Functional Inequality

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Charlotte Yuk-fan Ho - One of the best experts on this subject based on the ideXlab platform.

  • Instantaneous magnitudes and frequencies of signals with positivity constraints
    2014 9th International Symposium on Communication Systems Networks & Digital Sign (CSNDSP), 2014
    Co-Authors: Weichao Kuang, Charlotte Yuk-fan Ho, Bingo Wing-kuen Ling, Zhijing Yang
    Abstract:

    This paper proposes an optimization approach for representing instantaneous magnitudes and frequencies of signals. Signals are represented as the products of their magnitudes and the cosines of their phases. Also, both their instantaneous magnitudes and frequencies are positive. These two conditions are posed as linear Functional Inequality constraints. To have smooth signals, the sum of the total absolute values of the p th order derivatives of the magnitudes is minimized. To solve the optimization problem, the objective function is first converted to a linear objective function subject to linear Functional Inequality constraints. Finally, the Functional Inequality constraints are converted to the conventional linear equality constraints via the constraint transcription method. Experimental results show that the magnitudes obtained by our proposed method are much smoother than those obtained by existing methods.

  • CSNDSP - Instantaneous magnitudes and frequencies of signals with positivity constraints
    2014 9th International Symposium on Communication Systems Networks & Digital Sign (CSNDSP), 2014
    Co-Authors: Weichao Kuang, Charlotte Yuk-fan Ho, Bingo Wing-kuen Ling, Zhijing Yang
    Abstract:

    This paper proposes an optimization approach for representing instantaneous magnitudes and frequencies of signals. Signals are represented as the products of their magnitudes and the cosines of their phases. Also, both their instantaneous magnitudes and frequencies are positive. These two conditions are posed as linear Functional Inequality constraints. To have smooth signals, the sum of the total absolute values of the p th order derivatives of the magnitudes is minimized. To solve the optimization problem, the objective function is first converted to a linear objective function subject to linear Functional Inequality constraints. Finally, the Functional Inequality constraints are converted to the conventional linear equality constraints via the constraint transcription method. Experimental results show that the magnitudes obtained by our proposed method are much smoother than those obtained by existing methods.

  • Optimal Design of Cosine Modulated Nonuniform Linear Phase FIR Filter Bank via Both Stretching and Shifting Frequency Response of Single Prototype Filter
    IEEE Transactions on Signal Processing, 2014
    Co-Authors: Bingo Wing-kuen Ling, Charlotte Yuk-fan Ho
    Abstract:

    This paper designs an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of a single prototype filter. The total aliasing error of the filter bank is minimized subject to specifications on the maximum magnitude distortion of the filter bank and the maximum ripple magnitudes of the prototype filter over both the passband and the stopband. This paper proposes a joint constraint transcription and modified filled function method for solving the optimization problem. In particular, the Functional Inequality constraints are converted to discrete constraints via the constraint transcription method. The globally optimal solution of the nonconvex optimization problem can be found efficiently via the modified filled function method. Computer numerical simulation results show that our design outperforms existing designs.

  • Minimax passband group delay nonlinear fir filter design without imposing desired phase response
    2011 19th European Signal Processing Conference, 2011
    Co-Authors: Charlotte Yuk-fan Ho, Bingo Wing-kuen Ling
    Abstract:

    In this paper, a nonlinear phase finite impulse response (FIR) filter is designed without imposing a desired phase response. The maximum passband group delay of the filter is minimized subject to a positivity constraint on the passband group delay response of the filter as well as a specification on the maximum absolute difference between the desired magnitude square response and the designed magnitude square response over both the passband and the stopband. This filter design problem is a nonsmooth Functional Inequality constrained optimization problem. To tackle this problem, first, the one norm Functional Inequality constraint of the optimization problem is approximated by a smooth function so that the nonsmooth Functional Inequality constrained optimization problem is approximated as a noncon-vex Functional Inequality constrained optimization problem. Then, a modified filled function method is applied for finding the global minimum of the nonconvex optimization problem. Computer numerical simulation results show that our designed nonlinear phase peak constrained FIR filter could achieve lower minimum passband group delay than those of existing designs.

