A second order s-to-z transform and its implementation to IIR filter design

2014 ◽  
Vol 33 (5) ◽  
pp. 1831-1843 ◽  
Author(s):  
Dejan Mirković ◽  
Predrag Petković ◽  
Vančo Litovski
Keyword(s):  
Digital Filters ◽  
Group Delay ◽  
Transfer Functions ◽  
Filter Design ◽  
Second Order ◽  
Pass Band ◽  
Content Type ◽  
Iir Filter ◽  
Band Group ◽  
Iir Digital Filters

Purpose – The purpose of this paper is to design a tool for IIR digital filters obtained from analog prototypes, which preserves simultaneously the amplitude and the group delay response. Design/methodology/approach – A new s-to-z transform is developed based on a second order formula used for numerical integration of differential equations. Stability of the newly obtained transfer functions in the z-domain is proved to be preserved. Distortions introduced by the new transform into the original amplitude and group delay responses are studied. Findings – The new formula, when implemented to all-pole prototypes, exhibits lower selectivity than the original while reducing the pass-band group delay distortions. In the same time its structure is importantly simpler than the functions obtained by the well-known bilinear transform. When implemented to a prototype having “all kinds” of transmission zeros the resulting filter has almost ideally the same characteristic as the prototype. Research limitations/implications – The new transform may be used exclusively to synthesize even order filters. The new function is twice the order of the analog prototype. This kind of transformations are used to design IIR digital filters only. Low-pass transfer functions were studied being prototypes for all other cases. Originality/value – This is a new result never mentioned in the literature. Its effectiveness is confined to a niche problem when simultaneous sharp selectivity and low group delay distortions are sought.

Low computation digital down converter using polyphase IIR filter

Circuit World ◽  
2019 ◽  
Vol 45 (3) ◽  
pp. 169-178 ◽  
Author(s):  
Hiren K. Mewada ◽  
Jitendra Chaudhari
Keyword(s):  
Group Delay ◽  
Filter Design ◽  
Fir Filter ◽  
Linear Phase ◽  
Content Type ◽  
Iir Filters ◽  
Iir Filter ◽  
Alternative Option ◽  
Digital Down Converter ◽  
Sample Rate

Purpose The digital down converter (DDC) is a principal component in modern communication systems. The DDC process traditionally entails quadrature down conversion, bandwidth reducing filters and commensurate sample rate reduction. To avoid group delay, distortion linear phase FIR filters are used in the DDC. The filter performance specifications related to deep stopband attenuation, small in-band ripple and narrow transition bandwidth lead to filters with a large number of coefficients. To reduce the computational workload of the filtering process, filtering is often performed as a two-stage process, the first stage being a down sampling Hoegenauer (or cascade-integrated comb) filter and a reduced sample rate FIR filter. An alternative option is an M-Path polyphase partition of a band cantered FIR filter. Even though IIR filters offer reduced workload to implement a specific filtering task, the authors avoid using them because of their poor group delay characteristics. This paper aims to propose the design of M-path, approximately linear phase IIR filters as an alternative option to the M-path FIR filter. Design/methodology/approach Two filter designs are presented in the paper. The first approach uses linear phase IIR low pass structure to reduce the filter’s coefficient. Whereas the second approach uses multipath polyphase structure to design approximately linear phase IIR filter in DDC. Findings The authors have compared the performance and workload of the proposed polyphase structured IIR filters with state-of-the-art filter design used in DDC. The proposed design is seen to satisfy tight design specification with a significant reduction in arithmetic operations and required power consumption. Originality/value The proposed design is an alternate solution to the M-path polyphase FIR filter offering very less number of coefficients in the filter design. Proposed DDC using polyphase structured IIR filter satisfies the requirement of linear phase with the least number of computation cost in comparison with other DDC structure.

scholarly journals Comparison of Circular Symmetric Low-Pass Digital IIR Filter Design Using Evolutionary Computation Techniques

