Quadrature mirror filter

About: Quadrature mirror filter is a research topic. Over the lifetime, 955 publications have been published within this topic receiving 28900 citations.

Optimal Design of Complex Two-Channel IIR QMF Banks with Equiripple Response *

Abstract: The optimal design of complex infinite impulse response (IIR) two-channel quadrature mirror filter (QMF) banks with equiripple frequency response is considered. The design problem is appropriately formulated to result in a simple optimization problem. Therefore, based on a variant of Karmarkar's algorithm, we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the complex coefficients for the IIR QMFs. The effectiveness of the proposed technique is to form an appropriate Chebyshev approximation of a desired response and then find its solution from a linear subspace in several iterations. Finally, simulation results are presented for illustration and comparison.

Optimization of Linear Multiresolution Transforms for Scene Adaptive Coding

Abstract: Scene adaptive coders are constituted by the cascade of a linear transform, scalar quantization, entropy coding and a huffer con- trolled by a feedback loop for hit rate regulation. The main contrihu- tion of this paper is to derive an analytical criterion evaluating the performances of any perfect reconstruction linear transform in the frame of scene adaptive coding. This criterion is, thereafter, used in order to optimize linear multiresolution transforms. The optimization adapts the filters parameters to the codec features and to the statistics of the 2-D sources; so, we call these tranforms adapted multiresolution transforms (AMT's). The transforms under study are implemented by a cascade of separable perfect-reconstruction (PR) FIR two-band filter hanks that can change at each resolution level. Two types of filter banks are envisaged: the PR orthogonal quadrature mirror filter (QMF) bank, which allows to implement the orthogonal AMT and the PR linear-phase filter (LPF) bank, which implements the biorthogonal AMT. We per- form the optimization of the filters in their factorized lattice form, tak- ing the finite length of the multipliers into account. Our criterion also allows to show the performances achieved by these two linear multi- resolution transforms compared to other linear (multiresolution) transforms.

One and two-dimensional digital mutirate systems with applications in sub-sampling and bandlimited signal reconstruction

Abstract: This thesis deals with the two-dimensional (2D) multirate quadrature mirror filter (QMF) bank and new applications of 1D and 2D multirate filter bank concepts to the periodic nonuniform sampling and reconstruction of bandlimited signals. The potential use of multirate filter banks in the statistically optimal estimation of signals in the presence of wide-sense cyclostationary noise is also examined. The two-dimensional QMF bank is free from aliasing if and only if a certain polyphase matrix product related to the filter bank possesses the 2D pseudo-circulant property. A 2D FIR filter bank can be designed with the perfect reconstruction property if the polyphase matrix of its analysis filter bank is constrained to be a 2D lossless matrix. A design example is included. The losslessness constraint is satisfied by imposing a cascaded structure of first-degree lossless sections on the polyphase matrix. A limited factroization theorem is derived for 2D FIR lossless systems where the order in one of the two dimensions is limited to unity. In the area of nonuniform sampling of multiband bandlimited signals, the filter bank approach is utilized to derive a computationally efficient method for reconstructing bandlimited signals. The above scheme can also be viewed as a mean of compressing and reconstructing an oversampled bandlimited signal. It is shown that such a scheme has lower computational complexity than traditional methods of sampling rate alteration. The results can be extended to nonuniform sampling in two-dimensions using integer lattices. A further application of the multirate filter bank is in signal estimation in the presence of cyclostationary noise. The necessary and sufficient condition for the filter bank to preserve the wide-sense stationarity of the input is derived. Several applications where cyclostationary noise is present are indicated, and through the use of simulations the performance of the optimal filter bank can be compared with the conventional scalar optimal filter. The roundoff noise in orthogonal matrix building blocks is analyzed, since these building blocks are commonly present in filter bank implementations.

Convergence results on the design of QMF banks

Abstract: This correspondence considers the design of quadrature mirror filter (QMF) banks whose analysis and synthesis filters are FIR and have linear phase. The design criterion is of least-squares type. An iterative computation algorithm is proposed, and its convergence is proven that offers new insight to the design of QMF banks and relates it to a more general nonlinear optimization problem.