  • Optimal cosine modulated nonuniform linear phase FIR filter bank design via stretching and shifting frequency response of prototype filter
    2010 7th International Symposium on Communication Systems Networks & Digital Signal Processing (CSNDSP 2010), 2010
    Co-Authors: Charlotte Yuk-fan Ho, B.w.-k. Ling, L. Benmesbah
    Abstract:

    This paper proposes an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank design. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of the prototype filter. The total aliasing error of the filter bank is minimized subject to a specification on the maximum amplitude distortion of the filter bank as well as specifications on both the maximum passband ripple magnitude and the maximum stopband ripple magnitude of the prototype filter. This filter bank design problem is actually a Functional Inequality constrained optimization problem. Our recently developed integration approach is employed for solving the problem. Computer numerical simulation results show that our proposed design method outperforms existing design methods.

Bingo Wing-kuen Ling - One of the best experts on this subject based on the ideXlab platform.

  • Instantaneous magnitudes and frequencies of signals with positivity constraints
    2014 9th International Symposium on Communication Systems Networks & Digital Sign (CSNDSP), 2014
    Co-Authors: Weichao Kuang, Charlotte Yuk-fan Ho, Bingo Wing-kuen Ling, Zhijing Yang
    Abstract:

    This paper proposes an optimization approach for representing instantaneous magnitudes and frequencies of signals. Signals are represented as the products of their magnitudes and the cosines of their phases. Also, both their instantaneous magnitudes and frequencies are positive. These two conditions are posed as linear Functional Inequality constraints. To have smooth signals, the sum of the total absolute values of the p th order derivatives of the magnitudes is minimized. To solve the optimization problem, the objective function is first converted to a linear objective function subject to linear Functional Inequality constraints. Finally, the Functional Inequality constraints are converted to the conventional linear equality constraints via the constraint transcription method. Experimental results show that the magnitudes obtained by our proposed method are much smoother than those obtained by existing methods.

  • CSNDSP - Instantaneous magnitudes and frequencies of signals with positivity constraints
    2014 9th International Symposium on Communication Systems Networks & Digital Sign (CSNDSP), 2014
    Co-Authors: Weichao Kuang, Charlotte Yuk-fan Ho, Bingo Wing-kuen Ling, Zhijing Yang
    Abstract:

    This paper proposes an optimization approach for representing instantaneous magnitudes and frequencies of signals. Signals are represented as the products of their magnitudes and the cosines of their phases. Also, both their instantaneous magnitudes and frequencies are positive. These two conditions are posed as linear Functional Inequality constraints. To have smooth signals, the sum of the total absolute values of the p th order derivatives of the magnitudes is minimized. To solve the optimization problem, the objective function is first converted to a linear objective function subject to linear Functional Inequality constraints. Finally, the Functional Inequality constraints are converted to the conventional linear equality constraints via the constraint transcription method. Experimental results show that the magnitudes obtained by our proposed method are much smoother than those obtained by existing methods.

  • Optimal Design of Cosine Modulated Nonuniform Linear Phase FIR Filter Bank via Both Stretching and Shifting Frequency Response of Single Prototype Filter
    IEEE Transactions on Signal Processing, 2014
    Co-Authors: Bingo Wing-kuen Ling, Charlotte Yuk-fan Ho
    Abstract:

    This paper designs an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of a single prototype filter. The total aliasing error of the filter bank is minimized subject to specifications on the maximum magnitude distortion of the filter bank and the maximum ripple magnitudes of the prototype filter over both the passband and the stopband. This paper proposes a joint constraint transcription and modified filled function method for solving the optimization problem. In particular, the Functional Inequality constraints are converted to discrete constraints via the constraint transcription method. The globally optimal solution of the nonconvex optimization problem can be found efficiently via the modified filled function method. Computer numerical simulation results show that our design outperforms existing designs.

