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A Class of Wide-Band Linear-Phase FIR Differentiators Using a Two-Rate Approach and the Frequency-Response Masking Technique
Linköping University, Department of Electrical Engineering, Electronics System. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Electronics System. Linköping University, The Institute of Technology.
2011 (English)In: IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, ISSN 1549-8328, Vol. 58, no 8, 1827-1839 p.Article in journal (Refereed) Published
Abstract [en]

This paper introduces a class of wide-band linear-phase finite-length impulse response (FIR) differentiators. It is based on two-rate and frequency-response masking techniques. It is shown how to use these techniques to obtain all four types of linear-phase FIR differentiators. Design examples demonstrate that differentiators in this class can achieve substantial savings in arithmetic complexity in comparison with conventional direct-form linear-phase FIR differentiators. The savings achievable depend on the bandwidth and increase with increasing bandwidth beyond the break-even points which are in the neighborhood of 90% (80%) of the whole bandwidth for Type II and III (Type I and IV) differentiators. The price to pay for the savings is a moderate increase in the delay and number of delay elements. Further, in terms of structural arithmetic operations, the proposed filters are comparable to filters based on piecewise-polynomial impulse responses. The advantage of the proposed filters is that they can be implemented using non-recursive structures as opposed to the polynomial-based filters which are implemented with recursive structures.

Place, publisher, year, edition, pages
IEEE Press, 2011. Vol. 58, no 8, 1827-1839 p.
Keyword [en]
Differentiators, linear-phase FIR differentiators, minimax design, wide-band differentiators
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-70226DOI: 10.1109/TCSI.2011.2107270ISI: 000293713100013OAI: diva2:436994
Available from: 2011-08-26 Created: 2011-08-26 Last updated: 2012-02-16Bibliographically approved
In thesis
1. Efficient Realizations of Wide-Band and Reconfigurable FIR Systems
Open this publication in new window or tab >>Efficient Realizations of Wide-Band and Reconfigurable FIR Systems
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Complexity reduction is one of the major issues in today’s digital system designfor many obvious reasons, e.g., reduction in area, reduced power consumption,and high throughput. Similarly, dynamically adaptable digital systems requireflexibility considerations in the design which imply reconfigurable systems, wherethe system is designed in such a way that it needs no hardware modificationsfor changing various system parameters. The thesis focuses on these aspects ofdesign and can be divided into four parts.

The first part deals with complexity reduction for non-frequency selectivesystems, like differentiators and integrators. As the design of digital processingsystems have their own challenges when various systems are translated from theanalog to the digital domain. One such problem is that of high computationalcomplexity when the digital systems are intended to be designed for nearly fullcoverage of the Nyquist band, and thus having one or several narrow don’t-carebands. Such systems can be divided in three categories namely left-band systems,right-band systems and mid-band systems. In this thesis, both single-rate andmulti-rate approaches together with frequency-response masking techniques areused to handle the problem of complexity reduction in non-frequency selectivefilters. Existing frequency response masking techniques are limited in a sensethat they target only frequency selective filters, and therefore are not applicabledirectly for non-frequency selective filters. However, the proposed approachesmake the use of frequency response masking technique feasible for the non-frequency filters as well.

The second part of the thesis addresses another issue of digital system designfrom the reconfigurability perspective, where provision of flexibility in the designof digital systems at the algorithmic level is more beneficial than at any otherlevel of abstraction. A linear programming (minimax) based technique forthe coefficient decimation FIR (finite-length impulse response) filter design isproposed in this part of thesis. The coefficient decimation design method findsuse in communication system designs in the context of dynamic spectrum accessand in channel adaptation for software defined radio, where requirements can bemore appropriately fulfilled by a reconfigurable channelizer filter. The proposedtechnique provides more design margin compared to the existing method whichcan in turn can be traded off for complexity reduction, optimal use of guardbands, more attenuation, etc.

The third part of thesis is related to complexity reduction in frequencyselective filters. In context of frequency selective filters, conventional narrow-band and wide-band frequency response masking filters are focused, where variousoptimization based techniques are proposed for designs having a small number ofnon-zero filter coefficients. The use of mixed integer linear programming (MILP)shows interesting results for low-complexity solutions in terms of sparse andnon-periodic subfilters.

Finally, the fourth part of the thesis deals with order estimation of digitaldifferentiators. Integral degree and fractional degree digital differentiators areused in this thesis work as representative systems for the non-frequency selectivefilters. The thesis contains a minimax criteria based curve-fitting approach fororder estimation of linear-phase FIR digital differentiators of integral degree upto four.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. 47 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1424
National Category
Signal Processing
urn:nbn:se:liu:diva-74796 (URN)978-91-7519-972-6 (ISBN)
Public defence
2012-03-08, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 20:03 (English)
Available from: 2012-02-16 Created: 2012-02-08 Last updated: 2015-03-11Bibliographically approved

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