Design of minimum-phase finite-impulse-response digital filters

Digital filters play a central role in modern Digital Signal Processing (DSP) systems. Finite Impulse Response (FIR) filters can provide solutions with guaranteed stability and linear phase. However, the main disadvantage of conventional FIR filter designs is that they become computationally complex, especially in applications demanding narrow transition bandwidths. Therefore, designing FIR filters with very stringent specifications and a low complexity is currently an important challenge. In this chapter, a review of the recent methods to efficiently design low-complexity linear-phase FIR filters is presented. The chapter starts with an introduction to linear-phase FIR digital filters. Then, an overview of the design methods that have been developed in literature to design low-complexity FIR filters is presented. Finally, the most common and recent of these methods along with their corresponding special structures are explained.

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Design and Applications of Digital Filters

Encyclopedia of Information Science and Technology, Second Edition ◽

10.4018/978-1-60566-026-4.ch162 ◽

2011 ◽

pp. 1016-1023

Author(s):

Gordana Jovanovic Dolecek

Keyword(s):

Impulse Response ◽

Digital Filters ◽

Finite Impulse Response ◽

High Reliability ◽

Rapid Development ◽

Digital Signal ◽

Infinite Impulse Response ◽

Iir Filters ◽

Circuit Fabrication ◽

Analog Systems

Digital signal processing (DSP) is an area of engineering that “has seen explosive growth during the past three decades” (Mitra, 2005). Its rapid development is a result of significant advances in digital computer technology and integrated circuit fabrication (Jovanovic Dolecek, 2002; Smith, 2002). Diniz, da Silva, and Netto (2002) state that “the main advantages of digital systems relative to analog systems are high reliability, suitability for modifying the system’s characteristics, and low cost”. The main DSP operation is digital signal filtering, that is, the change of the characteristics of an input digital signal into an output digital signal with more desirable properties. The systems that perform this task are called digital filters. The applications of digital filters include the removal of the noise or interference, passing of certain frequency components and rejection of others, shaping of the signal spectrum, and so forth (Ifeachor & Jervis, 2001; Lyons, 2004; White, 2000). Digital filters are divided into finite impulse response (FIR) and infinite impulse response (IIR) filters. FIR digital filters are often preferred over IIR filters because of their attractive properties, such as linear phase, stability, and the absence of the limit cycle (Diniz, da Silva & Netto, 2002; Mitra, 2005). The main disadvantage of FIR filters is that they involve a higher degree of computational complexity compared to IIR filters with equivalent magnitude response (Mitra, 2005; Stein, 2000).

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FPGA-based Implementation of IIR Filter for Real-Time Noise Reduction in Signal

Journal of Natural Sciences and Engineering ◽

10.14706/jonsae2021316 ◽

2021 ◽

Vol 3 (1) ◽

Author(s):

Aladin Kapić ◽

Rijad Sarić ◽

Slobodan Lubura ◽

Dejan Jokić

Keyword(s):

Transfer Function ◽

Impulse Response ◽

Discrete Time ◽

Time Domain ◽

Digital Filters ◽

Finite Impulse Response ◽

Infinite Impulse Response ◽

Main Role ◽

Digital Implementation ◽

Iir Filter

Filtering of unwanted frequencies represents the main aspect of digital signal processing (DSP) in any modern communication system. The main role of the filter is to perform attenuation of certain frequencies and pass only frequencies of interest. In a DSP system, sampled or discrete-time signals are processed by digital filters using different mathematical operations. Digital filters are commonly categorized as Finite Impulse Response (FIR) and Infinite Impulse Response (IIR). This research focuses on the full VHDL implementation of digital second-order lowpass IIR filter for reducing the noisy frequencies on the FPGA board. The initial step is to determine, from continuous time domain function, the transfer function in the complex {s} domain, then map transfer function in complex {z} domain and finally calculate the difference equation in discrete-time domain of the system with adequate coefficients. Prior to the FPGA implementation, the IIR filter is tested in MATLAB using a signal with mixed frequencies and signal with randomly generated noise. The digital implementation is completed by using fixed-point binary vectors and clocked processes.

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Theory of the Design, and Operation of Digital Filters

10.1093/oso/9780198860792.003.0016 ◽

2021 ◽

pp. 797-823

Author(s):

Stevan Berber

Keyword(s):

Impulse Response ◽

Digital Filters ◽

Finite Impulse Response ◽

Transformation Method ◽

Infinite Impulse Response ◽

Bilinear Transformation ◽

Finite Impulse Response Filters ◽

Infinite Impulse Response Filters ◽

Basic Characteristics ◽

Impulse Response Filters

Chapter 16 present the theoretical basis for digital filters, including issues related to their design. The basic characteristics and structures of finite impulse response and infinite impulse response filters are presented and discussed. In addition, the ideal and practical transfer characteristics of the digital filters are defined. The basic advantage of finite impulse response filters is that they can be designed to have an exact linear phase. However, infinite impulse response filters are generally more efficient computationally. The methods for filters design and related algorithms, which are based on the bilinear transformation method, windowed Fourier series, and algorithms based on iterative optimization, are also presented.

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