Recent contributions showed the benefits of operatorfiltering for both preconditioning and fast solution strategies.While previous contributions leveraged laplacian-based filters, inthis work we introduce and study a different approach leveragingthe truncation of appropriately chosen spectral representationsof operators’ kernels. In this contribution, the technique isapplied to the operators of the 2D TE- and TM-electric fieldintegral equations (EFIE). We explore two different spectralrepresentations for the 2D Green’s function that lead to twodistinct types of filtering of the EFIE operators. Numerical resultscorroborate the effectiveness of the newly proposed approaches,also in the Calderón preconditioned EFIE.