  The capacitance of capacitive energy storage devices can not be directly
measured, but can be estimated from the input and output signals expressed in
the time or frequency domains. Here the time-domain voltage-charge relationship
in non-ideal electrochemical capacitors is treated as an ill-conditioned
convolution integral equation where the unknown capacitance kernel function is
to be found. This comes from assuming \emph{a priori} that in the frequency
domain the charge is equal to the product of capacitance by voltage. The
computation of a stable solution to this problem particularly when dealing with
experimental data is highly sensitive to noise as it may lead to an oscillating
output even in the presence of small errors in the measurements. In this work,
the problem is treated using Tikhonov's regularization method, where a degree
of damping is added to each singular value decomposition (SVD) component of the
solution, thus effectively filtering out the components corresponding to the
small singular values.
