This assignment is to use Matlab on a few simple tasks.

To complete this assignment, you will need the following files:
   Ab.dat  
   strass.m  
   H.dat  
   G.dat  
   y.dat  
You can get them from the Web page, or directly from my public ftp 
directory on science, /usr/pub/jgentle/csi801.
(Or anonymous ftp, then cd jgentle/csi801)

1. The data in the file Ab.dat represent an overdetermined system of  
   linear equations.  The first three columns are the coefficient matrix A  
   and the last column is the right-hand side b.  Extract the coefficient  
   matrix and the right-hand side into appropriate matrices, and then  
   solve the system A*x = b in the least squares sense.  (If you do not   
   know the expression for the LS solution, use elementary calculus to  
   determine a minimum of (b-A*x)'*(b-A*x).)  
   Print the solution, x.  
  
2. A fast way to multiply large matrices is the so-called Strassen  
   algorithm.    
   Retrieve the m-file strass.m, and apply it to the two matrices H and G  
   in H.dat and G.dat.  The m-file strass.m uses recursion.  When it  
   uses Strassen's algorithm, it requires the matrices  
   to have even dimension, but it will use conventional multiplication  
   for matrices smaller than a user-supplied size.  
   Print the (1,1) element and the (n,n) element in your solution, and  
   also print the value of nmin you used.  
  
3. Write an m-file for a function to do a bubble sort.  The function  
   should be called bubble (the file is bubble.m).  The function should  
   be invoked by   
     y = bubble(x)  
   (So that should be the first line of your bubble.m file; cf strass.m.)  
   Print your m-file.  
  
4. Retrieve the signal stored in y.dat.  This is a single channel noisy  
   signal that was sampled at 1000Hz.  It consists of two apparent   
   sinusoids.  Plot the signal (Just use plot(y).)  
   Now let's use a tenth-order lowpass Butterworth filter with a cutoff  
   frequency of 80 Hz to look at the signal further.  Do this by  
     [bb, aa] = butter(10, 80/500)  % normalize by the Nyquist frequency  
     z = filter(bb, aa, y)          %    (half the sample frequency)  
   Now plot z.    
   To see it better, now plot only the first 100 elements of z.  
   Print the number of peaks you see in the first 100 elements of z.