  In the previous four decades, a two-coil mutual inductance (MI) technique has
been widely employed in characterizing magnetic penetration depth, $\lambda$,
of superconducting films. However, the conventional methods used to obtain
$\lambda$ are not applicable to small-sized films with common shapes, which
limits the application of the MI technique in superconductivity research. Here,
we first employed the fast wavelet collocation (FWC) method to a two-coil
system and then proposed the possibility of directly obtaining the absolute
$\lambda$ of polygonal superconducting films with arbitrary sizes. To verify
its accuracy and advantages, we extracted the $\lambda$ values of square NbN
films with different sizes using the FWC and conventional flux leakage
subtraction (FLS) methods. Notably, the FLS method fails for a $5\times 5 \,
\rm mm^2$ film, which is attributed to the significant current peak at the film
edge. In contrast, the absolute $\lambda$ extracted using the FWC method was
independent of the film size. Finally, we established the applicability of the
FWC method to large coil spacings, which may pave the way for integrating
high-accuracy $\lambda$ measurements with the ionic liquid gating technique.
