• Journal of the Institute of Electronics Engineers of Korea SP
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• v.44 no.3
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• pp.105-112
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• 2007

In general, the earlier methods for the design of MAXFLAT FIR filters have existent problems due to the approximation algorithms used to approach MAXFLAT(maximally flat) response in the passband and the stopband.. The proposed approach advanced by using of MAXSHCUT(maximally sharp cutoff) condition in this paper clearly overcomes these problems. In this approach, we use a key parameter represented with filter-order and cutoff-frequency parameters for obtaining the lowpass filters with the MAXFLAT and MAXSHCUT characteristics in the frequency domain. Consequently, this design technique leads to new MAXFLAT and MAXSHCUT FIR digital filter, which can achieve sharp-cutoff responses with the stopband attenuation exceeding 100 dB almost everywhere.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.4C
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• pp.377-385
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• 2010

In this paper, a general and explicit technique is presented for determining the filter coefficients of maximally flat (MAXFLAT) FIR filter with the magnitude response exactly passing through a prescribed cutoff point. This technique is based on a general formula (i.e. impulse response) with an arbitrary cutoff point and permits direct computation of the coefficients of this filter type with a specified cutoff point. The technique provides an explicit method for choosing the order of flatness of the filter with the specified cutoff point. Also, in the paper, it is shown to give a computationally efficient and accurate solution to the design of the filters with the desired cutoff point.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.7C
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• pp.658-666
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• 2007

In general, the earlier linear-phase MAXFLAT(maximally flat) lowpass FIR filters have the main disadvantage of a gain response in the half frequency band $(0{\leq}w{\leq}{\pi}/2)$ by the closed form transfer functions used in design techniques for realizing them. Moreover, most of them has existent problems as follows : ripple error in the stopband, gentle-cutoff attenuation, phase and group delay and inexact cutoff frequency response. It is due to the approximation algorithms such as Chebyshev norm and Remez exchange which are used to approach MAXFLAT and linear-phase characteristics in frequency domain. In this paper, a new mathematically closed-form transfer function is introduced for the design of MAXFLAT lowpass FIR filters which have the zero-phase and wideband-gain response. In addition, we verify that the closed-form transfer function is easily realized due to our generalized formulas derived newly by using MAXFLAT conditions including an arbitrary cutoff point. This method is, therefore, useful for "simple and quick designs". Conclusively, we propose a technique for the design of new zero-phase wideband MAXFLAT lowpass FIR filters which can achieve sharp-cutoff attenuation exceeding 250 dB almost everywhere.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.7C
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• pp.451-458
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• 2011

Maximally flat (MAXFLAT) FIR filter design provides the advantage of giving a closed-form solution, but there still remains a problem of exactly and efficiently choosing the order of flatness for the accurate design of filters. This paper provides, through the modeling and analysis of a frequency-domain error function in the closed-form solution, how to determine the order of flatness. A proposed method, based on the frequency-domain error function, is accomplished by computing a minimum distance between its peak frequency and specified cutoff frequency. It is also shown that the proposed scheme is computationally efficient and accurate than the empirical formula given by Herrmann.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.44 no.4 s.316
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• pp.70-77
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• 2007

Two kinds of QMF(Quadrature Mirror Filter) pairs are used in JPEG2000 standard, which don't have QMF distortions. However, the QMF pairs have the main disadvantages such that there are gentle roll-off rate, ripples in the passband and unequal band decomposition. In this paper, Maxflat(maximally flat) QMF pairs with a half-band gain are proposed for overcoming these problems. Maxflat QMF pairs are realized due to generalized closed-form formulas, and the filters have maximally flat response in the passband/stopband as well as sharp roll-off rate in the transition band. Comparing proposed filters and JPEG2000's filters in frequency domain, it is found that proposed filters have better performance JPEG2000's filters. Moreover, Maxflat QMF pairs show stopband-attenuation exceeding 200 dB almost everywhere.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.2
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• pp.249-256
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• 1986

In this paper, we propose the MDM algorithm by which one can desing an FIR filter that is maximally flat and requires no multiplication. We use the modified MAXFLAT subroutive of Kaiser to achieve the maximally-flat characteristics. The filter coefficients are encoded in MDM-code and the optimal stepsize is determined the steepest- descent method. Simulation results shows that the FIR filter designed is almost maximally-flat in passband, but has about -30dB ripples in stopband due to MDM quantization error.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.3C
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• pp.271-280
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• 2008

M channel near-perfect-reconstruction(NPR) pseudo-QMF banks are a hybrid of conventional pseudo-QMF design and spectral factorization approach where the analysis and synthesis filters are cosine-modulated versions of the prototype-lowpass filter(p-LPF). However, p-LPF H(z) does not have linear-phase symmetry as well as magnitude-distortion optimization since it is obtained by spectral factorization of $2M^{-th}$ band filter $G(z)=z^{-(N-1)}H(z^{-1})H(z)$. A fair amount of attention, therefore, has been focused on the design of filter banks for reducing only alias-cancellation distortion without reconstructed-amplitude distortion. In this paper, we propose a new method for designing linear-phase p-LPF in NPR pseudo-QMF banks, which is based on Maxflat(maximally flat) FIR filters with closed-form transfer function. In addition, p-LPF H(z) is optimized in this approach so that the 2M-channel overall distortion response represented with $G(z)=H^2(z)$ approximately becomes an unit magnitude response. Through several examples of NPR pseudo-QMF banks, it is shown that the peek ripple of the overall magnitude distortion is less than $3.5{\times}10^{-4}\;({\simeq}-70dB)$ and analysis/synthesis filters have the sharp monotone-stopband attenuation exceeding 100 dB.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.10
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• pp.188-198
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• 2013

Maximally flat (MAXFLAT) half-band filters usually have wider transition band than other filters. This is due to the fact that the maximum possible number of zeros at $z={\pm}1$ is imposed, which leaves no degree of freedom, and thus no independent parameters for direct control of the frequency response. This paper describes a novel method for the design of FIR halfband filters with an explicit control of the transition-band width. The proposed method is based on a generalized Lagrange halfband polynomial (g-LHBP) with coefficients parametizing a 0-th coefficient $h_0$, and allows the frequency response of this filter type to be controllable by adjusting $h_0$. Then, $h_0$ is modeled as a steepness parameter of the transition band and this is accomplished through theoretically analyzing a polynomial recurrence relation of the g-LHBP. This method also provides explicit formulas for direct computation of design parameters related to choosing a desired filter characteristic (by trade-off between the transition-band sharpness and passband & stopband flatness). The examples are shown to provide a complete and accurate solution for the design of such filters with relatively sharper transition-band steepness than MAXFLAT half-band filters.