MultiplicationFree
PolynomialBased FIR Filters with an Adjustable
Fractional Delay
J. YliKaakinen
and T. Saramäki,
"Multiplicationfree
polynomialbased FIR filters with an adjustable
fractional delay," Circuits Syst. Signal
Process., vol. 25, no. 2, pp. 265–294,
Apr. 2006.
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Electronic version of an article published as
Circuits, Systems, and Signal Processing,
vol. 25, no. 2, pp. 265–294, Apr. 2006. (doi: 10.1007/s0003400525073)
© Copyright © 2006, Birkhäuser Boston. http://www.springer.com/birkhauser/engineering/journal/34
Abstract
An efficient coefficient quantization scheme is
described for minimizing the cost of implementing fixed
parallel linearphase finite impulse response (FIR)
filters in the modified Farrow structure introduced by
Vesma and Saramaki for generating FIR filters with an
adjustable fractional delay. The implementation costs
under consideration are the minimum number of adders and
subtracters when implementing these parallel subfilters
as a very largescale integration (VLSI) circuit. Two
implementation costs are under consideration to meet the
given criteria. In the first case, all the coefficient
values are implemented independently of each other as a
few signedpowersoftwo terms, whereas in the second
case, the common subexpressions within all the
coefficient values included in the overall
implementation are properly shared in order to reduce
the overall implementation cost even further. The
optimum finiteprecision solution is found in four
steps. First, the number of filters and their (common
odd) order are determined such that the given criteria
are sufficiently exceeded in order to allow some
coefficient quantization errors. Second, those
coefficient values of the subfilters having a negligible
effect on the overall system performance are fixed to be
zero valued. In addition, the experimentally observed
attractive connections between the coefficient values of
the subfilters, after setting some coefficient values
equal to zero, are utilized to reduce both the
implementation cost and the parameters to be optimized
even more. Third, constrained nonlinear optimization is
applied to determine for the remaining
infiniteprecision coefficients a parameter space that
includes the feasible space where the given criteria are
met. The fourth step involves finding in this space the
desired finiteprecision coefficient values for
minimizing the given implementation costs to meet the
stated overall criteria. Several examples are included
illustrating the efficiency of the proposed synthesis
scheme.
BibTeX
@Article{ylikaaJCSSP06,
author = {J. YliKaakinen and T. Saram{\"a}ki},
title = {Multiplicationfree
polynomialbased {FIR} filters with an adjustable
fractional
delay},
journal = "J. Circuits Syst. Signal Process.",
year = 2006,
volume = 25,
number = 2,
pages = {265294},
month = {Apr.}
}
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