Optical Filter Design and Analysis: A Signal Processing Approach

CHAPTER THREE

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 trun 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. The optical counterparts to these architectures are discussed in Chapters 4–6. For an in depth treatment of digital signal processing and digital filters, we refer the reader to texts such as [1–3,27–29].

3.1 LINEAR TIME-INVARIANT SYSTEMS

Filters, whether digital or optical, operate on an input signal to produce an output signal. The input and output signals may be functions of time or space ...