Toshinori Yoshikawa

Design of orthonormal symmetric wavelet filters using real allpass filters

Abstract In this paper, a class of real-valued orthonormal symmetric wavelet filters is constructed by using allpass filters, and a new method for designing the allpass-based wavelet filters with the given degrees of flatness is proposed. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez exchange algorithm and considering the flatness condition. Therefore, a set of filter coefficients can be easily computed by solving the eigenvalue problem, and the optimal solution in the minimax sense is obtained through a few iterations. Furthermore, the design of the maximally flat allpass-based wavelet filters is also included as a specific case, but it has a closed-form solution that is the same as in Selesnick (IEEE Trans. Signal Process. 46 (4) (April 1998) 1138–1141) so that the iteration procedure is not needed. Finally, some examples are designed to investigate the filter characteristics, and it is shown that the number of delay elements strongly influences the filter magnitude responses.

Design of FIR Nyquist filters with low group delay

A new method is proposed for designing FIR Nyquist filters with zero-crossing impulse response and low group delay. It is first shown that FIR Nyquist filters that satisfy the zero-crossing time-domain condition have a frequency response property where both the magnitude and phase responses in the passband are dependent on the stopband response. Therefore, the design problem will become a magnitude approximation in the stopband. The proposed procedure is based on the formulation of a linear problem by using the multiple Remez exchange algorithm in the stopband directly. Hence, the filter coefficients can be computed by solving linear equations, and the optimal solution with an equiripple stopband response is easily obtained after applying an iteration procedure. Although the proposed Nyquist filters have an approximate linear phase response, its group delay is lower than the conventional FIR Nyquist filters. The proposed procedure is computationally efficient because it only solves a set of linear equations. Finally, the characteristics of the low-delay FIR Nyquist filters are examined, and the performance is compared with the conventional FIR Nyquist filters.

A new class of orthonormal symmetric wavelet bases using a complex allpass filter

This paper considers the design of the whole sample symmetric (WSS) paraunitary filterbanks composed of a single complex allpass filter and gives a new class of real-valued orthonormal symmetric wavelet bases. First, the conditions that the complex allpass filter has to satisfy are derived from the symmetry and orthonormality conditions of wavelets, and its transfer function is given to satisfy these conditions. Second, the paraunitary filter banks are designed by using the derived transfer function from the viewpoints of the regularity and frequency selectivity. A new method for designing the proposed paraunitary filterbanks with a given degrees of flatness is presented. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez exchange algorithm. Therefore, the filter coefficients can be easily obtained by solving the eigenvalue problem, and the optimal solution is attained through a few iterations. Furthermore, both the maximally flat and minimax solutions are also included in the proposed method as two specific cases. The maximally flat filters have a closed-form solution without any iteration. Finally, some design examples are presented to demonstrate the effectiveness of the proposed method.

Complex Chebyshev approximation for IIR digital filters based on eigenvalue problem

This paper presents an efficient method for designing complex infinite impulse response digital filters in the complex Chebyshev sense. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez multiple exchange algorithm. Hence, the filter coefficients can be easily obtained by solving the eigenvalue problem to find the absolute minimum eigenvalue, and then the complex Chebyshev approximation is attained through a few iterations starting from a given initial guess. The proposed algorithm is computationally efficient because it not only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step. Some design examples are presented and compared with the conventional methods. It is shown that the results obtained by using the method proposed in this paper are better than those obtained by the conventional methods.

Design of orthonormal IIR wavelet filter banks using allpass filters

Abstract This paper presents a new method for designing two-band orthonormal IIR wavelet filter banks using allpass filters. It is well known that orthonormal wavelet bases can be generated by paraunitary filter banks. Thus, synthesis of orthonormal wavelet bases can be reduced to the design of paraunitary filter banks. In this paper, two-band orthonormal IIR wavelet filter banks using a parallel connection of two real allpass filters or a complex allpass filter are examined. From the regularity of wavelets, an additional flatness condition is required to impose on the filter banks. Then, the design problem of orthonormal IIR wavelet filter banks with a given flatness condition is discussed. By considering the given flatness condition and using the Remez exchange algorithm, the design problem can be formulated in the form of an eigenvalue problem. Therefore, a set of filter coefficients can be easily gotten by solving the eigenvalue problem to compute the absolute minimum eigenvalue, and the optimal solution with an equiripple response can be obtained after using an iteration procedure. The proposed method is computationally efficient since the efficient Remez exchange algorithm is employed, and the flatness condition can be arbitrarily specified. Some design examples are presented to demonstrate the effectiveness of the proposed method.

Design of two-channel IIR linear phase PR filter banks

Abstract In this paper, a novel method is proposed for designing two-channel biorthogonal perfect reconstruction filter banks with exact linear phase using noncausal IIR filters. Since the structurally perfect reconstruction implementation is adopted, the proposed filter banks are guaranteed to be a perfect reconstruction even when all filter coefficients are quantized. From the view point of wavelets, design of biorthogonal IIR linear phase filter banks with an additional flatness constraint is considered. The proposed design method is based on the formulation of a generalized eigenvalue problem by using Remez exchange algorithm. Hence, the filter coefficients can be obtained by solving the eigenvalue problem to compute the positive minimum eigenvalue, and the optimal solution in the Chebyshev sense is easily obtained through a few iterations. The proposed procedure is computationally efficient, and the flatness constraint can be arbitrarily specified. Some design examples are presented to demonstrate the effectiveness of the proposed method.

Design of causal IIR perfect reconstruction filter banks

This paper presents a new method for designing two channel biorthogonal IIR filter banks, which satisfy both the perfect reconstruction and causal stable conditions. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez multiple exchange algorithm. Therefore, the filter coefficients can be computed by solving the eigenvalue problem, and the optimal solution is easily obtained through a few iterations. One example is designed to demonstrate the effectiveness of the proposed method.

Moment of cepstrum and its applications

It is shown that the moments of a signal sequence and of its corresponding cepstral sequence are related in a way which obviates the need for the direct calculation of the cepstral coefficients. Hence, an ideal calculation for the moments of the cepstrum is possible even if the duration of the cepstrum is infinite. It is also possible to describe all the properties of a signal sequence from its moments. The effectiveness of this method is demonstrated in the problems of homomorphic deconvolution and echo removal. It is also shown that in linear filtering problems, the moments of the minimum-phase sequence are calculated from the corresponding linear-phase sequence without actually calculating the minimum-phase sequence. For a discrete-time real signal sequence with finite duration, complete equivalence is demonstrated between the signal sequence and its moments. This permits a new description and a new set of design specifications based on moments for such systems. >

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.

Closed-Form Design of Generalized Maxflat

Mth-band filters have found numerous applications in multirate signal processing systems, filter banks, and wavelets. In this paper, the design problem of generalized maxflat R-regular finite impulse response (FIR) Mth-band filters with a specified integer group delay at omega=0 is considered, and the closed-form expression for its impulse response is presented. The filter coefficients are directly derived by solving a linear system of Vandermonde equations that are obtained from the regularity condition of the maxflat R-regular FIR Mth-band filters via the blockwise waveform moments. Differing from the conventional FIR Mth-band filters with exactly linear phase responses, the generalized FIR Mth-band filters proposed in this paper have an arbitrarily specified integer group delay at omega=0. Moreover, a new efficient implementation of the generalized maxflat R-regular FIR Mth-band filters is proposed by making use of the relationship between the filter coefficients in the closed-form solution. Finally, several design examples are presented to demonstrate the effectiveness of the proposed FIR Mth-band filters