Showing papers on "Quadrature mirror filter published in 1993"

On the optimality of ideal filters for pyramid and wavelet signal approximation

Abstract: The reconstructed lowpass component in a quadrature mirror filter (QMF) bank provides a coarser resolution approximation of the input signal. Since the outputs of the two QMF branches are orthogonal, the transformation that provides the maximum energy compaction in the lowpass channel is also the one that results in the minimum approximation error. This property is used as a common strategy for the optimization of QMF banks, orthogonal wavelet transforms, and least squares pyramids. A general solution is derived for the QMF bank that provides the optimal decomposition of an arbitrary wide sense stationary process. This approach is extended to the continuous case to obtain the minimum error approximation of a signal at a given sampling rate. In particular, it is shown that the sine-wavelet transform is optimal for the representation at all scales of signals with non-increasing spectral density. >

Parametrization of compactly supported orthonormal wavelets

Abstract: The parametrization of two-channel reconstruction quadrature mirror filter banks is extended to obtain a single characterization of discrete orthonormal wavelets. In particular, it is shown that discrete orthonormal wavelets of support less than 2N-1, where N is an even integer, are parametrized by N-1 real parameters, each taking values in (0, 2 pi ). A parametrization of discrete orthonormal wavelets with a number of vanishing moments greater than one is also given. >

Multidimensional multirate filters and filter banks derived from one-dimensional filters

Abstract: A method by which every multidimensional (M-D) filter with an arbitrary parallelepiped-shaped passband support can be designed and implemented efficiently is presented. It is shown that all such filters can be designed starting from an appropriate one-dimensional prototype filter and performing a simple transformation. With D denoting the number of dimensions, the complexity of design and implementation of the M-D filter are reduced from O(N/sup D/) to O(N). Using the polyphase technique, an implementation with complexity of only 2N is obtained in the two-dimensional. Even though the filters designed are in general nonseparable, they have separable polyphase components. One special application of this method is in M-D multirate signal processing, where filters with parallelepiped-shaped passbands are used in decimation, interpolation, and filter banks. Some generalizations and other applications of this approach, including M-D uniform discrete Fourier transform (DFT) quadrature mirror filter banks that achieve perfect reconstruction, are studied. Several design example are given. >

Multiplierless 2-band perfect reconstruction quadrature mirror filter (PR-QMF) banks

Abstract: The Multiplierless Quadrature Mirror Filter concept is used in the design of analysis and synthesis filter banks to be used for the sub-band coding of various types of signals. The individual filters in the analysis and synthesis filter banks are designed to be near linear in phase, non-symmetrical in time, and to have equal bandwidth frequency responses. These multiplierless filters are relatively easy to implement in hardware and allow for the sub-band coding of signals with minimal computational complexity so as to result perfect signal reconstruction. Furthermore, these filters are particularly well suited for configuration in hierarchical sub-band structures.

A Spectral Factorization Approach to Pseudo-QMF Design

Abstract: A novel approach to the design of M-channel pseudo-quadrature mirror filter (QMF) banks is presented. In this approach, the prototype filter is obtained as a spectral factor of a 2M/sup th/ band filter. This completely eliminates the need for optimization, whereas in conventional pseudo-QMF designs the main computational effort is in optimization of the prototype. The aliasing cancellation constraint is derived such that all the significant aliasing terms are canceled. The overall transfer function of the analysis/synthesis system has an approximately flat magnitude response in the frequency region epsilon >

The design of weighted minimax quadrature mirror filters

Abstract: A technique for converting the constrained nonlinear optimization problem encountered in the design of weighted minimax quadrature mirror filters into an iterative unconstrained nonlinear optimization problem is presented. This renders the design of weighted minimax quadrature mirror filters possible. The technique is very efficient, typically taking about seven iterations to converge. A rapidly converging iterative procedure for solving the above nonlinear unconstrained optimization problem is also presented. This procedure typically requires less than five iterations to converge. >

Tree-structured nonlinear filter and wavelet transform for microcalcification segmentation in mammography

