In this work, we propose a novel method for the design of oversampled perfect reconstruction (PR) discrete Fourier transform (DFT) modulated filter banks (FB) for application to multi-carrier modulation (MCM). The PR property is enforced by employing a parametric class of paraunitary matrices to form the transmit/receive polyphase filters of the transceiver system. Specifically, the polyphase f...

Let P be an r×s matrix of Laurent polynomials with symmetry such that P(z)P∗(z) = Ir for all z ∈ C\{0} and the symmetry of P is compatible. The matrix extension problem with symmetry is to find an s × s square matrix Pe of Laurent polynomials with symmetry such that [Ir,0]Pe = P (that is, the submatrix of the first r rows of Pe is the given matrix P), Pe is paraunitary satisfying Pe(z)P∗e(z) = ...

This paper presents a paraunitary filter bank (PUFB) based on a direct lifting structure of a building block and its inverse transform for lossless-to-lossy image coding. Although the conventional liftingbased filter banks (LBFBs), which are constructed by lifting structures with integer coefficients and rounding operations, suffer from degradation of coding performance due to much rounding err...

This paper presents a new method for designing two-band orthonormal IIR wavelet "lter banks using allpass "lters. It is well known that orthonormal wavelet bases can be generated by paraunitary "lter banks. Thus, synthesis of orthonormal wavelet bases can be reduced to the design of paraunitary "lter banks. In this paper, two-band orthonormal IIR wavelet "lter banks using a parallel connection ...

In this paper we study the algebraic structure of the space of compactly supported orthonormal wavelets over real numbers. Based on the parametrization of wavelet space, one can deene a parameter mapping from the wavelet space of rank 2 (or 2-band, scale factor of 2) and genus g to the (g ? 1) dimensional real torus (the products of unit circles). By the uniqueness and exactness of factorizatio...

Feedback Delay Networks are one of the most popular and efficient means generating artificial reverberation. Recently, we proposed Grouped Network (GFDN), which couples multiple FDNs while maintaining system stability. The GFDN can be used to model reverberation in coupled spaces that exhibit multi-stage decay. block feedback matrix determines inter- intra-group coupling. In this article, expan...

z In this paper, the one-dimensional principal component lter banks (PCFB's) derived in 17] are generalized to higher dimensions. As presented in 17], PCFB's minimize the mean-squared error (MSE) when only Q out of P subbands are retained. Previously, 2D PCFB's were proposed in 16]. The work in 16] was limited to 2D signals and separable resampling operators. The formulation presented here is g...

In this paper, a design method of two-dimensional (2-D) orthogonal symmetric wavelets is proposed by using a lattice structure for multi-dimensional (M-D) linear-phase paraunitary filter banks (LPPUFB), which the authors have proposed as a previous work and then modified by Lu Gan et al. The derivation process for the constraints on the second-order vanishing moments is shown and some design ex...

Recently connections between the wavelet transform and lter banks have been established. We show that similar relations exist between the Gabor expansion and DFT lter banks. We introduce the \z-Zak transform" by suitably extending the discrete-time Zak transform and show its equivalence to the polyphase representation. A systematic discussion of parallels between DFT lter banks and Weyl-Heisenb...