Peak-constrained Least-squares Research Articles

Design of variable bandwidth symmetric/anti-symmetric FIR single-band PCLS lowpass and highpass filters

This paper proposes a reconfiguration design of variable bandwidth symmetric/anti-symmetric finite impulse response single-band peak-constrained least squares (PCLS) lowpass and highpass filters. When the bandwidth of the filter changes, a new set of filter coefficients is derived based on the old set of filter coefficients via a modified method of bisection. Since the proposed algorithm is very efficient, the new set of filter coefficients can be obtained in real time. Also, the new set of filter coefficients can be arbitrarily close to the globally optimal solution of the new PCLS optimization problem.

Empirical formula for designing a class of linear phase FIR single band PCLS filters

This paper presents an empirical formulation relating the filter length, the transition-band bandwidth, the cutoff frequency, the maximum passband-ripple magnitude, the maximum stopband-ripple magnitude and the total ripple energy of a class of linear phase finite impulse response (FIR) single band peak constrained least squares (PCLS) filters. Design examples are presented to demonstrate applications and accuracies of the presented formula.

A new approach to the weighted peak-constrained least-square error FIR digital filter optimal design problem

This paper deals with the design of linear-phase finite impulse response (FIR) digital filters using weighted peak-constrained least-squares (PCLS) optimization. The PCLS error design problem is fo...

Peak constrained least-squares QMF banks

This paper presents two peak constrained least-squares quadrature mirror filter (QMF) banks design methods. The proposed design methods minimize the least-squares error of the reconstruction response and the subband filter responses with respect to the ideal responses under the given peak constraints on the reconstruction error ripple and subband filter stopband ripple without explicit specification of the transition-band bandedges of the subband filters. The proposed iterative algorithms converge efficiently in all the simulations, and achieve QMF banks with better performances and lower computational complexities than that obtained by other algorithms in literature. Furthermore, design trade-off among the peak constrained reconstruction error ripple size, subband filter ripple size, and the subband filter transition-band bandwidth of the QMF banks can be obtained from the presented algorithm. Various design examples are presented to illustrate the versatilities of the proposed design methods.

Optimal design of complex FIR filters with arbitrary magnitude and group delay responses

This paper presents a method for the frequency-domain design of digital finite impulse response filters with arbitrary magnitude and group delay responses. The method can deal with both the equiripple design problem and the peak constrained least squares (PCLS) design problem. Consequently, the method can also be applied to the equiripple passbands and PCLS stopbands design problem as a special case of the PCLS design. Both the equiripple and the PCLS design problems are converted into weighted least squares optimization problems. They are then solved iteratively with appropriately updated error weighting functions. A novel scheme for updating the error weighting function is developed to incorporate the design requirements. Design examples are included in order to compare the performance of the filters designed using the proposed scheme and several other existing methods.

Numerically efficient optimal design of cosine-modulated filter banks with peak-constrained least-squares behavior

Several current applications related to signal compression and representation and high-speed transmission require very selective filter banks/transmultiplexers. A possible solution is to employ the cosine-modulated filter banks/transmultiplexers (CMFBTs) where the prototype filters satisfy demanding constraints with respect to both the total stopband energy and maximum stopband ripple. This work proposes an efficient procedure to design nearly-perfect reconstruction CMFBT prototype filters with peak-constrained least-squares characteristics using a modified weighted least-squares algorithm. Substantial flexibility is added in the design of the magnitude response of the prototype filter, ranging from minimum stopband energy to minimum stopband ripple, which may be required in many applications. Some constraints are imposed to the CMFBTs in order to control the direct transfer and aliasing distortion functions, related to the intercarrier and intersymbol interferences. Algebraic simplifications are also provided on the overall objective function and associated constraints, leading to substantial reduction on the computational burden of the optimization process. The procedure is proven to be very powerful in designing CMFBT systems satisfying multiple constraints as indicated by numerical examples.

