Chair: Thomas Parks, University at California, (USA)
Magdy T. Hanna, University of Bahrain (BAHRAIN)
Based on a discrete frequency domain formulation of the design problem of two-dimensional FIR filters, a closed form expression is derived for the matrix of filter coefficients without imposing any assumptions of having a symmetric, antisymmetric or zero-phase frequency response. The matrix in question is derived by minimizing the Frobenius norm of the difference between the matrices of the actual and ideal frequency responses at the points of a frequency grid. The method has the advantages of conceptual and computational simplicity.
Amin G. Jaffer, Hughes Aircraft Company
William E. Jones, Hughes Aircraft Company
Theagenis J. Abatzoglou, Lockheed Research Laboratories (USA)
This paper presents the design of 2-D complex FIR filters using the weighted integral least- squares error criterion (WLS). Both the cases of arbitrary magnitude with linear and arbitrary phase specifications are addressed. The solution of the linear phase case is obtained using the complex Lagrange multiplier formulation to incorporate the necessary constraints for linear phase response. This results in a computationally efficient filter design technique requiring the solution of a Hermitian Toeplitz-block-Toeplitz system of linear equations for which fast algorithms are available. Two illustrative filter design examples are also presented.
Ivan W. Selesnick, Rice University (USA)
Markus Lang, Rice University (USA)
C. Sidney Burrus, Rice University (USA)
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 $L_2$ filter and a continuum of Chebyshev filters as special cases.
Markus Lang, Rice University (USA)
The Problem of allpass filter design for phase approximation and equalization in the Chebyshev sense is solved by using a generalized Remez algorithm. Convergence to the unique optimum is guaranteed and is achieved rapidly in the actual implementation. The well-known numerical problems for higher degree filters are analyzed and solved by a simple approach. Possible applications are: design of filters with a desired phase response (e.g., a delay element), the design of phase equalizers, or the design of recursive filters with magnitude prescriptions using parallel allpass filters. For the latter the algorithm can be modified to allow arbitrary tolerance schemes for the magnitude response.
Paolo Gentili, Universita di Ancona (ITALY)
Francesco Piazza, Universita di Ancona (ITALY)
Aurelio Uncini, Universita di Ancona (ITALY)
This paper presents an efficient genetic approach to the design of digital finite impulse response (FIR) filters with coefficients constrained to be sums of power-of-two terms. To obtain such efficiency, i.e. a reduction of computational costs and an improvement in performance, a specific filter coefficient coding scheme has been studied and implemented. The resulting genetic algorithm (GA) is explained and compared experimentally with other state-of- the-art design techniques on several power-of-two FIR filter design cases. It can be seen that the proposed genetic technique is able to attain results as good or better than the other methods. Moreover it can be easily implemented on parallel hardware.
Chaur-Heh Hsieh, Chung Cheng Institute of Technology (REPUBLIC OF CHINA)
Ying-Luan Han, Chung Cheng Institute of Technology (REPUBLIC OF CHINA)
Chung-Ming Kuo, Chung Cheng Institute of Technology (REPUBLIC OF CHINA)
Yue-Dar Jou, Chung Cheng Institute of Technology (REPUBLIC OF CHINA)
Recently, the Weighted Least Square (WLS) technique for the FIR filter design has received wide attention, since it is computationally more efficient than other minimax techniques. However for two-dimensional (2-D) filter design, the conventional WLS technique rearranges the frequency samples and the impulse filter coefficients with 2-D form into 1-D form, thus the WLS technique results in expensive computation. This paper presents a new 2-D FIR filter design method which retains the frequency samples and impulse filter coefficients in their 2-D form. Experimental results show that the new technique is computationally very efficient and leads to nearly-optimal approximations.
G.D. Cain, University of Westminster (UK)
A. Yardim, University of Westminster (UK)
P. Henry, ESIEE - Paris (FRANCE)
Non-optimal FIR filters used for fractional-sample delay, despite their wideband nature, are shown to benefit significantly from application of windowing. Here simple raised-cosine windows prove to be very effective, particularly if they are cast as asymmetric modifications of their conventional forms. The offset von Hann window is surprisingly potent when the number of coefficients is large and window offset coincides with the fractional delay required of the overall filter.
Theagenis J. Abatzoglou, Lockheed Research Laboratories
Amin G. Jaffer, Hughes Aircraft Company (USA)
A design of 2-D complex FIR filters is proposed by minimizing the pth power norm used to measure the deviation of the FIR filter response from a desired filter response. The solution of this problem cannot be obtained in closed form except for p=2; for arbitrary p>2 we present an approach which treats the problem from a complex variable point of view. An iterative scheme is described based on the complex Newton method to find the solution. It has the feature that, starting with p=2, the value of p is increased after each iteration. Because the objective function is convex any local extremum is the global minimum. Convergence can be attained after a moderate number of iterations. A characterization theorem for factorization of 2-D FIR filters in terms of 1-D filters is derived. This has strong implications for large order 2-D filter design. Two filter design examples are included.
M.A. Masnadi-Shirazi, Shiraz University (IRAN)
M. Ghasemi, Shiraz University (IRAN)
The main contribution of this paper is to use the Laguerre networks in frequency domain, and to design the digital filters based on the specified frequency response. This filter design yields appropriate linear phase, with lower ripples in stopband and passband compared to the conventional FIR filters. Both, analytical and numerical approaches for Laguerre digital filter design will be introduced in details and the results will be shown through some examples. The procedure is based on minimizing the mean-square-error (MSE) between the frequency response of the desired filter and its corresponding Laguerre network frequency response.
B. Vo, Curtin University of Technology
A. Cantoni, Curtin University of Technology
K.L. Teo, University of Western Australia (AUSTRALIA)
The discrete-time envelope constrained (EC) filtering problem can be formulated as a quadratic programming (QP) problem with linear inequality constraints. In this paper, the QP problem is approximated by an unconstrained minimization problem with two parameters. These parameters can be selected so that given an acceptable deviation from the norm of the optimal EC filter, the solution to the unconstrained problem satisfies both the deviation and the envelope constraints. Newton's method with line search is applied to solve the unconstrained problem iteratively.