function y = tx(v,gev)

% Multiplication of the Toeplitz matrix T with a vector v.
% v:   the vector to be applied;
% gev: the eigenvalues of the circulant matrix
%      in which T is embedded, see A.3;
% y:   the result of the multiplication.

n = length(v);
y = zeros(2*n,1);
y(1:n) = v;

y = ifft(fft(y).*gev);
y = y(1:n);
if norm(imag(y)) < 1.0e-14 % check if y is real
   y = real(y);
end
