Please show full solution and explanation
Consider the following two functions h (t) and f (t).

and

(a) Plot h(t) and f(t).
(b)Use the convolution integral to calculate the convolution g (t) of the function h (t) with f (t) and plot.

Please show full solution and explanation Consider the following two functions h (t) and f (t)....
t?, t<3 . Express the function f(t) = le4t, 3St<5 In terms of unit step functions and compute it's Laplace transform
solve with steps and please write as clear as possible.
Determine, analytically, the convolution y(t)-r(t) * h(t), where a(t)0, otherwise, and h(t) 1, 1<t < 3 o, otherwise.
Suppose that X has the probability density function f(x) = { 2x 0 < x < 1 0 otherwise Which of the following is the moment generating function of X? 2 et t 2 et t2 2 t2 O t2 2 eet t 2 ett t2 t e eut-1 t
Find the Laplace transform of the given function
Solve the integral equation
f(t) = { 0 < t < 2 t 22 t y(t) = 4t – 3 y(z)sin(t – z)dz 0
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
3. Consider the function f(t) = ' π2 , with f(t) = f(t +2r). 0<t<π (a) Sketch f(t) by hand for-3r < t < 3T. (b) Determine the general Fourier Series for f(t). (c) Use MATLAB to plot f(t) and the n = 4 Fourier series representation on the same set of axes for -t<T
Integral Transform
Find the Laplace transform for the periodic function f(t) = f(t+2) and f(t) = t for 0 <t< 2.
(a) Show that the functions f(t) = t2t1 and g(t) = t3 are linearly dependent on 0 < t < 1 and on -1<t< 0 (b) Show that f(t) and g(t) are linearly independent on -1 <t<1. (c) Show that W(f,g)(t) is zero for all -1<t<1.
Please help me solve this differential Equation
show all steps
Find a continuous solution satisfying +y-f(x), where f() Ji 10 { 0<r<1 > 1 and y(0) -0.
2. Consider the function 3 I < (a) Find the Laplace transform of f by direetly using the integral definition of a Laplace transform. (b) Write f in es of step functions, and use the t-shiting theorem to find the Laplace transform of f. (c) Use MATLAB to find the Laplace transform of f