Showing papers on "Quadrature mirror filter published in 1992"

Multirate Systems and Filter Banks

Abstract: 1. Introduction 2. Review of Discrete-Time Systems 3. Review of Digital Filters 4. Fundamentals of Multirate Systems 5. Maximally Decimated Filter Banks 6. Paraunitary Perfect Reconstruction Filter Banks 7. Linear Phase Perfect Reconstruction QMF Banks 8. Cosine Modulated Filter Banks 9. Finite Word Length Effects 10. Multirate Filter Bank Theory and Related Topics 11. The Wavelet Transform and Relation to Multirate Filter Banks 12. Multidimensional Multirate Systems 13. Review of Discrete-Time Multi-Input Multi-Output LTI Systems 14. Paraunitary and Lossless Systems Appendices Bibliography Index

Wavelets and filter banks: theory and design

Abstract: The wavelet transform is compared with the more classical short-time Fourier transform approach to signal analysis. Then the relations between wavelets, filter banks, and multiresolution signal processing are explored. A brief review is given of perfect reconstruction filter banks, which can be used both for computing the discrete wavelet transform, and for deriving continuous wavelet bases, provided that the filters meet a constraint known as regularity. Given a low-pass filter, necessary and sufficient conditions for the existence of a complementary high-pass filter that will permit perfect reconstruction are derived. The perfect reconstruction condition is posed as a Bezout identity, and it is shown how it is possible to find all higher-degree complementary filters based on an analogy with the theory of Diophantine equations. An alternative approach based on the theory of continued fractions is also given. These results are used to design highly regular filter banks, which generate biorthogonal continuous wavelet bases with symmetries. >

Cosine-modulated FIR filter banks satisfying perfect reconstruction

Abstract: The authors obtain a necessary and sufficient condition on the 2M (M=number of channels) polyphase components of a linear-phase prototype filter of length N=2 mM (where m=an arbitrary positive integer), such that the polyphase component matrix of the modulated filter is lossless. The losslessness of the polyphase component matrix, in turn, is sufficient to ensure that the analysis/synthesis system satisfies perfect reconstruction (PR). Using this result, a novel design procedure is presented based on the two-channel lossless lattice. This enables the design of a large class of FIR (finite impulse response)-PR filter banks, and includes the N=2M case. It is shown that this approach requires fewer parameters to be optimized than in the pseudo-QMF (quadrature mirror filter) designs and in the lossless lattice based PR-QMF designs (for equal length filters in the three designs). This advantage becomes significant when designing long filters for large M. The design procedure and its other advantages are described in detail. Design examples and comparisons are included. >

Design of quadrature mirror filters with linear phase in the frequency domain

Abstract: The design of quadrature mirror filter (QMF) banks whose analysis and synthesis filters have linear phase is considered. Because the design problem in the frequency domain is a highly nonlinear optimization problem, a linearization technique is proposed. An analytical solution formula is obtained, leading to a very efficient procedure. Computer simulations show that the design technique achieves better results in fewer iterations than conventional approaches when starting at the same preset initial guess. Moreover, the technique produces almost the same good results in six iterations if it starts at a better initial guess compared to the preset initial guess. By incorporating the technique with a weighted least squares, (WLS) algorithm, the design of QMF banks whose overall reconstruction error is minimized in the minimax sense over the entire frequency band is facilitated. Computer simulations for illustration and comparison are provided. >

A filter based bit allocation scheme for subband compression of HDTV

Abstract: The authors compare the subband compression capabilities of eight filter sets (consisting of linear-phase quadrature mirror filters (QMFs), perfect reconstruction filters, and nonlinear phase wavelets) at different bit rates, using-a filter-based bit allocation procedure. Using DPCM and PCM in HDTV subband coding, it is found that QMFs have an edge over the rest. >

High-speed A/D conversion incorporating a QMF bank

Abstract: A structure for analog-to-digital (A/D) conversion capable of attaining high speed and using an array of lower-speed A/D converters is introduced. The structure is based on a quadrature mirror filter (QMF) bank, except that the analysis filter bank is a switched-capacitor circuit, whereas the synthesis filter bank is normally a digital circuit. It is shown that the effect of mismatches among the A/D converters in the array is considerably reduced by the QMF bank. Simulation and experimental results verifying the good performance of the proposed approach are included. >