Abstract: The development of an extensive array of algorithms for both image enhancement and feature extraction for microcalcification cluster detection is reported. Specific emphasis is placed on image detail preservation and automatic or operator independent methods to enhance the sensitivity and specificity of detection and that should allow standardization of breast screening procedures. Image enhancement methods include both novel tree structured non-linear filters with fixed parameters and adaptive order statistic filters designed to further improve detail preservation. Novel feature extraction methods developed include both two channel tree structured wavelet transform and three channel quadrature mirror filter banks with multiresolution decomposition and reconstruction specifically tailored to extract MCC's. These methods were evaluated using fifteen representative digitized mammograms where similar sensitivity (true positive (TP) detection rate 100%) and specificity (0.1 - 0.2 average false positive (FP) MCC's/image) was observed but with varying degrees of detail preservation important for characterization of MCC's. The image enhancement step proved to be very critical to minimize image noise and associated FP detection rates for MCC's or individual microcalcifications.

A practical approach to fractal-based image compression

Abstract: A technique for image compression is based on a very simple type of iterative fractal. A wavelet transform (quadrature mirror filter pyramid) is used to decompose an image into bands containing information from different scales (spatial frequencies) and orientations. The conditional probabilities between these different scale bands are then determined, and used as the basis for a predictive coder. The wavelet transform's various scale and orientation bands have a great deal of redundant, self-similar structure in the form of multi-modal conditional probabilities, so that linear predictors perform poorly. A simple histogram method is used to determine the multi-modal conditional probabilities between scales. The resulting predictive coder is easily integrated into existing subband coding schemes. >

A linear phase two-channel filter bank allowing perfect reconstruction

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.<>

Partial spectrum reconstruction using digital filter banks

Abstract: The problem of reconstructing a part of the spectrum is reduced to designing the filter bank to satisfy a set of conditions. For the case considered here, these conditions cannot be satisfied simultaneously, so perfect reconstruction is not possible. The necessary and sufficient conditions on the filters so that the resulting filter bank cancels most alias components are found. Such filter banks are called partial alias cancellation filter banks. The product of the polyphase transfer matrices of these filter banks must be a block pseudocirculant matrix. An algorithm design procedure is discussed, and examples are given to demonstrate the theory. >

Theory and design of multidimensional QMF sub-band filters from 1-D filters and polynomials using transforms

Abstract: The general theory of designing multidimensional quadrature mirror filters (QMF) for use in sub-band coding systems using the McClellan transform [1] is presented. It was recently shown that the McClellan transform could be used to generate 2-D diamond-shape QMF filters [2]. The proofs of the diamond-shape case are formalised and generalise to other shapes, sampling rasters and dimensions. It is possible and even more convenient to design QMF filter banks by performing transformations on a class of real-valued polynomials. Examples are given of two-dimensional diamond and fan-shape filters and three-dimensional tetrad filters designed using this transformation technique.

The design of nonuniform-band maximally decimated filter banks

Abstract: A design method for nonuniform-band maximally decimated filter banks is presented. It is based on the quadrature mirror filter (QMF) design method and allows the direct frequency domain design of two-band filter banks having arbitrary rational decimation ratios. The numerical design of nonuniform-band filter banks is achieved using a simple structure in which elementary modulators are used in the highpass channel to obtain almost-perfect reconstruction. >

Regular M-band wavelets and applications

Abstract: M-band generalizations of the FIR (finite impulse response) wavelets of I. Daubechies (1988) have been introduced. The authors present a set of explicit construction techniques for these M-band wavelet filters, and the results of their application to image compression. A characterization of several equivalent notions of Nth-order regularity for M-band perfect reconstruction filters is presented. This characterization is used to devise a closed-form expression for Nth-order regular wavelet lowpass filters. The construction of a full M-band filter bank given a lowpass filter and a rank M unitary matrix is completed. Several of these new wavelets are applied to image coding. >

Wideband speech coding in 7.2 kbit/s

Abstract: A novel method for coding wideband speech at medium bit rates is proposed. A subband approach is adopted, using sharp cut-off filters to split the speech into lower and upper bands. This allows the upper-band to be very coarsely quantized without introducing significant distortion at low frequencies in the reconstructed speech, which would normally occur using short QMF (quadrature mirror filter). A standard CELP (code excited linear prediction) coder is used for the low-frequency band, and the upper band is quantized using a second-order predictor and gain shape vector quantization at 0.05 bit sample, yielding an overall bit rate of 7.2 kbit/s. The overall effect is to produce a wideband coder that has almost the same computational requirements as a narrowband CELP coder and only a slight increase in the bit rate. >

