This paper addresses a polyphase structure of spectral graph wavelets and filter banks. We consider two-channel critically sampled graph filter banks. In classical signal processing, polyphase structure of filter banks is very useful since downsampler (upsampler) can be placed before analysis filtering (after synthesis filtering). We theoretically derive that a similar structure is also possibl...

Dual wavelet frames and their associated dual framelet filter banks are often constructed using the oblique extension principle. In comparison with the construction of tight wavelet frames and tight framelet filter banks, it is indeed quite easy to obtain some particular examples of dual framelet filter banks with or without symmetry from any given pair of low-pass filters. However, such constr...

Quincunx filter banks are two-dimensional, two-channel, nonseparable filter banks. They are widely used in many signal processing applications. In this thesis, we study the design and applications of quincunx filter banks in the processing of two-dimensional digital signals. Symmetric extension algorithms for quincunx filter banks are proposed. In the one-dimensional case, symmetric extension i...

The purpose of this paper is twofold. First, a comprehensive review is performed on the existing two-channel FIR filter banks as well as on the design techniques proposed in the literature for designing these banks. We concentrate on alias-free banks. These banks can be first classified into perfect-reconstruction and nearly perfect-reconstruction banks. The nearly perfectreconstruction filter ...

This paper shows the efficiency of using constrained optimization for designing two-channel low-delay finite impulse response filter banks. The filter banks under consideration are quadrature mirror filter (QMF) banks and perfect reconstruction (PR) biorthogonal filter banks. The design problems for both types of banks are stated as constrained minimization problems in forms that enables us to ...

In this paper, we present a method for designing lossless versions of two-channel FIR filter banks. We demonstrate that equal length PR FIR filter banks can be decomposed into 2-point transforms and unequal length into interpolative predictions. The lossless versions of the filter banks are obtained by replacing every constituent module by the corresponding lossless version. This method allows ...

Despite the great popularity of critically-decimated filter banks, oversampled filter banks are useful in applications where data expansion is not a problem. We studied oversampled filter banks and showed that for some popular classes of filter banks it is not possible to obtain perfect reconstruction with rational (non-integer) oversampling ratios. Nevertheless, it is always possible to oversa...

Abstract – This paper introduces two-channel FIR filter banks synthesized using the frequencyresponse masking approach. The proposed filter banks have a lower computational complexity compared with conventional filter banks, especially when the individual filters have narrow transition bands. One price to pay is a somewhat increased overall delay. A design example is included illustrating the e...

In this paper, theoretical properties of deinterlacer banks are analyzed. Deinterlacer banks are novel filter banks in the sense that a progressive video sequence is separated into two progressive video sequences of a half frame rate and, furthermore, interlaced sequences are produced as intermediate data. Unlike the conventional filter banks, our deinterlacer banks are constructed in a way uni...

Perfect reconstruction (PR) filter banks have found numerous applications, and have received much attention in the literature. For linear filter banks, necessary and sufficient conditions for PR have been established for most practical situations. Recently, nonlinear filter banks have been proposed for image coding applications. These filters are generally simple, and produce better results tha...