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C S Urrus - One of the best experts on this subject based on the ideXlab platform.

  • constrained least square design of FIR Filters without specified transition bands
    IEEE Transactions on Signal Processing, 1996
    Co-Authors: Iva W Selesnick, M Lang, C S Urrus
    Abstract:

    This paper puts forth the notion that explicitly specified transition bands have been introduced in the filter design literature in part as an indirect approach for dealing with discontinuities in the desired frequency response. We suggest that the use of explicitly specified transition bands is sometimes inappropriate because to satisfy a meaningful optimality criterion, their use implicitly assumes a possibly unrealistic assumption on the class of input signals. This paper also presents an algorithm for the design of peak constrained lowpass FIR Filters according to an integral square error criterion that does not require the use of specified transition bands. This rapidly converging, robust, simple multiple exchange algorithm uses Lagrange multipliers and the Kuhn-Tucker conditions on each iteration. The algorithm will design linear- and minimum-phase FIR Filters and gives the best L/sub 2/ filter and a continuum of Chebyshev Filters as special cases. It is distinct from many other filter design methods because it does not exclude from the integral square error a region around the cut-off frequency, and yet, it overcomes the Gibbs' phenomenon without resorting to windowing or 'smoothing out' the discontinuity of the ideal lowpass filter.

  • constrained least square design of FIR Filters without specified transition bands
    International Conference on Acoustics Speech and Signal Processing, 1995
    Co-Authors: Iva W Selesnick, M Lang, C S Urrus
    Abstract:

    We consider the design of digital Filters and discuss the inclusion of explicitly specified transition bands in the frequency domain design of FIR Filters. We put forth the notion that explicitly specified transition bands have been introduced in the filter design literature as an indirect and sometimes inadequate approach for dealing with discontinuities in the desired frequency response. We also present a rapidly converging, robust, simple algorithm for the design of optimal peak constrained least square lowpass FIR Filters that does not require the use of transition bands. This versatile algorithm will design linear and minimum phase FIR Filters and gives the best L/sub 2/ filter and a continuum of Chebyshev Filters as special cases.

  • iterative reweighted least squares design of FIR Filters
    IEEE Transactions on Signal Processing, 1994
    Co-Authors: C S Urrus, J A Arreto, Iva W Selesnick
    Abstract:

    Develops a new iterative reweighted least squares algorithm for the design of optimal L/sub p/ approximation FIR Filters. The algorithm combines a variable p technique with a Newton's method to give excellent robust initial convergence and quadratic final convergence. Details of the convergence properties when applied to the L/sub p/ optimization problem are given. The primary purpose of L/sub p/ approximation for filter design is to allow design with different error criteria in pass and stopband and to design constrained L/sub 2/ approximation Filters. The new method can also be applied to the complex Chebyshev approximation problem and to the design of 2D FIR Filters. >

Iva W Selesnick - One of the best experts on this subject based on the ideXlab platform.

  • constrained least square design of FIR Filters without specified transition bands
    IEEE Transactions on Signal Processing, 1996
    Co-Authors: Iva W Selesnick, M Lang, C S Urrus
    Abstract:

    This paper puts forth the notion that explicitly specified transition bands have been introduced in the filter design literature in part as an indirect approach for dealing with discontinuities in the desired frequency response. We suggest that the use of explicitly specified transition bands is sometimes inappropriate because to satisfy a meaningful optimality criterion, their use implicitly assumes a possibly unrealistic assumption on the class of input signals. This paper also presents an algorithm for the design of peak constrained lowpass FIR Filters according to an integral square error criterion that does not require the use of specified transition bands. This rapidly converging, robust, simple multiple exchange algorithm uses Lagrange multipliers and the Kuhn-Tucker conditions on each iteration. The algorithm will design linear- and minimum-phase FIR Filters and gives the best L/sub 2/ filter and a continuum of Chebyshev Filters as special cases. It is distinct from many other filter design methods because it does not exclude from the integral square error a region around the cut-off frequency, and yet, it overcomes the Gibbs' phenomenon without resorting to windowing or 'smoothing out' the discontinuity of the ideal lowpass filter.

  • constrained least square design of FIR Filters without specified transition bands
    International Conference on Acoustics Speech and Signal Processing, 1995
    Co-Authors: Iva W Selesnick, M Lang, C S Urrus
    Abstract:

    We consider the design of digital Filters and discuss the inclusion of explicitly specified transition bands in the frequency domain design of FIR Filters. We put forth the notion that explicitly specified transition bands have been introduced in the filter design literature as an indirect and sometimes inadequate approach for dealing with discontinuities in the desired frequency response. We also present a rapidly converging, robust, simple algorithm for the design of optimal peak constrained least square lowpass FIR Filters that does not require the use of transition bands. This versatile algorithm will design linear and minimum phase FIR Filters and gives the best L/sub 2/ filter and a continuum of Chebyshev Filters as special cases.

