Yasunori Sugita

A design method for separable-denominator 2D IIR filters using a stability criterion based on the system matrix

In this paper, we propose designing method for separable-denominator two-dimensional Infinite Impulse Response (IIR) filters (separable 2D IIR filters) by Successive Projection (SP) methods using a stability criterion based on the system matrix. It is generally known that separable 2D IIR filters are stable if and only if each of the denominators is stable. Therefore, the stability criteria of 1D IIR filters can be used for separable 2D IIR filters. A stability criterion based on the system matrix is a necessary and sufficient condition to guarantee stability in 1D IIR filters. Therefore, separable 2D IIR filters obtained by the proposed method have a smaller error ripple than those obtained by the conventional method.

Designing FIR Digital Filters with the Specified Maximum Group Delay Errors

This paper describes a design method of FIR digital filters that meet simultaneously amplitude and group delay specifications using successive projection method. The proposed method allows the direct approximation of the group delay characteristics, and it can also restrict the group delay characteristics within the preselected allowable errors. It is shown by numerical examples that the proposed method provides very good results compared with the previous methods.

A design method of minimum phase FIR filters with complex coefficients

In this paper, we present a directly design method of minimum phase FIR filters with complex coefficients using successive projections (SP) method. In general, it is necessary to restrict the zeros of transfer function inside the unit circle or on the unit circle to directly obtain the transfer function of minimum phase FIR filters. We use Rouches theorem for coefficient update algorithm in SP method to restrict the zeros of the transfer function inside the unit circle and on the unit circle. Therefore, the transfer function of minimum phase FIR filter is obtained without factorization by using the proposed method. Moreover, the proposed method is also able to obtain the transfer function of real coefficients by considering the imaginary part of complex coefficients as the zero. The usefulness of the proposed method is verified through some examples.

Design of IIR digital filters with arbitrary flatness using iterative quadratic programming

This paper presents a design method of Chebyshev-type and inverse-Chebyshev-type infinite impulse response (IIR) filters with an approximately linear phase response. In the design of Chebyshev-type filters, the flatness condition in the stopband is preincorporated into a transfer function, and an equiripple characteristic in the passband is achieved by iteratively solving the QP problem using the transfer function. In the design of inverse-Chebyshev-type filters, the flatness condition in the passband is added to the constraint of the QP problem as the linear matrix equality, and an equiripple characteristic in the stopband is realized by iteratively solving the QP problem. To guarantee the stability of the obtained filters, we apply the extended positive realness to the QP problem. As a result, the proposed method can design the filters with more high precision than the conventional methods. The effectiveness of the proposed design method is illustrated with some examples.

A two-stage design of IIR filters using quadratic programming and particle swarm optimization

A two-stage design method of infinite impulse response (IIR) digital filters with a smaller group delay error is presented in this paper. In the first stage, the complex chebyshev approximation based on Quadratic Programming (QP) is applied to obtain a stable IIR filter with an approximately constant group delay in the passband. In the second stage, to improve only the group delay response of the obtained filter in stage 1, the group delay error minimization problem which has a maximum amplitude error constraint is solved using Particle swarm optimization (PSO). Compared with the conventional methods, the proposed method can design the IIR filters with about the same amplitude response and a smaller group delay error. The usefulness of the proposed method is verified through some examples.

DESIGN OF QUASI-EQUIRIPPLE IIR FILTERS WITH PRESCRIBED FLATNESS AND APPROXIMATELY LINEAR PHASE

In this paper, we propose a method for designing quasiequiripple infinite impulse response (IIR) filters with prescribed flatness and approximately linear phase characteristics. In the proposed method, the flatness condition in stopband is preincorporated into the transfer function and the design problems are formulated as an iterative quadratic programming (QP) problem. The flatness condition in passband is added to the QP problem as the linear matrix equality. As a result, the proposed method can design the IIR filters which have an equiripple response and prescribed flatness in passband or stopband or both. Finally, we show some design examples and confirm the effectiveness of the proposed method.

A successive projections method with a changeable maximum allowable deviation

A applicability of Successive Projections (SP) method is wide. In the previous SP method which is an iterative approximation method, only one extreme frequency point at which the deviation from the given specification is maximized is used in the update of the filter coefficients. We extended to SP method which can update the filter coefficients by the multiple extreme frequency points using Fritz Johns theorem. In this method, the solution is obtained less iteration number than the previous method. However, because it is necessary to decide the maximum allowable error experientially, there is the case that the solution does not converge and the obtained filter does not have equiripple characteristics. In this paper, we present a design method of linear phase FIR filters by SP method updating maximum allowable error. The updating maximum allowable error analytically solves such as Remez algorithm. Finally, we confirm the effectiveness of propose method through several examples.

Reducing Stopband Peak Errors of R-Regular 4th-Band Linear Phase FIR Filters by Superimposing

R-regular Mth band filters are an important class of digital filters and are used in constructing Mth-band wavelet filter banks, where the regularity is essential. But this kind of filter has larger stopband peak errors compared with a minimax filter of the same length. In this paper, peak errors in stopband of R-regular 4th-band filters are reduced by means of superimposing two filters with successive regularities. Then the stopband peak errors in the resulting filters are compared with the original ones. The results show that the stopband peak errors are reduced significantly in the synthesized filter that has the same length as the longer one of the two original filters, at the cost of regularity.