A waveguide-based wide free-spectral-range (FSR) triple ring resonator (TRR) as an optical filter has been investigated in this article. The transmittance of the TRR is presented in Z-domain. The delay line signal processing approach and Mason's gain formula have been used to develop the transmittance of the TRR. The TRR in the article is capable of providing an FSR up to 605 GHz with lower crosstalk limited within -10 dB. Another efficacious scheme of TRR with much wider FSR of 1029 GHz and with reduced unit delay length is presented in the article. Here also crosstalk, as well as resonance loss, remains within reasonable limits. The FSRs obtained using the present TRR architectures in this work are until now reported as maximum for a corresponding class of optical ring resonators. The issues of group delay and dispersion, two important parameters associated with high frequency optical communication have been addressed in this article.