Scalar quantization error analysis for image subband coding using QMFs

Abstract: The authors analyze the coding errors due to quantization by explicitly incorporating a mathematical model for a Lloyd-Max quantizer into a quadrature mirror filter (QMF) splitting and reconstruction scheme (P. H. Westerink et al., 1988). This approach explicitly incorporates quantization errors into a QMF system by means of a quantizer model. This makes it possible to discriminate between different types of coding errors, such as the aliasing error. Other errors that can be distinguished are a QMF design error, a signal error, and a random error, which is uncorrelated with the original image. Both a mean-squared error calculation and a subjective judgment of the coding errors show that the aliasing errors can be neglected for filter lengths of 12 taps or more. The signal error determines the sharpness of the reconstructed image, while the random error is most visible in the flat areas. >

A linear phase two-channel filter bank allowing perfect reconstruction (image coding)

Abstract: Describes a perfect-reconstruction two-channel QMF (quadrature mirror filter) bank, in which the analysis and synthesis filters have linear phases. First, a technique for designing filter banks is presented. Next, the results of two examples demonstrate that the method can lead to good filters although its procedure is very simple; also, this yields filters without multipliers such as the SSKF (symmetric short kernel filter) bank. >

Perfect reconstruction modulated filter banks

Abstract: New modulated filter banks having the perfect reconstruction property, called perfect reconstruction modulated filter (PRMF) banks, are described. This new framework provides the set of equations to be verified for perfect reconstruction in the general case. In the case of analysis and synthesis filters obtained by the classical cosine modulation of a symmetrical prototype filter h, it gives also the analytic forms of all the possible PRMF banks, with filter length NF shorter than 8.SB, with SB the number of subband channels. Filter banks known as TDAC, MLT, ELT, etc., are particular PRMF banks with NF=2.k.SB, but many other filters exist, with NF odd for example. Odd length filters have a lot of interesting properties. >

Reflected boundary conditions for multirate filter banks

Abstract: Several methods for applying perfect reconstruction quadrature mirror filter (PR QMF) banks to finite-length signals are described and compared. Although simple periodization produces a transform that does not increase the size of the transformed signal, it has the disadvantage of introducing a jump discontinuity at the signal's boundary. Various methods of transforming smoother extensions are considered and analyzed in terms of their ability to conserve data storage costs and reproduce the signal in a numerically efficient manner. A complete classification of two-channel schemes based on periodizing symmetric (reflected) signal extensions and using linear phase filters is described, for both even- and odd-length signals. More general techniques based on transforming linear signal extrapolations and truncating the resulting subbands to conserve data size are also presented. An example using reflected boundary extension is discussed. >

Rotation and gray-scale transform invariant texture recognition using hidden Markov model

Abstract: In the first stage of the proposed scheme the quadrature mirror filter (QMF) bank is used as the wavelet transform to decompose the texture image into subbands. Gray scale transform invariant features are then extracted from each subband image. In the second stage, the sequence of subbands is modeled as a hidden Markov model (HMM), and one HMM is designed for each class of textures. During recognition, the unknown texture is matched against all models. The best matched model identifies the texture class. The angles of rotation in the experiments are selected randomly in between -90 degrees and 90 degrees . Up to 95% classification accuracy is reported. >

General theory of time-reversed inversion for perfect reconstruction filter banks

Abstract: It is shown how to invert a MIMO system with the transfer matrix E(z). Assuming that (det E(z)) does not have any zeros on the unit circle the time-reversal technique can be used to obtain a stable inverse system. Due to the time-reversal, proper initial conditions have to be chosen so that perfect reconstruction can be achieved. Using the state-space descriptions of linear systems, it is shown that the initial condition that guarantees perfect recovery is in fact the final condition of the original system. One important application of the technique is that for any analysis filters in an analysis/synthesis filter bank, a stable implementation of the synthesis filter bank can always be derived. Hence, constraints such as FIR filters and the paraunitary property are not necessary to assure stability of the synthesis filters. >

Quadrature filter with real conversion

Abstract: A quadrature decimation filter with real output formed from a mixture of both in-phase and quadrature signals by upconversion and alternating stream combination. The in-phase and quadrature branch computations run simultaneously with a delay of the in-phase data stream relative to the quadrature data stream so that a common filter coefficient may be used simultaneously in nonzero branch computations.

