a) Derive the Fourier integral representation of $f(x) = \begin{cases…
Previous year question for Numerical Methods & Transform Calculus.
Question
a) Derive the Fourier integral representation of $f(x) = \begin{cases} 10, & 0 \le x \le 3 \\ 5, & 6 \le x \le 9 \\ 0, & \text{otherwise} \end{cases}$ at which points, if any, does the Fourier integral fail to converge to $f(x)$? To what value, does the integral converge at those points?
b) State and prove convolution property for Fourier transforms.
c) Using Laplace transform techniques, evaluate $\int\limits_{0}^{\infty} \frac{\sin^3 t}{t} dt$.
- Year: 2018
- Subject: Numerical Methods & Transform Calculus