Design of High-Order Extrapolated Impulse Response FIR Filters with Signed Powers-of-Two Coefficients |
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Authors: | Yanfei Cao Kai Wang Wenjiang Pei Yujie Liu Yifeng Zhang |
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Affiliation: | 1. School of Information Science and Engineering, Southeast University, No. 2 Sipailou, Nanjing, Jiangsu, 210096, P.R. China
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Abstract: | 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 0.81N∼0.29N adders are required for 18-bit N-order FIR filters (N=335∼3261) to meet the given magnitude response specifications. |
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