Problem 2 ( 50 points) You are given functions x(t) = u(t)-ut-1/2) and y(t) = e(ult)...
Problem 3, (25 pts) Consider the integral y(t)x(t) dr where x(t)-ult +1)-u(t -1) Find the Fourier transform Y(au) by using the differentiation and the integrati domain properties. Reduce your answer t o the simplest form possible as a function of sinc(u). sin(θ)sene-o siren Formulas: sine(θ)
Find the frqeuncy response and impulse response of the
system with the output y(t) for the next input x(t)
Please, Solve (a) and (c)
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it is Linear Systems Analysis class
1.4-1 Sketch the signals (a) u(t-5)-uſt-7)(b) uſt-5)+u(t-7) (c) lu(t-1)-ut-2)] (d) (t - 4)[u(t - 2) - uſt - 4)]
clear writing please and thank you
Problem 2. Given the PDE ut + uy = u? u(3,0) = g(x) for IER, >0, for ER. (a) Sketch the characteristic curve that passes through P(2,3) in the xt-plane. Find u(2,3) without using the exact solution ulit, t). (b) Use the method of characteristics to find the solution u(, t).
5.5 Starting with the Fourier transform pair 2 sin(S2) X(t) = u(t + 1) – ut - 1) = X(92) = S2 and using no integration, indicate the properties of the Fourier transform that will allow you to compute the Fourier transform of the following signals (do not find the Fourier transforms): (a) xz(t) = -u(t + 2) + 2u(t) – u(t – 2) (b) xz(t) = 2 sin(t)/t (C) X3 (t) = 2[u(t + 0.5) - ut - 0.5)]...
partial differential equations
EXERCISE 3.20 Consider the problem ut =u" + u for u(0,t) u(1, t) 0, u(x,0) f(x). ze(0, 1), t>0, Show that dt and conclude that Use this estimate to bound the difference between two solutions in terms of the difference between the initial functions. Does this problem have a unique solution for each initial function f?
EXERCISE 3.20 Consider the problem ut =u" + u for u(0,t) u(1, t) 0, u(x,0) f(x). ze(0, 1), t>0, Show that...
Problem # 3 [20 Points] Solve PDE: ut = uxx - u, 0 < x < 1, 0 < t < ∞ BCs: u(0, t)=0 u(1, t)=0 0 < t < ∞ IC: u(x, 0) = sin(πx), 0 ≤ x ≤ 1 directly by separation of variables without making any preliminary trans- formation. Does your solution agree with the solution you would obtain if transformation u(x, t)= e(caret)(-t) w(x, t) were made in advance?
Please help me solve this problem step by step
Consider the following signals: X(t) = e-4u(t). h(t) = e3t (ult – 2) – uſt – 8)). (a) Sketch h(t) and x(t). (b) Determine y(t) = h(t) * x(t). (c) Answer the following questions about the function y(t) you found on the previous page: (i) Is y(t) guaranteed to be equal to zero for any values of t? If so, which values of t? (ii) What does y(t) look like as...
8. (a) Find the Fourier transform of the signal by direct integration. f(t) = ((t-5)+e-Y(-5))u(t-5) (5 points) (b) Use the convolution theorem of Fourier transform, find the convolution of the following signals: (5 points) x(t) = 5e-4tu(t) and h(t) = 7e-3tu(t)
answer a and b only
Suppose that two continuous time signal are given by x(t) and v(t) as: x(t) = u(t) - 2u(t - 1) + u(t - 2) v(t) = u(t)- uſt - 1) Answer the following questions: (a) Plot signals x(t) and v(t). (b) Find the convolution of y(t) = x(t-3) = v(t) (c) Plot for y(t).