Biorthogonal modulated "lter banks, when compared to paraunitary ones, provide the advantage that the overall system delay can be chosen independently of the "lter length, thus allowing to design low delay "lter banks. They have recently been studied by several authors. In this paper, we connect two di!erent design methods, namely the quadratic constrained least-squares optimization and the pri...

The design of optimal prototype lters for multiresolution signal decomposition is considered. Filters will be optimized with respect to the following quality criteria: a) maximum coding gain of subband coding over PCM; b) minimum approximation error for zonal sampling. Only in the special case of paraunitary systems both criteria are nearly equivalent. As an example for more general systems, th...

This paper gives a practical method of extending an nr 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 2 T, it can be extended to a matrix with nonvanishing determin...

This paper presents boundary optimization techniques for the processing of arbitrary-length signals with paraunitary multirate filter banks. The boundary filters are designed to maximize the coding gain while providing an ideal dc behavior where all filters except the low-pass filters have zero mean. Moreover, solutions are presented that have similar frequency responses as the original subband...

A construction approach for the 3-band tight wavelet frames by factorization of paraunitarymatrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3-band tight wavelet frames. Further, the paramete...

The general factorization of a linear-phase paraunitary filter bank (LPPUFB) is revisited and we introduce a class of lapped orthogonal transforms with extended overlap (GenLOT). In this formulation, the discrete cosine transform (DCT) is the order-l GenLOT, the lapped orthogonal transform is the order-:! GenLOT, and so on, for any filter length which is an integer multiple of the block size. A...

This paper, introduces a new lter bank structure called the perfect reconstruction circular convolution (PRCC) lter bank. These lter banks satisfy the perfect reconstruction properties, namely, the paraunitary properties in the discrete frequency domain. We further show how the PRCC analysis and synthesis lter banks are completely implemented in this domain and give a simple and a exible method...