  • Minimax passband group delay nonlinear fir filter design without imposing desired phase response
    2011 19th European Signal Processing Conference, 2011
    Co-Authors: Charlotte Yuk-fan Ho, Bingo Wing-kuen Ling
    Abstract:

    In this paper, a nonlinear phase finite impulse response (FIR) filter is designed without imposing a desired phase response. The maximum passband group delay of the filter is minimized subject to a positivity constraint on the passband group delay response of the filter as well as a specification on the maximum absolute difference between the desired magnitude square response and the designed magnitude square response over both the passband and the stopband. This filter design problem is a nonsmooth Functional Inequality constrained optimization problem. To tackle this problem, first, the one norm Functional Inequality constraint of the optimization problem is approximated by a smooth function so that the nonsmooth Functional Inequality constrained optimization problem is approximated as a noncon-vex Functional Inequality constrained optimization problem. Then, a modified filled function method is applied for finding the global minimum of the nonconvex optimization problem. Computer numerical simulation results show that our designed nonlinear phase peak constrained FIR filter could achieve lower minimum passband group delay than those of existing designs.

  • Design of Near-Allpass Strictly Stable Minimal-Phase Real-Valued Rational IIR Filters
    IEEE Transactions on Circuits and Systems II: Express Briefs, 2008
    Co-Authors: Charlotte Yuk-fan Ho, Bingo Wing-kuen Ling, Mohammad Shikh-bahaei
    Abstract:

    In this brief, a near-allpass strictly stable minimal-phase real-valued rational infinite-impulse response filter is designed so that the maximum absolute phase error is minimized subject to a specification on the maximum absolute allpass error. This problem is actually a minimax nonsmooth optimization problem subject to both linear and quadratic Functional Inequality constraints. To solve this problem, the nonsmooth cost function is first approximated by a smooth function, and then our previous proposed method is employed for solving the problem. Computer numerical simulation result shows that the designed filter satisfies all Functional Inequality constraints and achieves a small maximum absolute phase error.

A. Cantoni - One of the best experts on this subject based on the ideXlab platform.

  • Robust design of Transmit Pulse Shape
    2000 10th European Signal Processing Conference, 2000
    Co-Authors: B. Vo, A. Cantoni
    Abstract:

    This paper considers the design of Transmit Pulse Shapes such that after transmission through a dispersive channel, the distorted pulse at the receiver fits in a prescribed template. The norm of the transmit pulse is minimized so as to reduce the effect of cross-talk at the receiver end. This design problem is formulated as a Quadratic Programming problem with affine Functional Inequality constraints. In practice, errors in the implementation of the optimal filter cause the received pulse to violate the template constraints. We present a robust formulation which incorporate the uncertainties to ensure that the constraints are satisfied even in the presence of implementation errors. This technique is applied to determine the transmit pulse shape to be programmed on a Siemens FALC54, a T1 Line Interface Unit.

  • FIR filters in continuous-time envelope constrained filter design
    1997 IEEE International Conference on Acoustics Speech and Signal Processing, 1997
    Co-Authors: B. Vo, A. Cantoni, T. Ho, V. Sreeram
    Abstract:

    Consider a continuous-time filter the structure of which is comprised of an A/D converter, an FIR filter, a D/A converter and an analog post-filter. The envelope constrained (EC) filtering problem for this filter structure is to design the digital component so as to minimize the effect of the input noise whilst satisfying the constraint that the noiseless response of the filter to a specified excitation fits into a prescribed envelope. This problem is formulated as a quadratic programming (QP) problem with Functional Inequality constraints. Approximating this continuum of constraints by a finite set, the problem is solved by QP via an active set strategy.

  • Envelope constrained filter with linear interpolator
    IEEE Transactions on Signal Processing, 1997
    Co-Authors: Ba-ngu Vo, A. Cantoni
    Abstract:

    The envelope constrained (EC) filtering problem is the minimization of the noise gain of the filter while satisfying the constraint that its noiseless response to a specified input lies within a prescribed envelope. Using a hybrid filter consisting of an A/D converter, an FIR filter, and a linear interpolator, the problem is posed as a Functional Inequality constrained optimization problem. A technique for solving this problem is proposed by approximating it with a conventional unconstrained optimization problem that is then solved by a descent direction-based algorithm.

