Efficient 1D and circular symmetric 2D FIR filters with variable cutoff frequencies using the Farrow structure and multiplier-block

IEEE International Symposium on Circuits and Systems, Sydney, NSW, Australia, 6-9 May 2001This paper proposes new structures for realizing 1D and circular symmetric 2D FIR filters with variable cutoff frequencies. They are based on the interpolation of the impulse responses using the Farrow structure. The coefficients of the sub-filters in the Farrow structure are represented in sum-of-powers-of-two (SOPOT) coefficients, which can easily be implemented as simple shifts and additions. Furthermore, using the transposed form realization of the sub-filters, all the SOPOT coefficients can be implemented by a single multiplier-block exploiting the redundancy among the SOPOT coefficients. Several design examples are given to demonstrate the effectiveness and feasibility of the proposed approach.published_or_final_versio

New design and realization techniques for a class of perfect reconstruction two-channel FIR filterbanks and wavelets bases

This paper proposes two new methods for designing a class of two-channel perfect reconstruction (PR) finite impulse response (FIR) filterbanks (FBs) and wavelets with K-regularity of high order and studies its multiplier-less implementation. It is based on the two-channel structural PR FB proposed by Phoong et al. The basic principle is to represent the K-regularity condition as a set of linear equality constraints in the design variables so that the least square and minimax design problems can be solved, respectively, as a quadratic programming problem with linear equality constraints (QPLC) and a semidefinite programming (SDP) problem. We also demonstrate that it is always possible to realize such FBs with sum-of-powers-of-two (SOPOT) coefficients while preserving the regularity constraints using Bernstein polynomials. However, this implementation usually requires long coefficient wordlength and another direct-form implementation, which can realize multiplier-less wavelets with K-regularity condition up to fifth order, is proposed. Several design examples are given to demonstrate the effectiveness of the proposed methods. © 2004 IEEE.published_or_final_versio

On the design and implementation of a class of multiplier-less two-channel 1-D and 2-D nonseparable PR FIR filterbanks

This paper proposes a new design and implementation method for a class of multiplierless 2-channel 1D and 2D nonseparable perfect reconstruction (PR) filterbanks (FB). It is based on the structure proposed by S.M. Phoong et al. (see IEEE Trans. Sig. Proc., vol.43, p.649-64, 1995) and the use of multiplier blocks (MB). The latter technique allows one to further reduce the number of adders in implementing these multiplier-less FB by almost 50%, compared to the conventional method using sum of powers of two coefficients (SOPOT) alone. Furthermore, by generalizing the 1D to 2D transformation of Phoong et al., new 2D PR FBs with quincunx, hourglass, and parallelogram spectral support are obtained. These nonseparable FBs can be cascaded to realize new multiplierless PR directional FB for image processing and motion analysis. Design examples are given to demonstrate the usefulness of the proposed method.published_or_final_versio

The design of digital all-pass filters using second-order cone programming (SOCP)

This brief proposes a new method for designing digital all-pass filters with a minimax design criterion using second-order cone programming (SOCP). Unlike other all-pass filter design methods, additional linear constraints can be readily incorporated. The overall design problem can be solved through a series of linear programming subproblems and the bisection search algorithm. The convergence of the algorithm is guaranteed. Nonlinear constraints such as the pole radius constraint of the filters can be formulated as additional SOCP constraints using Rouche's theorem. It was found that the pole radius constraint allows an additional tradeoff between the approximation error and the stability margin. The effectiveness of the proposed method is demonstrated by several design examples and comparison with conventional methods. © 2005 IEEE.published_or_final_versio

A new method for designing FIR filters with variable characteristics

This letter proposes a new method for designing finite-impulse response (FIR) filters with variable characteristics. The impulse response of the variable digital filter (VDF) is parameterized as a linear combination of functions in the spectral or tuning parameters. Using the least square objective function, the optimal solution is obtained by solving a system of linear equations. Design results show that this method is simple and effective in designing FIR VDF with good frequency characteristics. Furthermore, by using piecewise polynomial, instead of ordinary polynomial, more complicated frequency characteristics, or larger tuning range can be approximated.published_or_final_versio