  • iterative reweighted least squares design of FIR Filters
    IEEE Transactions on Signal Processing, 1994
    Co-Authors: C S Urrus, J A Arreto, Iva W Selesnick
    Abstract:

    Develops a new iterative reweighted least squares algorithm for the design of optimal L/sub p/ approximation FIR Filters. The algorithm combines a variable p technique with a Newton's method to give excellent robust initial convergence and quadratic final convergence. Details of the convergence properties when applied to the L/sub p/ optimization problem are given. The primary purpose of L/sub p/ approximation for filter design is to allow design with different error criteria in pass and stopband and to design constrained L/sub 2/ approximation Filters. The new method can also be applied to the complex Chebyshev approximation problem and to the design of 2D FIR Filters. >

Tianbo Deng - One of the best experts on this subject based on the ideXlab platform.

  • hybrid structures for low complexity variable fractional delay FIR Filters
    IEEE Transactions on Circuits and Systems, 2010
    Co-Authors: Tianbo Deng
    Abstract:

    This paper proposes a pair of new structures for implementing low-complexity odd-order and even-order variable fractional-delay (VFD) FIR Filters using hybrid structures with both even-order and odd-order subFilters. For odd-order VFD filter design, the main idea is to replace the conventional even-symmetric odd-order (type-2) subFilters with the cascade of a type-2 half-delay filter and even-symmetric even-order (type-1) subFilters. This is because the magnitude responses of type-2 subFilters are zero at frequency ? = ?, which causes large approximation errors, especially for wideband VFD filter design. Similarly, for even-order VFD filter design, the conventional odd-symmetric even-order (type-3) subFilters are replaced with the cascade of a type-2 half-advance filter and odd-symmetric odd-order (type-4) subFilters. This replacement avoids the zero magnitude responses at frequency ? = ? of type-3 subFilters and makes low-complexity wideband VFD filter design possible. As compared with the existing Farrow structures with either odd-order subFilters (odd-order design) or even-order subFilters (even-order design), the hybrid structures consist of three types of FIR Filters (type-1 and type-4 subFilters, as well as type-2 half-delay or half-advance filter). Replacing type-2 subFilters with type-1 ones (odd-order design) and replacing type-3 subFilters with type-4 ones (even-order design) can significantly reduce the VFD filter complexity for wideband designs. Design examples are given to illustrate the effectiveness of both odd-order and even-order hybrid structures.

  • weighted least squares design of variable fractional delay FIR Filters using coefficient symmetry
    IEEE Transactions on Signal Processing, 2006
    Co-Authors: Tianbo Deng, Yong Lia
    Abstract:

    Our previous work has shown that the coefficient symmetry can be efficiently exploited in designing variable finite-impulse-response (FIR) Filters with simultaneously tunable magnitude and fractional-delay responses. This paper presents the optimal solutions for the weighted-least-squares (WLS) design of variable fractional-delay (VFD) FIR Filters with same-order and different-order subFilters through utilizing the coefficient symmetry along with an imposed coefficient constraint. In deriving the closed-form error functions, since the Taylor series expansions of sin(omegap) and cos(omegap) are used, the numerical integrals using conventional quadrature rules can be completely removed, which speeds up the WLS design and guarantees the optimality of the final solution. Two design examples are given to illustrate that the proposed WLS methods can achieve better design with significantly reduced VFD filter complexity and computational cost than the existing ones including the WLS-SVD approach. Consequently, the proposed WLS design is the best among all the existing WLS methods so far

  • weighted least squares method for designing arbitrarily variable 1 d FIR digital Filters
    Signal Processing, 2000
    Co-Authors: Tianbo Deng
    Abstract:

    Abstract Variable digital Filters with variable cutoff frequencies can be designed by frequency transformation methods. Such methods are simple, but they are not applicable to the design of variable Filters with arbitrarily variable frequency responses. This paper proposes an efficient method for designing variable one-dimensional (1-D) finite-impulse-response (FIR) digital Filters with arbitrarily variable magnitude characteristics and specified linear or nonlinear phase responses. FIRst, each coefficient of the variable FIR filter is assumed to be a multi-dimensional (M-D) polynomial of spectral parameters that specify different variable magnitude characteristics. Then we present a pair of least-squares algorithms for finding the optimal polynomial coefficients by minimizing the weighted squared error between the desired variable frequency response and the actual frequency response. The FIRst one is for designing 1-D FIR Filters with variable magnitude response and linear-phase, and the second one is for designing variable 1-D FIR Filters with variable magnitude response and nonlinear-phase. Although the FIRst algorithm can be regarded as a special case of the second one, using the FIRst one in the linear case can simplify the design significantly. The proposed methods are very straightforward and efficient for designing variable digital Filters with arbitrarily variable magnitude responses and specified linear or nonlinear phases.

