A very efficient technique to drastically reduce the
number of multipliers and adders in implementing
linear-phase finite-impulse response (FIR) digital
filters in applications demanding a narrow transition
band is to use the frequency-response masking (FRM)
approach originally introduced by Lim. The arithmetic
complexity can be even further reduced using a common
filter part for constructing the masking filters
originally proposed by Lim and Lian. A drawback in the
above-mentioned original FRM synthesis techniques is
that the subfilters in the overall implementations are
separately designed. In order to further reduce the
arithmetic complexity in these two FRM approaches, the
following two-step optimization technique is proposed
for simultaneously optimizing the subfilters. At the
first step, a good suboptimal solution is found by using
a simple iterative algorithm. At the second step, this
solution is then used as a start-up solution for further
optimization being carried out by using an efficient
unconstrained nonlinear optimization algorithm. An
example taken from the literature illustrates that both
the number of multipliers and the number of adders for
the resulting optimized filter are less than 80%
compared with those of the FRM filter obtained using the
original FRM design schemes in the case where the
masking filters are separately implemented. If a common
filter part is used for realizing the masking filters,
then an additional reduction of more than 10% is
achieved compared with the optimized design with
separately implemented masking filters.
2005 | [1] |
Yong Ching Lim and R. Yang,
"On the synthesis
of very sharp decimators and interpolators using
the frequency-response masking technique,"
IEEE Trans. Signal Process, vol. 53, no. 4,
pp. 1387–1397, Apr. 2005.
|
| [2] |
Jianghong Yu and Yong Lian,
"Interpolation
factor analysis for jointly optimized
frequency-response masking filters,"
in Proc. IEEE Int. Symp. Circuits Syst.,
Kobe, Japan, May 23–26, 2005,
pp. 2016–2019.
|
| [3] |
Yong Ching Lim and Ya Jun Yu,
"Synthesis of very
sharp Hilbert transformer using the
frequency-response masking technique,"
IEEE Trans. Signal Process, vol. 53, no. 7,
pp. 2595–2597, July 2005.
|
| [4] |
Yong Ching Lim, Ya Jun Yu, and Tapio Saramäki
"Optimum masking
levels and coefficient sparseness for Hilbert
transformers and half-band filters designed
using the frequency-response masking
technique,"
IEEE Trans. Circuits Syst., vol. 52, no. 11,
pp. 2444–2453, Nov. 2005.
|
| [5] |
Ya Jun Yu, Kok Lay, Teo, Yong Ching Lim, and Guohui Zhao
"Extrapolated
impulse response filter and its application in
the synthesis of digital filters using the
frequency-response masking technique,"
Signal Processing, vol. 85,
pp. 581–590, 2005.
|
2006 | [6] |
Luiz C. R. de Barcellos, Paulo S. R. Diniz, and Sergio L. Netto,
"A
generalized oversampled structure for
cosine-modulated transmultiplexers and filter
banks,"
J. Circuists, Systems, Signal Process., vol. 25, no. 2,
pp. 131–151, Apr. 2006.
|
| [7] |
H. Johansson,
"Two
Classes of frequency-response masking
linear-phase FIR filters for interpolation and
decimation,"
J. Circuists, Systems, Signal Process., vol. 25, no. 2,
pp. 175–200, Apr. 2006.
|
2007 | [8] |
Yong Ching Lim, Ya Jun Yu, and Tapio Saramäki
"FRM approach for Hilbert tranformer synthesis," in Proc.
