Find the inverse Laplace transform of e-2s 8 - s2 о (1 - е')u(2 — t) О (1- e-?)(1 - и(t - 2)) O (1- et-2)u(t – 2) O (1- e')u(t – 2) O (1– et-2)

Q: 1. Let F : L² (R¹) → L²(R¹) be the Fourier transform. That is: 1 F(f) = = √e-i(+1) e-i(x,x) f(x) dx.…

A: Problem is solved using concept of Fourier Transform.

Q: Find the Fourier transform of 8(t+2) + 8(t – 2).

A:

Q: 2. (a) Show that gi(t)g2(t) G₁(f) * G₂(f) where denotes convolution and gi(t) = G₁(f), 92(t)=G₂(f).…

A: We start with the time-domain signals and their Fourier transforms:Now, the convolution in the time…

Q: Find the given inverse transform (1) c{ (i) L-1 s2 + 6s + 1 1 1 (ii) L-1 |(s – 1)3 ™ s² + 2s – 8

A: The Laplace transform of a function f(t) is defined as Lf(t)=∫0∞e-stf(t)dt. If F(s) is the Laplace…

Q: Show that x(t) * u(t) x(t)dt %3D and find its Fourier transform.

A:

Q: The Fourier Transform of * x(t) = [u(t)-u(t-2)][u(t) – u(t − 1)] 8(t - 0.5) cos(2πt) - O exp(j0.5w)…

A:

Q: 1 1 1 1 1 (z + 1)(z + 3) z +4 (z + 1)(z + 3) 1 1 2 z + 1 2 z + 3 3 1 1 1 2 z + 1 2 z +3' 1 1 1 1 +…

A: By using partial fraction method we solve the required problem as follows :

Q: 3. Find the inverse Laplace transform. a) 8s2 − 4s + 12/s(s2 + 4)

A:

Q: the Inverse Fourier Transform x(t) of each signal X(w) given below. X(w) = -4 sinc² X(w) = πd(w − 1)…

A: "Since you have posted multiple questions, we will provide the solution only to the specified sub…