quadinv

 calculates the quadratic inverse eigenvectors

 Input
 N: number of samples
 NW: time-bandwidth product

 Output
 V: The quadratic inverse eigenvectors
 E: the quadratic inverse eigenvalues

0001 function [V,E] = quadinv(N,NW)
0002 
0003 % calculates the quadratic inverse eigenvectors
0004 %
0005 % Input
0006 % N: number of samples
0007 % NW: time-bandwidth product
0008 %
0009 % Output
0010 % V: The quadratic inverse eigenvectors
0011 % E: the quadratic inverse eigenvalues
0012 
0013 
0014 x = 0:N-1;
0015 indx = find(x);
0016 y = ones(size(x))*(2*NW/N)^2;
0017 
0018 y(indx) = (sin(2*pi*NW*x(indx)/N)./(pi*x(indx))).^2;
0019 
0020 M = toeplitz(y);
0021 [C,D] = eig(N*M);
0022 
0023 tmp = diag(D);
0024 
0025 K = 4*NW;
0026 
0027 V = sqrt(N)*C(:,N:-1:N-K+1);
0028 
0029 E = tmp(N:-1:N-K+1);
0030 
0031 for ii =1:K
0032   if(sum((N-1-2*x)'.*V(:,ii))<0)
0033     V(:,ii) = flipud(V(:,ii));
0034   end;
0035 end;
0036 
0037 return;