Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2000 • Question 7

Question

Math 6420 • PDE Fall 2000 • Question 7

  1. Find the Fourier transform of \(\dfrac {\sin x}{x}\).
  2. Suppose that the Fourier transform of the function \(f(t)\) is 0 for frequencies whose absolute value is greater than \(\pi /h\). Find the representation of \(f(t)\) in terms of sinc functions.

Raw LaTeX

\begin{enumerate}
\item[(a)] Find the Fourier transform of \(\dfrac{\sin x}{x}\).
\item[(b)] Suppose that the Fourier transform of the function \(f(t)\) is 0 for frequencies
whose absolute value is greater than \(\pi/h\). Find the representation of \(f(t)\) in terms of
sinc functions.
\end{enumerate}

Topic Tags

Absolute Stability and A-Stability Adjoint Operators and Riesz Representation Fourier Transform and Sampling Theory Linear Programming and Optimization