Design and Analysis of Finite/Infinite Impulse Response Optical Filter for Signal Processing

The key to analyzing the optical filter using z-transform is that each delay be an integer multiple of a unit delay length. A coupler is just the point where two paths (wave guide) are brought together so that their evanescent field overlap and a power transfer from one port to other exist. The lattice structures allow a systematic approach to filter synthesis. They are suitable forms for performing the various signal processing operations. Compared to other forms, lattice structure has some advantageous characteristics. Recirculating/infinite impulse response (feed-backward) and nonrecirculating/finite impulse response (feed-forward) delay line are two structures that are basic to fiber-optic signal processing. Similarly, we can form the system consist of many more coupler system. In this paper we have analyzed the response of each combination. Later on we try to connect the z-transform domain into Laplace by replacing z=e^sT. By replacing the z by the expansion of e^sT for some number of elements we can obtain the similar types of response to check the validity of our approximations. Here in s-domain we can easily apply control theory concepts on these transfer formulas. In the end we have tried to obtain the time domain response of filter by using the z approximation in s.