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 buffer controlled by a feedback loop for bit rate regulation. The main contribution 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, the authors call these transforms adapted multiresolution transforms (AMTs). The transforms under study are implemented by a cascade of separable perfect-reconstruction (PR) FIR two-band filter banks 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. They perform the optimization of the filters in their factorized lattice form, taking the finite length of the multipliers into account. Their criterion also allows them to show the performances achieved by these two linear multiresolution transforms compared to other linear (multiresolution) transforms. >

Multi-complementary filter bank

Abstract: An octave-spaced complementary filter bank that provides aliasing-free subband signal processing and perfect reconstruction is presented The transition bandwidth of the splitting filters can be controlled independently by basis filters, which in turn are realized by multirate complementary filters The design of the filter bank is presented >

Perfect reconstruction modulated filter banks without cosine constraints

Abstract: The theory of perfect reconstruction (PR) quadrature mirror filter (QMF) banks is used to analyze the general class of modulated filter banks (MFBs). It is found that there is an inherent tradeoff between the constraints imposed on the prototype and the modulation matrix to achieve PR. The authors propose a set of constraints on the modulation to achieve PR while retaining the desirable power complementary conditions on the polyphase components. The prototype filter can then be designed using the two-channel lossless lattice. It is surprising that the complete solution to this set of constraints is generated by the set of unitary matrices. This greatly increases the possible choices of modulation in the design of finite-impulse-response PR QMF banks. The usefulness of the proposed approach is demonstrated by deriving several existing MFBs, such as the extended lapped transform, as special cases of the unitary class of solution. >

New results on multidimensional filter banks and wavelets

Abstract: New results on multidimensional filter banks and wavelets are presented. Emphasis is placed on the two-dimensional case with sampling by 2 in each dimension. It is shown how, by using an appropriate cascade structure, nonseparable filters being both orthogonal and linear phase can be obtained, a construction not possible when one-dimensional systems are used separately. The condition for having at least one zero of the lowpass filter at all aliasing frequencies (necessary for convergence) is given. A first design example of two-dimensional orthonormal wavelets with symmetries is presented, together with a demonstration of continuity. >

Low Delay Coding of Speech and Audio Using Nonuniform Band Filter Banks

Abstract: Over the last decade, analysis-synthesis systems based on maximally decimated filter banks have emerged as one of the important techniques for speech and audio coding. For speech and audio signals, the analysis-synthesis filter bank can be thought of as modeling the human auditory system, where the critical band model of aural perception is reflected in the design of the filter banks. The constraints imposed by the aural model are best met by nonuniform analysis-synthesis systems in which the bandwidths of the channels increase with increasing frequency.

Design of Two-Channel Perfect Reconstruction QMF

Abstract: This paper proposes a design method for the FIR two-channel perfect quadrature mirror filter (QMF) with the linear phase. The two-channel perfect QMF can be designed by Vetterli's method, where a system of equations representing the condition for the perfect reconstruction of the signal is solved. The filter designed by this method, however, does not, in general, have good frequency characteristics. This paper presents the design for the two-channel QMF with a perfect reconstruction and a good amplitude characteristic. The method is based on Vetterli's method, and a constraint to approximate the amplitude characteristic in the frequency domain is added to the condition of perfect reconstruction in time domain. Then Remez' algorithm is applied to the derived system of equations. The construction of the two-channel perfect QMF, when the coefficient is quantized, also is discussed. Furthermore, a method is shown in which the two-dimensional (2-D) perfect QMF is designed by applying the McClellan transformation to the obtained 1-D QMF. The condition for the McClellan transformation for the perfect reconstruction is derived.

A new design of 2-D nonseparable hexagonal quadrature-mirror filter banks

Abstract: A new design method for 2-D nonseparable hexagonal quadrature mirror filter banks is proposed. The new method involves minimizing an objective function containing two error terms, one dealing with the perfect reconstruction condition and the other with intra-band aliasing. The method makes full use of the symmetry of hexagonal FIR filters, which leads to a considerable reduction in the amount of computation required by the optimization. This method is compared with one proposed by Simoncelli and Adelson (1990) and is shown to yield superior results. >

A compound primitive operator approach to the realisation of video sub-band filter banks