Efficient design of a class of multiplier-less perfect reconstruction two-channel filter banks and wavelets with prescribed output accuracy

The 11th IEEE Signal Processing Workshop on Statistical Signal Processing, Singapore, 6-8 August 2001This paper proposes a novel algorithm for the design and hardware reduction of a class of multiplier-less two-channel PR filter banks (FBs) using sum-of-powers-of-two (SOPOT) coefficient. It minimizes a more realistic hardware cost, such as adder cells, subject to a prescribe output accuracy taking into account of the rounding and overflow effects, instead of using just the SOPOT terms as in conventional method. Furthermore, by implementing the filters in the FBs using multiplier-block (MB), significant overall saving in hardware resources can be achieved. An effective random search algorithm is also proposed to solve the design problem, which is also applicable to PR IIR FBs with highly nonlinear objective functions.published_or_final_versio

The design of a class of perfect reconstruction two-channel FIR linear-phase filterbanks and wavelets bases using semidefinite programming

This paper proposes a new method for designing a class of two-channel perfect reconstruction (PR) linear-phase FIR filterbanks (FBs) and wavelets previously proposed by Phoong et al. By expressing the given K-regularity constraints as a set of linear equality constraints in the design variables, the design problem using the minimax error criterion can be solved using semidefinite programming (SDP). Design examples show that the proposed method is very effective and it yields equiripple stopband response while satisfying the given K-regularity condition.published_or_final_versio

On the design and efficient implementation of the Farrow structure

This letter proposes an efficient implementation of the Farrow structure using sum-of-powers-of-two (SOPOT) coefficients and multiplier-block (MB). In particular, a novel algorithm for designing the Farrow coefficients in SOPOT form is detailed. Using the SOPOT coefficient representation, coefficient multiplication can be implemented with limited number of shifts and additions. Using MB, the redundancy between multipliers can be fully exploited through the reuse of the intermediate results generated. Design examples show that the proposed method can greatly reduce the complexity of the Farrow structure while providing comparable phase and amplitude responses.published_or_final_versio

The design of a class of prefect reconstruction two-channel FIR and wavelets filterbanks using constrained least squares method and semidefinite programming

This paper proposes two new methods for designing a class of 2-channel PR FIR filterbanks and wavelets with K-regularity of high order. The K-regularity constraints are expressed as a set of linear constraints in the design variables. The first method formulates the design problem as a quadratic programming problem with linear equality constraints (QPLC), which can be solved using the method of Lagrange multiplier. The second design method employs the minimax error criteria and solves the design problem as a semidefinite programming problem (SDP). By removing the redundant variables, the equality constraints are automatically imposed into the design problem. The optimization problem is then formulated as a linear convex objective function subject to a union of affine set which can be represented by a set of linear matrix inequalities. Hence they can be solved using existing SDP solver. Design examples are given to demonstrate the effectiveness of the proposed methods.published_or_final_versio

The minimax design of digital all-pass filters with prescribed pole radius constraint using semidefinite programming (SDP)

This paper proposes a new method for designing digital all-pass filters with a minimax design criterion using semidefinite programming (SDP). The frequency specification is first formulated as a set of linear matrix inequalities (LMI), which is a bilinear function of the filter coefficients and the ripple to be minimized. Unlike other all-pass filter design methods, additional linear constraints can be readily incorporated. The overall design problem turns out to be a quasi-convex constrained optimization problem (solved using the SDP) and it can be solved through a series of convex optimization sub-problems and the bisection search algorithm. The convergence of the algorithm is guaranteed. Nonlinear constraints such as the pole radius constraint of the filters can also formulated as LMIs using the Rouche's theorem. It was found that the pole radius constraint allows an additional tradeoff between the approximation error and the stability margin in finite wordlength implementation. The effectiveness of the proposed method is demonstrated by several design examples.link_to_subscribed_fulltex