Application of Neural Network in Design of Digital Filters

5.1 INTRODUCTION Any action on a signal that modifies the spectral content of the signal is called filtering. This includes the enhancement or suppression of certain features of the signal and is usually achieved by the use of linear time invariant systems. There are situations where the system may change with time in a particular manner; such systems are called adaptive filters. In this section, we describe fixed filters only. There are two broad classes of digital filters. The first class is called finite impulse response (FIR) filters, since their response to an impulse dies away in a finite number of samples. FIR filters are developed as non-recursive structures and are inherently simpler to design. The second class of digital filters is recursive filters. The impulse responses of recursive filters are composed of sinusoids that exponentially decay in amplitude. This makes their impulse responses infinitely long. Because of this characteristic, recursive filters are called infinite impulse response (IIR) filters. An IIR filter can be represented by either difference equation or state space form. The state space form in general involves more numbers of coefficients than a transfer function unless it is represented as one of the canonical forms. Howev er, there are many benef its from using a state space model in the analysis, design, and implementation of digital filters. First, the state space model, with the exception of canonical structures, is more robust than a transfer function representation. In other words, it exhibits less coefficient sensitivity. Second, various forms of state space models possess distinctive properties that are desirable in different applications. For instance, the balanced realization exhibits superior performance in the context of minimizing scaling and round-off noise. Third, the major part of modern control theory is based on the state space model. Furthermore, the difference function representation could be uniquely determined by the state space form representation. The reverse is not necessarily true. In this chapter, the state space model will be utilized for the IIR filter design. In the above filter representations, all inputs, outputs or states are function of a single variable, which is time in most cases. We call these types of filters one-dimensional (1-D) filters. There are other types of filters in which the inputs, outputs and states are the function of more than one variable. One example is