Yong Lia - One of the best experts on this subject based on the ideXlab platform.

  • weighted least squares design of variable fractional delay FIR Filters using coefficient symmetry
    IEEE Transactions on Signal Processing, 2006
    Co-Authors: Tianbo Deng, Yong Lia
    Abstract:

    Our previous work has shown that the coefficient symmetry can be efficiently exploited in designing variable finite-impulse-response (FIR) Filters with simultaneously tunable magnitude and fractional-delay responses. This paper presents the optimal solutions for the weighted-least-squares (WLS) design of variable fractional-delay (VFD) FIR Filters with same-order and different-order subFilters through utilizing the coefficient symmetry along with an imposed coefficient constraint. In deriving the closed-form error functions, since the Taylor series expansions of sin(omegap) and cos(omegap) are used, the numerical integrals using conventional quadrature rules can be completely removed, which speeds up the WLS design and guarantees the optimality of the final solution. Two design examples are given to illustrate that the proposed WLS methods can achieve better design with significantly reduced VFD filter complexity and computational cost than the existing ones including the WLS-SVD approach. Consequently, the proposed WLS design is the best among all the existing WLS methods so far

Haka Johansso - One of the best experts on this subject based on the ideXlab platform.

  • on the design of sparse half band like FIR Filters
    Asilomar Conference on Signals Systems and Computers, 2007
    Co-Authors: Osca Gustafsso, L S Debrunne, V Debrunne, Haka Johansso
    Abstract:

    In this work we consider the design of sparse FIR Filters, i.e. Filters with few non-zero multiplications. The considered Filters have half-band like properties, but with slightly relaxed specifications compared with actual half-band Filters. We propose a filter design technique where the number of non-zero filter coefficients is minimized. It is shown by examples that it is possible to take advantage of an increased passband ripple only to obtain a half-band like solution with fewer non-zero multiplications. Decreasing the passband edge only does not give such a direct improvement.

  • minimax design of adjustable bandwidth linear phase FIR Filters
    IEEE Transactions on Circuits and Systems I-regular Papers, 2006
    Co-Authors: Pe Lowenborg, Haka Johansso
    Abstract:

    This paper considers the design of digital linear-phase finite-length impulse response (FIR) Filters that have adjustable bandwidth(s) whereas the phase response is fixed. For this purpose, a structure is employed in which the overall transfer function is a weighted linear combination of fixed subFilters and where the weights are directly determined by the bandwidth(s). Minimax design techniques are introduced which generate globally optimal overall Filters in the minimax (Chebyshev) sense over a whole set of filter specifications. The paper also introduces a new structure for bandstop and bandpass Filters with individually adjustable upper and lower band edges, and with a substantially lower arithmetic complexity compared to structures that make use of two separate adjustable-bandwidth low-pass and high-pass Filters in cascade or in parallel. Design examples are included in the paper.

  • reconstruction of nonuniformly sampled bandlimited signals by means of time varying discrete time FIR Filters
    EURASIP Journal on Advances in Signal Processing, 2006
    Co-Authors: Haka Johansso, Pe Lowenborg
    Abstract:

    This paper deals with reconstruction of nonuniformly sampled bandlimited continuous-time signals using time-varying discrete-time finite-length impulse response (FIR) Filters. The main theme of the paper is to show how a slight oversampling should be utilized for designing the reconstruction Filters in a proper manner. Based on a time-frequency function, it is shown that the reconstruction problem can be posed as one that resembles an ordinary filter design problem, both for deterministic signals and random processes. From this facts, an analytic least-square design technique is then derived. Furthermore, for an important special case, corresponding to periodic nonuniform sampling, it is shown that the reconstruction problem alternatively can be posed as a filter bank design problem, thus with requirements on a distortion transfer function and a number of aliasing transfer functions. This eases the design and offers alternative practical design methods as discussed in the paper. Several design examples are included that illustrate the benefits of the proposed design techniques over previously existing techniques.

  • on the design of adjustable fractional delay FIR Filters
    IEEE Transactions on Circuits and Systems Ii: Analog and Digital Signal Processing, 2003
    Co-Authors: Haka Johansso, Pe Lowenborg
    Abstract:

    This brief considers minimax design of adjustable fractional delay finite-impulse response (FIR) Filters. We employ a filter structure that, in the paper by Vesma and Saramaki in 1997, is referred to as the modified Farrow structure which makes use of a number of linear-phase FIR subFilters. Previously, only the cases where all subFilters are of equal order have been considered. In this brief, we propose a design technique that in general produces subFilters of different orders which results in a lower overall arithmetic complexity. Design examples are included, illustrating the efficiency of the proposed design technique.