Answer to Quiz 12 Fri 27 Apr 2007

1. Take two random vectors x and y of length 10. (use rand). Multiply their FFT transform componentwise and apply the inverse FFT transform to the result. Compare the last coefficient in the result with the 10-th entry in conv(x,y).
   Give all relevant MATLAB commands you used.

   Answer:

          x = rand(1,10);  y = rand(1,10);
          fx = fft(x);     fy = fft(y);
          fz = fx .* fy;
          z1 = conv(x,y);
          z2 = ifft(fz);
          z1(10) - z2(10)
   

2. Give all MATLAB commands to create a sparse 100-by-100 matrix of the form

       
           1   2   3   ...  100 
           2   1   0   ...   0 
           3   0   1   ...   0
           :   :   :         :
          100  0   0   ...   1 
   

   Answer:

           i = [1:100};
           e = ones(1,100);
           a = sparse(i,i,e);
           b = sparse(e,i,i);
           m = a + b + a';
           m(1,1) = 1;