Design of High-Order Extrapolated Impulse Response FIR Filters with Signed Powers-of-Two Coefficients

Expensive multiplication operations can be replaced by simpler additions and hardwired shifters so as to reduce power consumption and area size, if the coefficients of a digital filter are signed power-of-two (SPT). As a consequence, FIR digital filters with SPT coefficients have been widely studied...

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Vydáno v:Circuits, systems, and signal processing Ročník 30; číslo 5; s. 963 - 985
Hlavní autoři: Cao, Yanfei, Wang, Kai, Pei, Wenjiang, Liu, Yujie, Zhang, Yifeng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston SP Birkhäuser Verlag Boston 01.10.2011
Springer Nature B.V
Témata:
Algorithms
Circuits and Systems
Computer simulation
Design engineering
Digital filters
Electrical Engineering
Electronics and Microelectronics
Engineering
Extrapolation
FIR filters
Impulse response
Instrumentation
Quadratic programming
Signal processing
Signal,Image and Speech Processing
Transformers
Extrapolated impulse response (EIR)
Signed power-of-two (SPT)
Sequential quadratic programming relaxation (SQPR)
ISSN:0278-081X, 1531-5878
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Shrnutí:Expensive multiplication operations can be replaced by simpler additions and hardwired shifters so as to reduce power consumption and area size, if the coefficients of a digital filter are signed power-of-two (SPT). As a consequence, FIR digital filters with SPT coefficients have been widely studied in the last three decades. However, most approaches for the design of FIR filters with SPT coefficients focus on filters with length less than 100. These approaches are not suitable for the design of high-order filters because they require excessive computation time. In this paper, an approach for the design of high-order filters with SPT coefficients is proposed. It is a two-step approach. Firstly, the design of an extrapolated impulse response (EIR) filter is formulated as a standard second-order cone programming (SOCP) problem with an additional coefficient sensitivity constraint for optimizing its finite word-length effect. Secondly, the obtained continuous coefficients are quantized into SPT coefficients by recasting the filter-design problem into a weighted least squares (WLS) sequential quadratic programming relaxation (SQPR) problem. To further reduce implementation complexity, a graph-based common subexpression elimination (CSE) algorithm is utilized to extract common subexpressions between SPT coefficients. Simulation results show that the proposed method can effectively and efficiently design high-order SPT filters, including Hilbert transformers and half-band filters with SPT coefficients. Experiment results indicate that 0.81 N ∼0.29 N adders are required for 18-bit N -order FIR filters ( N =335∼3261) to meet the given magnitude response specifications.
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ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-010-9259-4