The most commonly used 2-D filter banks are separable filter banks, which can be obtained by cascading two 1-D filter banks in the form of a tree. The supports of the analysis and synthesis filters in the separable systems are unions of four rectangles. The natural nonseparable generalization of such supports are those that are unions of four parallelograms. In this paper, we study four paralle...

It is a challenging task to design orthogonal filter banks, especially multidimensional (MD) ones. In the onedimensional (1D) two-channel finite impulse response (FIR) filter bank case, several design methods exist. Among them, designs based on spectral factorizations (by Smith and Barnwell) and designs based on lattice factorizations (by Vaidyanathan and Hoang) are the most effective and widel...

In this paper, we develop a method to construct non-redundant directional wavelet filter banks. Our method uses a special class of filters called Neville filters and can construct non-redundant wavelet filter banks in any dimension for any dilation matrix. The resulting filter banks have directional analysis highpass filters, thus can be used in extracting directional contents in multi-D signal...

This paper presents methods for the design of non-uniform filter banks. The filter bank structure is obtained from a uniformly modulated filter bank by using an allpass transform which has a lossless frequency function and a nonlinear phase function. The proposed design method includes quadratic optimization with linear constraints. Considered applications are subband adaptive filtering and sub...

This paper presents methods for the design of nonuniform filter banks. The filter bank structure is obtained from an uniformly modulated filter bank by using an allpass transform which has a lossless frequency function and a nonlinear phase function. The proposed design methods include linear and quadratic frequency domain criteria and linear constraints. Considered applications are subband ada...

The performance of subband image coders depends on the proper choice of filter banks. It is therefore desirable to find algorithms for optimizing the filter banks. A theory for finding jointly optimized analysis and synthesis filter banks with arbitrary filter lengths and arbitrary delay through the filter bank is proposed. Theoretical results are included. Comparisons are made against the well...

In this paper, we present a method of approximating a given 2D filter using the orthogonal wavelet filter banks. Construction of 2D orthogonal wavelet filter banks is still an open problem. In this paper, a family of orthogonal wavelet filter banks based on 2D lattice structure are used to approximate the desirable filter. By virtue of this structure, we approximate the given filter step by ste...

In this paper, a novel technique for the design of two-channel Quadrature Mirror Filter (QMF) banks with linear phase in frequency domain is presented. To satisfy the exact reconstruction condition of the filter bank, low-pass prototype filter response in pass-band, transition band and stop band is optimized using unconstrained indirect update optimization method. The objective function is form...

The significant advantage of modified discrete Fourier transform (MDFT) filter banks over the conventional discrete Fourier transform (DFT) filter banks is the structure inherent alias cancellation in the former. When the number of channels is increased, the filters in the filter bank need to be of sharp transition width. This increases the complexity of the filters and hence that of the filter...

Perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in `(Z). These frames are the subject of this paper. First, necessary and sufficient conditions on a filter bank for implementing a frame or a tight frame expansion are established, as well as a necessary and sufficient condition for perfect reconstruction using FIR filters after an FIR analysis. Comp...