Efficient Realizations of Wide-Band and Reconfigurable FIR Systems

Abstract: 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 require?exibility considerations in the design which imply recon?gurable systems, wherethe system is designed in such a way that it needs no hardware modi?cationsfor changing various system parameters. The thesis focuses on these aspects ofdesign and can be divided into four parts.The ?rst part deals with complexity reduction for non-frequency selectivesystems, like di?erentiators 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 selective?lters. Existing frequency response masking techniques are limited in a sensethat they target only frequency selective ?lters, and therefore are not applicabledirectly for non-frequency selective ?lters. However, the proposed approachesmake the use of frequency response masking technique feasible for the non-frequency ?lters as well.The second part of the thesis addresses another issue of digital system designfrom the recon?gurability perspective, where provision of ?exibility in the designof digital systems at the algorithmic level is more bene?cial than at any otherlevel of abstraction. A linear programming (minimax) based technique forthe coe?cient decimation FIR (?nite-length impulse response) ?lter design isproposed in this part of thesis. The coe?cient decimation design method ?ndsuse in communication system designs in the context of dynamic spectrum accessand in channel adaptation for software de?ned radio, where requirements can bemore appropriately ful?lled by a recon?gurable channelizer ?lter. The proposedtechnique provides more design margin compared to the existing method whichcan in turn can be traded o? for complexity reduction, optimal use of guardbands, more attenuation, etc.The third part of thesis is related to complexity reduction in frequencyselective ?lters. In context of frequency selective ?lters, conventional narrow-band and wide-band frequency response masking ?lters are focused, where variousoptimization based techniques are proposed for designs having a small number ofnon-zero ?lter coe?cients. The use of mixed integer linear programming (MILP)shows interesting results for low-complexity solutions in terms of sparse andnon-periodic sub?lters.Finally, the fourth part of the thesis deals with order estimation of digitaldi?erentiators. Integral degree and fractional degree digital di?erentiators areused in this thesis work as representative systems for the non-frequency selective?lters. The thesis contains a minimax criteria based curve-?tting approach fororder estimation of linear-phase FIR digital di?erentiators of integral degree upto four.