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1226 ◽  
Author(s):  
Omar Avalos ◽  
Erik Cuevas ◽  
Jorge Gálvez ◽  
Essam H. Houssein ◽  
Kashif Hussain
Keyword(s):  
Evolutionary Computation ◽  
Transfer Functions ◽  
Filter Design ◽  
Statistical Treatment ◽  
Optimization Methods ◽  
Intelligence Community ◽  
Infinite Impulse Response ◽  
Iir Filters ◽  
Iir Filter ◽  
Wide Range

The design of two-dimensional Infinite Impulse Response (2D-IIR) filters has recently attracted attention in several areas of engineering because of their wide range of applications. Synthesizing a user-defined filter in a 2D-IIR structure can be interpreted as an optimization problem. However, since 2D-IIR filters can easily produce unstable transfer functions, they tend to compose multimodal error surfaces, which are computationally difficult to optimize. On the other hand, Evolutionary Computation (EC) algorithms are well-known global optimization methods with the capacity to explore complex search spaces for a suitable solution. Every EC technique holds distinctive attributes to properly satisfy particular requirements of specific problems. Hence, a particular EC algorithm is not able to solve all problems adequately. To determine the advantages and flaws of EC techniques, their correct evaluation is a critical task in the computational intelligence community. Furthermore, EC algorithms are stochastic processes with random operations. Under such conditions, for obtaining significant conclusions, appropriate statistical methods must be considered. Although several comparisons among EC methods have been reported in the literature, their conclusions are based on a set of synthetic functions, without considering the context of the problem or appropriate statistical treatment. This paper presents a comparative study of various EC techniques currently in use employed for designing 2D-IIR digital filters. The results of several experiments are presented and statistically analyzed.

Digital Stable IIR Band Pass Filter Design Using Seeker Optimization Technique

2014 ◽  
Vol 905 ◽  
pp. 406-410 ◽  
Author(s):  
S.K. Saha ◽  
Rajib Kar ◽  
D. Mandal ◽  
S.P. Ghoshal
Keyword(s):  
Filter Design ◽  
Fitness Function ◽  
Stop Band ◽  
Infinite Impulse Response ◽  
Pass Band ◽  
Band Pass Filter ◽  
Pass Filter ◽  
Iir Filter ◽  
Real Coded Genetic Algorithm ◽  
Band Pass

This paper presents a novel, control parameter independent evolutionary search technique known as Seeker Optimization Algorithm (SOA) for the design of a eighth order Infinite Impulse Response (IIR) Band Pass (BP) filter. A new fitness function has also been adopted in this paper to improve the stop band attenuation to a great extent. The performance of the SOA based IIR BP filter design has proven to be much superior as compared to those obtained by real coded genetic algorithm (RGA) and standard particle swarm optimization (PSO) in terms of highest sharpness at cut-off, smallest pass band ripple, highest stop band attenuation, smallest stop band ripple and also the fastest convergence speed with assured stability recognized by the pole-zero analysis of the designed optimized IIR filter.

Performance assessment of controller designed for electrical systems with second order dynamics

2020 ◽  
Vol 39 (6) ◽  
pp. 1345-1362
Author(s):  
K. Ghousiya Begum
Keyword(s):  
Design Methodology ◽  
Transfer Functions ◽  
Direct Synthesis ◽  
Synthesis Method ◽  
Second Order ◽  
Reference Tracking ◽  
Content Type ◽  
Electrical Systems ◽  
Error Index ◽  
Index Value

Purpose An assessment technique that analyzes the servo and regulatory characteristics of the proportional integral derivative controller is designed for time-delayed second-order stable processes. Design/methodology/approach The minimum theoretical error expression for integral of the absolute errors (IAE_o) is obtained from the preferred servo and regulatory transfer functions dependent on the step changes in reference and load variables. Findings The error-based index is outlined to estimate the controller that is derived using internal model-based control or direct synthesis method. The ratio between derived IAE_o and the IAE_actual gained from the loop response that experiences step input variations gives rise to a dimensionless error index. This error index measures the behaviour of the controller by considering the index value. If the error index value is larger than 0.8, then the effort taken by the controller is good or else retuning is expected. Originality/value The efficacy of the index to validate the controller is verified by applying on a few second-order electrical processes. The results are simulated for both reference tracking and load rejection tasks to demonstrate the rationality of the presented index.

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