The design of arbitrary-length cosine-modulated filter banks and wavelets, satisfying perfect reconstruction

Abstract: FIR filter banks which satisfy the perfect-reconstruction (PR) property can be obtained by cosine modulation of a linear-phase prototype filter of length N=2mM, where M is the number of channels. A PR cosine-modulated filter bank is presented for which the length of the prototype filter is arbitrary. Additional regularity conditions are imposed on the filter bank to obtain the cosine-modulated orthonormal bases of compactly supported wavelets. Design examples are given. >

A measure of aliasing energy in multiresolution signal decomposition

Abstract: An analysis of band energy distributions in perfect reconstruction (PR) multirate systems is presented, and the effects of aliasing are evaluated. A performance measure called nonaliasing energy ratio (NER) is defined. The merit of the new measure is emphasized with performance comparisons of the popular block transforms and two-band PR-QMF based hierarchical filter banks. It is shown that the new measure complements the widely used energy compaction measure and is consistent with the subjective performance results. >

Adaptive multidimensional perfect reconstruction filter banks using McClellan transformations

Abstract: A technique for the design of 2D nonseparable perfect reconstruction filter banks is developed where the isopotentials of the frequency response can be optimized and adapted to local signal statistics. By employing existing odd-length symmetric perfect reconstruction filterbanks as the 1D normal filters for a 2D filter parameterized by the McClellan transformation, conditions under which the resulting 2D filter bank retains the perfect reconstruction property are derived. A two-parameter transformation function is developed whose optimization involves a simple constrained least-squares problem in which the feasible set lies on a circle. The results have practical applications in many areas of image and video processing where multirate filterbanks are used. >

Subband coding of video using an edge-based vector quantization technique for compression of the upper bands

Abstract: A new subband video coding technique is introduced which utilizes several memoryless vector quantizing (VQ) schemes for encoding the various layers. A set of quadrature mirror filter banks was applied to the motion compensated frame differences (MCFDs) of the moving sequences to produce seven nonuniform bands. The upper bands displayed a significant amount of information at edge locations, these being the positions where the baseband of each layer was observed to have a similar behavior. Therefore, an edge-detecting operator, e.g., Laplacian or a Gaussian, was incorporated into the video compression model to extract the perceptually important locations of the upper bands from their correspondingly encoded baseband, thus eliminating the need for transmission of their addresses. Promising results were obtained which are suitable for low-bit-rate video applications where videophone and videoconferencing systems may be realized. >

VLSI architectures of two-dimensional filters for HDTV coding

Abstract: Key components for implementation of HDTV subband coding schemes are filter banks for band splitting at the transmitter side and for band synthesis at the receiver side. The authors deal with VLSI architectures and implementations of these filters. To reduce hardware cost and size, VLSI realizations of filter banks by dedicated circuits are considered. The impact of the filter algorithms, architectural structures and circuit technique on the implementation is explained. In particular, the advantages of quadrature mirror filters (QMFs) for the hardware implementation of two-dimensional HDTV filter banks are presented. The potential of dedicated circuit design with consideration of all a priori knowledge is illustrated for a 14*10 tap QMF filterbank with on-chip line memories. >

Sub-band coding of HDTV images using GQMF

Abstract: The Letter describes a low complexity intraframe sub-band image coding algorithm suitable for video coding applications. A new class of quadrature mirror filter (QMF), called the generalised quadrature mirror filter (GQMF), with smaller overall delay, is introduced. In this approach, the spectra of the HDTV signals are first decomposed into smaller frequency bands where the baseband is DPCM encoded and the high bands are PCM encoded. For optimum performance, an efficient entropy coder is designed that significantly reduces the overall bit rate. It is shown that high quality HDTV images can be obtained at bit rates as low as 34Mbit/s with a considerable reduction in complexity.

Design and parameterization of M-band orthonormal wavelets

Abstract: The authors generalize the parameterization of 2-band (or dyadic) wavelet to the M-band case. A complete characterization of M-band wavelets is given, including a recipe for constructing such wavelets. It is shown that M-band wavelets can be constructed from a perfect reconstruction filter bank with added regularity conditions. The regularity conditions are important both for the numerical stability of the resulting approximation procedures and for increased compactness of the signal representations with such wavelets. >

Design of two-dimensional non-separable QMF banks

Abstract: Two-dimensional non-separable quadrature mirror filters (2-D QMFs) are designed. An iterative algorithm is used for the optimization of a prototype diamond-shaped filter. The variations of the reconstruction error as a function of the size and specifications of the prototype filter are tabulated. >

A novel spectral factorization method and its application in the design of filter banks and wavelets

Abstract: One of the difficulties encountered in spectral factorization is achieving computational accuracy when computing a spectral factor whose zeros are on the unit circle and/or the order is high. An iterative approach is presented for computing the spectral factor accurately. It is shown that the new method performs well and can be used in the design of filter banks satisfying perfect reconstruction and orthonormal compactly supported wavelets. Design examples are included. >

