Multidimensional Signal and Color Image Processing Using Lattices

10Analysis and Design of Multidimensional FIR Filters

10.1 Introduction

This chapter presents and analyzes a number of examples of multidimensional discrete‐domain FIR filters that are often used, along with some issues of design. As discussed in Section 3.8, an FIR filter has a unit‐sample response that is zero outside of a finite set of sample locations . The frequency response is given by the finite sum

(10.1)

It is periodic, with one period given by any unit cell of the reciprocal lattice . Filter design often involves finding the filter unit‐sample response such that the frequency response meets certain requirements or specifications. We first start with a few ad hoc designs that are widely used.

10.2 Moving Average Filters

The moving average filter simply takes the average of the pixel values over the region shifted to the output point ,

(10.2)

where denotes the number of elements ...