2 nd Mediterranean Conference on Embedded Computing MECO - 2013 Budva, Montenegro Efficient Recursive Implementation of Multiplierless FIR Filters Miroslav Lutovac University Singidunum, Faculty of Informatics and Computing Belgrade, Serbia mlutovac@singidunum.ac.rs Vlastimir Pavloviü University of Niš Faculty of Electronic Engineering, Niš, Serbia vlastimir.pavlovic@elfak.ni.ac.rs Maja Lutovac Robot controllers LOLA Institute Belgrade, Serbia maja.lutovac@li.rs Abstract—The efficient implementation of selective multiplierless digital FIR filter is very desired solution for low-power consumption applications. Filter requirements such as sharp transition and large stop-band attenuation require very high filter order and usually large power consumption. The solution of this problem can be to use predefined hardware filter structures with small number of operations per input sample in spite of the very high filter order. In this paper we provide a systematic approach for solving the problem using computer algebra system (CAS). The methodology is based on (1) sketching the filter structure that is known to have excellent properties appropriate as embedded solution, (2) automated building the knowledge into CAS in a form of the schematic description, (3) automated derivation of filter properties such as transfer functions or implementation codes, (4) defining a strategy for combining intermediate results, and (5) plotting the frequency responses in order to verify the final solution. Keywords- CIC filters; FIR filters; filter structures; recursive filters; symbolic processing I. INTRODUCTION The efficiency of the implementation of digital filter on a programmable or dedicated hardware can be considerable improved by using the same hardware more than ones during the sampling period [1]. A small number of operations per input sample are probably the most important due to the fact that power consumptions are mainly results of the transition in logic circuits from one state to another. Also the number of multiplications should be reduced to the minimal number because this is the most expensive component in the hardware implementation [2]. A large number of methods for improving the efficiency of digital filters have been presented in many papers [1-3]. One of the most popular techniques is to use the lower order filter sections in cascade connection in order to implement a higher order filter. The main drawback of cascaded connection can be very large pass-band ripple. Different techniques can be used for reduction of the increased pass-band ripple [1]. The basic idea of this paper is to start the filter design with a filter structure that is simple for implementation and with a small number of operations per input sample. In order to retain very high stop-band attenuation, the same circuitry can be used several times. Instead of reducing the pass-band ripple as in [3], the stop-band attenuation can be significantly increased using the different number of delays in the known digital filter structure, as it is presented in this paper. This approach can be very attractive for multirate processing [4]. This paper is divided in 3 sections. In the second section, the principal structure of CIC (Cascaded Integrator Comb) filter is reviewed as the basic structure. It is also proposed the filter structure that is suitable for efficient implementation. The third section presents analysis of one structure using computer algebra system and symbolic processing. In section four a several examples are presented including procedures for obtaining efficient solutions. The last section is a conclusion. II. FILTER STRUCTURE A. CIC filters The cascaded integrator comb filter is the most frequently used filter of its class, due to very low complexity [5]. It is implemented by cascading the integrator and comb filter. Thus, CIC implementation does not require usage of multipliers. The efficient implementation of the CIC filter requires only two adders and two delay elements. On the other hand, CIC filter has poor frequency characteristics. The selectivity can be improved using the multistage modified comb filters [5]. The application of comb-based digital filters has become very intense in multirate systems, because of their low complexity and low power consumption, as well as the possibility of working at high sampling rates [4]. Filter sharpening can be used so that the implementation is a good compromise between computational complexity of the resulting filter and its frequency characteristics. Although this type of filter is finite impulse responses (FIR) filter, that is a filter whose impulse response is of finite duration, it can be implemented using recursive structures. This work was supported by the Ministry of Education and Science of Serbia under Grant TR-32023. 128