Find the fourier transform of the function

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Reference no: EM133199063

Advanced Mathematics

Learning Outcome 1: Find and apply Laplace Transforms and their inverse to solve differential and integral equations
Learning Outcome 2: Find the Fourier sine and Fourier cosine transforms of functions and its inverse.
Learning Outcome 3: Determine discrete Fourier Transform and inverse discrete Fourier transform of a function

Assignment Objective
To test the Knowledge and understanding of the student for the above mentioned LO. This includes testing of their knowledge on the procedure, computational ability and accuracy of steps on the topics mentioned in the LO.

Question 1. Find the Laplace transform of the following function:

f(t) = Me^Ntsin²(Mt) + Mt²cosh(3t) - M cos(Mt) sin(Nt)

Question 2. Compute the Inverse Laplace Transform of F(s) = Ms-N/(s+4)(s²+s-2) using partial fractions.

Question 3. a. Solve the following Initial value problem by using Laplace transforms:

y′ + by = (M - 9); y(0) = aM + 5

(Note: Where a is the sum of last two digits of your MEC Id number and b is the biggest number in your ID)

b. Let f(t) = t² - e-t and g(t) = t find (f ∗ g)(t)

Question 4. a. Find the Fourier transform of the function f(x) = { x             0 < x < M
                                                                           M - x       M < x < N
b. Find the Fourier sine transform of f(x) = {Nx² 0 < x < N
                                                              0    Otherwise

Question 5. If the Discrete Fourier Transform of the four point sequence {a, b, c, d} is given by {0, 2i, 0, 4i}, then find the points {a, b, c, d} by applying inverse Discrete Fourier transformation.

Reference no: EM133199063

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