A Methodology for Rapid Prototyping Peak-Constrained Least-Squares Bit-Serial Finite Impulse Response Filters in FPGAs

Area-efficient peak-constrained least-squares (PCLS) bit-serial finite impulse response (FIR) filter implementations can be rapidly prototyped in field programmable gate arrays (FPGA) with the methodology presented in this paper. Faster generation of the FPGA configuration bitstream is possible with a new application-specific mapping and placement method that uses JBits to avoid conventional general-purpose mapping and placement tools. JBits is a set of Java classes that provide an interface into the Xilinx Virtex FPGA configuration bitstream, allowing the user to generate new configuration bitstreams. PCLS coefficient generation allows passband-to-stopband energy ratio (PSR) performance to be traded for a reduction in the filter's hardware cost without altering the minimum stopband attenuation. Fixed-point coefficients that meet the frequency response and hardware cost specifications can be generated with the PCLS method. It is not possible to meet these specifications solely by the quantization of floating-point coefficients generated in other methods.

The design of peak-constrained least squares FIR filters with low-complexity finite-precision coefficients

A method for the design of peak-constrained least squares (PCLS) finite-impulse response (FIR) digital filters with low-complexity finite-precision coefficients (FPC) based on Adams' optimality criterion and an efficient local search is presented. Simple quantization of the infinite precision coefficients typically leads to filter designs which fail to meet the frequency response, passband to stopband energy ratio (PSR) and coefficient complexity (number of coefficient adders and subtractors) specifications. It is shown that it is possible to design a filter with an acceptable PSR that meets the frequency response specification while using a reduced number of adders and subtractors.

Design of stable IIR digital filters with equiripple passbands and peak-constrained least-squares stopbands

This paper describes an algorithmic development for the design of stable infinite impulse response (IIR) digital filters with equiripple passbands and peak-constrained least-squares stopbands. Central to the development is a re-formulation of the design problem as an iterative quadratic programming problem where the stability and equiripple passbands and peak-constrained requirements are met by imposing a system of linear inequality constraints while the LSS property is satisfied by minimizing a weighted least-squares type objective function.

PCLS IIR digital filters with simultaneous frequency response magnitude and group delay specifications

This paper presents the peak-constrained least-squares (PCLS) approach to designing IIR digital filters. PCLS IIR digital filters that meet simultaneous specifications on the frequency response magnitude and the group delay are introduced. As a point of reference, we consider the IIR digital filter design problem that appears in Deczky's (1972) classic paper and in the popular textbook by Oppenheim and Schafer (1989). In addition, the same design problem appears in the IIR filter design chapter by Higgins and Munson (1993) in the Handbook for Digital Signal Processing. By using our new algorithm with simultaneous optimization of the frequency response magnitude and the group delay, we obtain a dramatic improvement in the solution of this classic IIR digital filter design problem. Starting from the same filter structure and the same specifications for the frequency response magnitude as in the works of Deczky, Oppenheim and Schafer, and Higgins and Munson, we are able to reduce the group delay ripple by a factor of 35. In another design problem that originated in Deczky's work, we use PCLS optimization to reduce the group delay ripple by a factor of 40 at the same time we reduce the stopband energy by 6 dB, without sacrificing any other performance measure. The group delay ripple in this IIR digital filter example is reduced to only /spl plusmn/0.002 samples.

Peak-constrained least-squares optimization

We presented the basic concepts for peak-constrained least-squares (PCLS) optimization in previous papers. We present advanced PCLS optimization concepts in this paper. This paper discusses only a few of the many ways that PCLS design problems can be formulated. We believe that the PCLS optimality criterion can be customized to fit virtually any practical application. For example, PCLS optimization can readily be used to design equalizers in the prefilter-equalizer or interpolated FIR implementations of filters.

FIR digital filters with least-squares stopbands subject to peak-gain constraints

The use of digital filters with peak-constrained least weighted-squared errors (PCLWSE) is proposed. The emphasis is on PCLWSE filters with equiripple passbands and peak-constrained least-squares (PCLS) stopbands. The stopband energy is minimized subject to a constraint on the maximum stopband gain. A design algorithm is presented, and examples are discussed. Each example provides the unique optimal solution to the corresponding design problem. The tradeoff between the peak stopband gain and the total stopband energy is examined. It is shown that the most inefficient filters have minimax or least-squares stopbands. In particular, the stopband energy for minimax filters can be significantly reduced with almost no change in the peak stopband gain. Also, the peak stopband gain for filters with least-squares stopbands can be significantly reduced with almost no change in the total stopband energy. These results are supported by mathematical analysis, and examples are provided.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>