Digital Filter Concepts for Optical Filters

In this chapter, we present digital filter concepts along with comparisons between digital and optical filters. The advantage of relating digital and optical filters is that numerous algorithms developed for digital filters can be used to design optical filters. Linear system theory is the foundation for analyzing signals in the time and frequency domains, and is reviewed first for both continuous and discrete signals. Then, we introduce the following three major filter classes: moving average (MA), autoregressive (AR) and autoregressive moving average (ARMA) filters. The filter magnitude, group delay and dispersion are given in terms of the Z-transform description. Single-stage optical filters are introduced next along with their Z-transform descriptions. Then, we turn out attention to multi-stage filters, which are required to closely approximate a desired magnitude or phase response. Examples of digital filter design techniques are given for each filter class, and an overview of multi-stage digital filter architectures is presented.