaTeX: y(0^-) = 1, x(t) u(t) = u(t). y ( 0 − ) = 1 ,...
Determine Laplace Transform of 8(t) = u(t – 2)u(t – 3) [hint: {[u(t)] :)] = :) Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
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
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...
Determine the Laplace transform of x(t) = t2 u(t – 1) (b) Use Laplace transform to solve the following differential equation for t ≥ 0. ? 2?(?) ?? 2 + 3 ??(?) ?? + 2?(?) = (? −? ????)?(?); ?(0) = 1; ??(0) ?? = −3
signal and system 8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2 8) By using Laplace transform determine the transfer function and the impulse response of the system with equation below. y) is the output and u) is the input to the system + 6 dt2