A subsection of the radiating spiral arm, placed in parallel, induces a bandstop response at a notch frequency proportional to the resonant length of the strip. Detailed parametric study on the effect of variation of design parameters for an Archimedean spiral antenna and the resonant parallel strip (RPS) is presented. Empirical analysis on phase velocity on the radiating spiral arms allows characterization of RPS in terms of its resonant length. Identified systematic relation between design parameters and filter response is applied to design an antenna for the 3.1-10.5 GHz operating band with the notch response over the IEEE 802.11a band, 5.15-5.95 GHz. Successful implementation is demonstrated through performance comparison between simulated and experimental results.