Int. Conf. Inform. Technol. & Appl., Harbin, China,
Jan. 15–18, 2007,
pp. 670–673.
|
| [9] |
Peyman Arian,
"Computationally Efficient
Decimators, Interpolators, and Narrow
Transition-Band Linear-Phase Finite Impulse
Response (FIR) Filters,"
PhD Thesis, Dept. of Inform. Tech., Tampere
Univ. of Tech., Finland, 2007.
|
| [10] |
Jianghong Yu and Yong Lian,
"Design equations
for jointly optimized frequency-response masking
filters,"
J. Circuists, Systems, Signal Process., vol. 26, no. 1,
pp. 27–42, Feb. 2007.
|
| [11] |
Zhiping Lin and Yongzhi Liu,
"FRM filter
design with group delay constraint using
second-order cone programming," in
Proc. IEEE Int. Symp. Circuits Syst.,
New Orleans, LA, USA, May 27–30, 2007,
pp. 2954–2957.
|
| [12] |
Yong Ching Lim, Ya Jun Yu, Kok Lay Teo, and Tapio Saramäki
"FRM-based
FIR filters with minimum coefficient
sensitivities," in Proc. IEEE
Int. Symp. Circuits Syst., New Orleans, LA,
USA, May 27–30, 2007,
pp. 2962–2965.
|
| [13] |
Yong Ching Lim, Ya Jun Yu, Kok Lay Teo and Tapio Saramäki,
"FRM-based
FIR filters with optimum finite word-length
performance,"
IEEE Trans. Signal Process. vol. 55, no. 6,
pp. 2914–2924, June 2007.
|
2008 | [14] |
Wu-Sheng Lu and Takao Hinamoto,
"Design of
frequency-response-masking FIR filters using
SOCP with coefficient sensitivity
constraint," in Proc. IEEE
Int. Symp. Circuits Syst., Seattle, WA,
USA, May 18–21, 2008,
pp. 2442–2445.
|
| [15] |
Yongzhi Liu and Zhiping Lin,
"Optimal design
of frequency-response masking filters with
reduced group delays," IEEE
Trans. Circuits Syst.—I: Regular
Papers, vol. 55, no. 6, pp. 1560–1570,
July 2008.
|
| [16] |
Sai Mohan Kilambi, Behrouz
Nowrouzian and Yifan Wu,
"A novel
diversity-controlled genetic algorithm for rapid
optimization of bandpass FRM FIR digital
filters over CSD multiplier coefficient
space,"
J. Circuists, Systems, Signal Process.,
vol. 27, no. 5, pp. 599–625, 2008.
|
| [17] |
Xiao-Hua Wang and Yi-Gang He,
"A
neural network approach to FIR filter design
using frequency-response masking technique,"
Signal Processing, vol. 88, no. 12, pp. 2917–2926, 2008.
|
| [18] |
Farooq, Umar,
"Efficient
architectural transformation of multirate
recursive filters,"
PhD Thesis, Dept. of Elect. Eng.,
Univ. of Engineering and Technology, Taxila,
Pakistan, 2008.
|
| [19] |
Xiao-Hua Wang, Yi-Gang He, and Tian-Zan Li,
"Neural
network algorithm for designing FIR filters
utilizing frequency-response masking
technique,"
J. Comput. Sci. Technol., vol. 24, no. 3, pp. 463–471, 2009.
|
2010 | [20] |
Yong Ching Lim,
"Fourier
series optimization: Minimizing the number of
nonzero coefficients," in
Proc. Int. Conf. Optimization and
Control, Guiyang, China, July 18–23,
2010, pp. 261–276.
|
2012 | [21] |
David Ernesto Troncoso Romero and Gordana Jovanovic
Dolecek,
"Digital FIR Hilbert transformers: Fundamentals and
efficient design methods,"
MATLAB – A Fundamental Tool for Scientific
Computing and Engineering Applications, Vasilios N. Katsikis
(Ed.), pp. 445–482, Intech, 2012.
|
| [22] |
David Ernesto Troncoso Romero, Miriam Guadalupe Cruz Jimenez, and Gordana Jovanovic Dolecek,
"Design of FIR Hilbert transformers using a
combined frequency response masking/frequency
transformation approach," in
Proc. Int. Midwest Symp. Circuits Syst.,,
Boise, USA, Aug. 5–8, 2012,
pp. 960–963. doi: 10.1109/MWSCAS.2012.6292181
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