Transformations for FIR and IIR Filters’ Design

V. N. Stavrou,Nikos E. Mastorakis,I. G. Tsoulos

doi:10.3390/sym13040533

Abstract

In this paper, the transfer functions related to one-dimensional (1-D) and two-dimensional (2-D) filters have been theoretically and numerically investigated. The finite impulse response (FIR), as well as the infinite impulse response (IIR) are the main 2-D filters which have been investigated. More specifically, methods like the Windows method, the bilinear transformation method, the design of 2-D filters from appropriate 1-D functions and the design of 2-D filters using optimization techniques have been presented.

Highlights

In the non-recursive filter structures the output depends only on the input, and in the recursive filter structures the output depends both on the input and on the previous outputs
The Recursive filters have been employed in science and technology for issues like signal processing, control signals, radar signals, astronomy signals, medical image processing and x-ray enhancements, among others
Finite Impulse Response (FIR) filters are the best choice for applications like adaptive filters, averaging filters, speech analysis, spatial beamforming, and multirate signal processing, among others

Summary

Introduction

There are two types of digital filters: the Finite Impulse Response (FIR) filters or NonRecursive filters and the Infinite Impulse Response (IIR) filters or Recursive filters [1,2,3,4,5]. The Recursive filters have been employed in science and technology for issues like signal processing, control signals, radar signals, astronomy signals, medical image processing and x-ray enhancements, among others. The Non-Recursive filters are almost everywhere in applications where phase linearity has to be ensured. FIR filters are the best choice for applications like adaptive filters, averaging filters, speech analysis, spatial beamforming (spatial filtering), and multirate signal processing, among others. Methods like the Windows and the Bilinear Transformation method have been used to design FIR and IIR digital filters.

Finite Impulse Response Filters and Infinite Impulse Response Filters

FIR Filters

IIR Filters

Direct Design of 2-D Filters from Appropriate 1-D Functions

Design of 2-D Filters Using Optimization Techniques

Conclusions