Mathematics of Signal Representations

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, f₀); 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 M₄. If you cannot find them analytically, use Matlab. How are the eigenvectors related to the matrix F₄ defined as in (3.2) on page 135?