PR-QMF design with Bernstein polynomials

Abstract: A generalized, parametric PR-QMF (perfect reconstruction quadrature mirror filter) design technique based on the Bernstein polynomial approximation is developed. The parametric nature of this solution provides very useful insights into the PR-QMF problem. Several well-known orthonormal wavelet filters, PR-QMFs, are shown to be the special cases of the proposed technique. The energy compaction performance of a few popular signal decomposition techniques is presented for AR(1) signal sources. It is shown that the QMF filter banks considered here outperform the block transforms, as expected. >

A family of wavelets which are dilatable by simple IIR filters (EEG analysis)

Abstract: The family of wavelets called neural wavelets has zero mean, spectral peak at a frequency varies as square root n and 20 n dB/decade rolloff where n is the order of the wavelet. The effective duration shortens with increasing n for a given t/sub 0/, where the parameter t/sub 0/ allows time scaling of the wavelets. A simple infinite impulse response (IIR) filter is developed which expands or contracts the wavelet and can be designed to change the order n. The filter is used to detect partially overlapping constituent wavelets of a composite waveform. Filter design and noise sensitivity are discussed. >

Finite wordlength effects in quadrature mirror filter banks

Abstract: The authors investigate the effects of finite wordlength on the performance of QMF (quadrature mirror filter) banks implemented with fixed-point arithmetic. A statistical model for roundoff errors is used to predict the output roundoff noise in each subband. The amplitudes of the parasitic oscillations which are due to a DC component in each subband are predicted with the same model. For two's complement arithmetic, the authors discuss the effects of truncation and rounding, and present analysis results. A general framework for analyzing different splitting schemes is given. The enhancement of roundoff noise for low frequencies is obvious. It is pointed out that parasitic frequency components can be avoided if two's complement rounding is used, while roundoff noise can only be reduced by increasing the wordlength. >

Multiresolution image decomposition for processing reconnaissance images

Abstract: Recent increases in focal plane size and spatial resolution, coupled with the introduction of multi-spectral sensor suites in tactical reconnaissance platforms, have exponentially increased the volume of image data to be processed. This paper proposes the use of a quadrature mirror filter compression technique whereby intrinsic multiresolution pyramid decomposition can simplify implementation of many of the algorithms required to exploit these images. A subband coding system, based on the spatial frequency and orientation of the decomposed images, is presented. Implementation of additional algorithms based on multiresolution pyramid decomposition is also discussed. These algorithms include: edge detection and restoration, real-time minification of large E-O images for screening purposes and interpolation with electronic zooming for target identification.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Support constraints for M-band alias-free filter banks

Abstract: A new formulation of the system equations that describe the behavior of the one-dimensional M-band maximally decimated analysis/synthesis filter bank system is presented. The development incorporates the effects of the shift-varying nature of the upsampling and downsampling operations. By explicitly including the filter regions of support, one is able to derive a more general expression for the relationships that must exist between the analysis and synthesis filters in order to cancel all interband aliasing. From this expression one can find (1) the M/sup M-1/ distinct sets of analysis and synthesis filters from which an M-band alias-free filter bank can be constructed, and (2) the constraints on how these filters, once designed, can be shifted without destroying their aliasing cancellation properties. >

Nonuniform perfect‐reconstruction systems for quadrature mirror filter banks

Abstract: By decreasing the decimation ratio to one less than the number of channels, a perfect-reconstruction quadrature mirror filter (QMF) system can be constructed with the following innovative features: (1) the band division, which in the past has been uniform, can be made nonuniform; (2) the equivalent delay, which has usually been as large as the order of the dividing filter, can now be reduced to a size equal to the decimation ratio minus 1; (3) the number of channels, which has been restricted to a power of 2, can now be arbitrary. In addition, the traditional method employs spectral decomposition, while the proposed method employs Euclidean division. Euclidean structure (the realization of Euclidean division on a network) and lattice structure are considered as methods of constructing a filter that does not produce an aliasing distortion for the finite word length.

Real time implementation of wavelet transform in a dual DSP56001 system

Abstract: The wavelet transform has recently emerged as a powerful tool for nonstationary signal analysis. Normally, the orthogonal discrete wavelet transform is implemented in critically sampled quadrature mirror filter banks. It is demonstrated how the discrete wavelet transform can be implemented in a two DSP 56001 system. The authors use a dual DSP system and develop an algorithm code for the real time implementation of the wavelet transform. This method can also be extended to the two-dimensional wavelet transform. >