# Mathematics of Signal Representations

## Math 4355 - Spring 2013 - Homework

**Assignment 9, due Thursday, April 11**

- Review Sections 3.1, up to and including 3.1.3. To motivate two
of the
exercises, read 3.1.5. Familiarize yourself with the fft function
in Matlab. The indices do NOT run from 0 to n-1 as in the book (or
in class)! If x is a vector
of length N, then X=fft(x) is given by

with
.

- Do exercises on p.156: 4 (just plot the function in (3.8) specified by
the values of a,b,c, f
_{0}); 5 (compare the frequency with
maximal value with
the one appearing in the definition of u in (3.8)); 7; 14 (a), (b) and in (c), only find the
eigenvalues and eigenvectors of M_{4}. If you cannot find them
analytically, use Matlab. How are the eigenvectors related to the matrix
F_{4} defined as in (3.2) on page 135?