B.w.-k. Ling - One of the best experts on this subject based on the ideXlab platform.

  • Combined optimal pulse width modulation and pulse frequency modulation strategy for controlling switched mode DC–DC converters over a wide range of loads
    IET Control Theory & Applications, 2012
    Co-Authors: B.w.-k. Ling, C. Bingham, H.h.-c. Iu
    Abstract:

    This paper develops a combined optimal pulse width modulation (PWM) and pulse frequency modulation (PFM) strategy for controlling switched mode DC-DC converters. The peak ripple magnitudes of both the output-voltages and -currents during all operating modes over a wide range of loads are minimised subject to specifications on the minimum efficiency bounds of the converters. This problem is posed as a multi-objective Functional Inequality constrained optimal control problem. By expressing the initial state of each operating mode at the steady state as a function of the switched time instants, as well as applying the time scaling transform method and the constraint transcription method, the multi-objective Functional Inequality constrained optimal control problem is converted to a conventional optimal control problem. Finally, a control parameterisation technique is applied to solve the problem. Computer numerical simulations show that the combined control strategy could achieve low peak ripple magnitudes of both the output-voltages and -currents for all operating modes over a wide range of loads and guarantees the satisfaction of the specifications on the minimum efficiency bounds of the converter over a wide range of loads.

  • Optimal cosine modulated nonuniform linear phase FIR filter bank design via stretching and shifting frequency response of prototype filter
    2010 7th International Symposium on Communication Systems Networks & Digital Signal Processing (CSNDSP 2010), 2010
    Co-Authors: Charlotte Yuk-fan Ho, B.w.-k. Ling, L. Benmesbah
    Abstract:

    This paper proposes an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank design. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of the prototype filter. The total aliasing error of the filter bank is minimized subject to a specification on the maximum amplitude distortion of the filter bank as well as specifications on both the maximum passband ripple magnitude and the maximum stopband ripple magnitude of the prototype filter. This filter bank design problem is actually a Functional Inequality constrained optimization problem. Our recently developed integration approach is employed for solving the problem. Computer numerical simulation results show that our proposed design method outperforms existing design methods.

B. Vo - One of the best experts on this subject based on the ideXlab platform.

  • Robust design of Transmit Pulse Shape
    2000 10th European Signal Processing Conference, 2000
    Co-Authors: B. Vo, A. Cantoni
    Abstract:

    This paper considers the design of Transmit Pulse Shapes such that after transmission through a dispersive channel, the distorted pulse at the receiver fits in a prescribed template. The norm of the transmit pulse is minimized so as to reduce the effect of cross-talk at the receiver end. This design problem is formulated as a Quadratic Programming problem with affine Functional Inequality constraints. In practice, errors in the implementation of the optimal filter cause the received pulse to violate the template constraints. We present a robust formulation which incorporate the uncertainties to ensure that the constraints are satisfied even in the presence of implementation errors. This technique is applied to determine the transmit pulse shape to be programmed on a Siemens FALC54, a T1 Line Interface Unit.

  • FIR filters in continuous-time envelope constrained filter design
    1997 IEEE International Conference on Acoustics Speech and Signal Processing, 1997
    Co-Authors: B. Vo, A. Cantoni, T. Ho, V. Sreeram
    Abstract:

    Consider a continuous-time filter the structure of which is comprised of an A/D converter, an FIR filter, a D/A converter and an analog post-filter. The envelope constrained (EC) filtering problem for this filter structure is to design the digital component so as to minimize the effect of the input noise whilst satisfying the constraint that the noiseless response of the filter to a specified excitation fits into a prescribed envelope. This problem is formulated as a quadratic programming (QP) problem with Functional Inequality constraints. Approximating this continuum of constraints by a finite set, the problem is solved by QP via an active set strategy.