An algorithm is presented for fast implementation of time-varying wavelet packets maintaining perfect reconstruction throughout transitions. It is based on filter banks known as the extended lapped transforms in an association following the paths of a binary-tree. Methods for pruning or expanding the branches of the tree are presented and a discussion on adaptation issues is carried. Recently, ...

A maximally decimated filter bank system (with possibly unequal decimation ratios in the subbands) can be regarded as a generalization of the short-time Fourier transformer. In fact, it is known that such a “filter bank transformer” is closely related to the wavelet transformation. A natural question that arises when we conceptually pass from the traditional Fourier transformer to the filter ba...

This paper gives a practical method of extending an n× r matrix P (z), r ≤ n, with Laurent polynomial entries in one complex variable z, to a square matrix also with Laurent polynomial entries. If P (z) has orthonormal columns when z is restricted to the torus T, it can be extended to a paraunitary matrix. If P (z) has rank r for each z ∈ T, it can be extended to a matrix with nonvanishing dete...

In this paper, we generalize the Hadamard transform to the the case of lapped transform A matrix A(z) is a lapped Hadamard transform if it satisfies A ~ ( ~ ' ) A ( ~ ) = a~ for some integer a and all the entries of its coefficient matrices are i1. Many methods have been proposed to construct lapped Hadamard matrices. In this paper, we will study these matrices using the theory of paraunitary f...

In this paper, the fast implementation of cosine-modulated filter bank (CMFB) is revisited. A class of paraunitary CMFBs with arbitrary length is considered. By further reorganizing of the polyphase component matrix and using the linear-phase property of the prototype filter, we obtain a more efficient implementation structure for the CMFB, in which we use 2 x 2 lossless matrices instead of 2 x...

We apply the theory of Weyl-Heisenberg frames (WHFs) to oversampled FIR and IIR DFT filter banks (FBs). We show that the polyphase matrices provide a matrix representation of the frame operator, and we find conditions on a DFT FB to provide a WHF expansion. We also show that paraunitary and biorthogonal DFT FBs correspond to tight and exact WHFs, respectively, and that the frame bounds can be o...

This paper investigates the theory and structure of a large subclass of M-channel linear phase perfect reconstruction FIR lter banks | systems with analysis and synthesis lters of length subclass of systems, we rst investigate the necessary conditions for the existence of linear phase perfect reconstruction lter banks. Next, we develop a complete and minimal factorization for all even-channel l...

Oversampled filter banks (OSFB) have been considered for channel coding, since their redundancy can be utilised to permit the detection and correction of channel errors. In this paper, we propose an OSFB based channel coder for a correlated additive Gaussian noise channel, of which the noise covariance matrix is assumed to be known. Based on a suitable factorisation of this matrix, we develop a...

A filter bank is referred to as cosine modulated when all the analysis and synthesis filters are cosine modulated versions of one or two prototypes. The one-dimensional (1D) cosine modulated filter bank (CMFB) is wellknown for low design cost and low complexity. In the application of subband coding, it is sometimes desirable that the individual filters have linear phase. In this paper, we will ...