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Fixed-point implementation of infinite impulse response notch filters

Pinheiro, E.C. ; Postolache, O. ; Girão, P.M.

Metrology and Measurement Systems Vol. XVII, Nº 2, pp. 217 - 232, June, 2010.

ISSN (print): 0860-8229
ISSN (online): 0860-8229

Journal Impact Factor: 0,925 (in 2014)

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Abstract
Many studies have been developed aiming to improve digital filters realizations recurring to intricate structures and analysing probabilistically the error’s behaviour. The work presented in this paper analyses the feasibility of fixed-point implementation of classical infinite impulse response notch filters: Butterworth, Chebyshev I and II, and elliptic. To scrutinize the deformations suffered for distinct design specifications, it is assessed the effect of the quality factor and normalized cut-off frequency in the number of significant bits necessary to represent the filter’s coefficients. The implications brought to field-programmable gate arrays (FPGA) implementation are also verified.
The work focuses especially on the implementation of power line notch filters used to improve the signal-to-noise ratio in biomedical signals. The results obtained, when quantizing the digital notch filters, show that by applying second-order sections decomposition, low-order digital filters may be designed using only part of double precision capabilities. High-order notch filters with harsh design constrains are implementable using double precision, but only in second-order sections. Thus, it is revealed that to optimize computation time in real-time applications an optimal digital notch filter implementation platform should have variable arithmetic precision.
Considering these implementation constrains it is finally estimated the utmost operation performance when implementing digital notch filters in Xilinx Virtex-5 field-programmable gate arrays. The influence of several design specifications, e.g. type and order, in the filter’s behaviour was evaluated, namely in regard to order, type, input and coefficients’ number of bits, quality factor and cut-off frequency. Finally the implications and potential applications of such results are discussed.