  Previous applications of the enclosure method with a finite set of
observation data to a mathematical model of electrical impedance tomography are
based on the assumption that the conductivity of the background body is
homogeneous and known. This paper considers the case when the conductivity is
homogeneous and unknown. It is shown that, in two dimensions if the domain
occupied by the background body is enclosed by an ellipse, then it is still
possible to extract some information about the location of unknown cavities or
inclusions embedded in the body without knowing the background conductivity
provided the Fourier series expansion of the voltage on the boundary does not
contain high frequency parts (band limited) and satisfies a non vanishing
condition of a quantity involving the Fourier coefficients.