Abstract: A new video subband filtering architecture appropriate for VLSI implementation is presented. The system employs a reduced complexity multiply-accumulate structure realized using an extension to the primitive operator graph synthesis technique. This, in conjunction with a data multiplexing regime which implements a two channel quadrature mirror filter on a single finite impulse response (FIR) structure, has facilitated the fabrication of a sixty-four subband coder/decoder on a single gate array. The circuitry is reconfigurable, allowing vertical and horizontal filtering in analysis or synthesis mode. The authors describe the conceptual development of the new approach and present novel architectural features associated with its implementation. Also included are complexity comparisons with conventional approaches. >

A family of arbitrary length modulated orthonormal wavelets

Abstract: S. C. Chan and C. W. Kok (1993) established the conditions on the modulation for the modulated filter bank to be perfect-reconstruction (PR) when the linear phase prototype filter is of length 2mM and satisfies the power complementary condition. It was found that the modulation is generated by the class of unitary matrices. It is shown that similar unitary classes of solutions also exist for the case M = 2mM + /spl beta/. This greatly increases the possible choices of modulation and filter length in the design of finite impulse response (FIR) PR quadrature mirror filter (QMF) banks. Moreover, additional regularity conditions are imposed on the filter banks to obtain a unitary class of modulated orthonormal compactly supported wavelets. >

Design of 2-dimensional perfect reconstruction filter banks for arbitrary sampling lattices

Abstract: A design method of 2-dimensional perfect reconstruction filter banks for arbitrary sampling lattices is presented. Filter banks are constructed by a 2D nth band filter which consists of some delays and 2D interpolated all-pass networks. It is shown that the analysis and synthesis part is constructed by combining the polyphase structure of a 2D Nth-band digital filter and 2D discrete Fourier transform (DFT). >

QMF banks design and implementation perspectives

Abstract: A framework for the design of two-channel quadrature mirror filter (QMF) banks is described. The design is performed using FIR (finite impulse response) as well as IIR (infinite impulse response) filters. A comparison is provided among design techniques to illustrate the advantages and disadvantages of such filters, and their implementation is considered. >

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.

Enhanced beamforming techniques for broad-band satellite applications

Abstract: The adaptive beamforming techniques are an essential part of future satellite communication systems. Their use has until very recently been confined into expensive high performance military applications. Recent advances in VLSI technology and modern DSP techniques have meant that adaptive beamforming techniques can be used in lower cost, commercial applications. The authors present a novel subband adaptive beamformer (SAB) that uses quadrature mirror filter (QMF) banks to generate the subbands. The initial results point out that the QMF-SAB could be more advantageous to use in terms of convergence speed and cancellation performance over fullband adaptive beamformers (FAB). >

Perfect reconstructional multidimensional filter banks with time-varying basis functions

Abstract: Many multidimensional signals of interest are nonstationary and thus have statistical characteristics that change temporally and/or spatially. It is reasonable to expect that time-varying transforms can better model M-D signals than time-invariant ones. We discuss time-varying multidimensional filter banks with adaptive filter coefficients. The focus is on the design of exact reconstructing multidimensional adaptive filter banks. We extend our 1-D time-varying filter bank design method to multiple dimensions to consider the design of perfect reconstructing time-varying nonseparable filter banks. The resulting design method is simple, elegant and extremely powerful. >

On the design of near perfect reconstruction pseudo QMF banks

Abstract: A new approach to the design of M-channel pseudo quadrature mirror filter (QMF) banks is presented. The analysis and synthesis filters are cosine-modulated versions of the prototype filters. The prototype filter is constrained to be a linear-phase spectral-factor of a 2M/sup th/ band filter. As a result, the reconstructed signal has no amplitude nor phase distortions. The only error at the output is aliasing, which is comparable to the stopband attenuation of the prototype filter. Using this approach, it is possible to design a pseudo-QMF bank where the stopband attenuation of the analysis (and thus synthesis) filters is on the order of 100 dB. Consequently, the resulting reconstruction error is also on the order of -100 dB. An example is included to demonstrate the theory. >

HDTV data carrier separation using a multiplexing filter

Abstract: An interleaving, symbol-shaping quadrature demodulator architecture that demodulates the two data carriers in the digital video signal used in the advanced digital high definition television (AD-HDTV) system is described. The demodulator accepts separate 10-b digitized intermediate frequency (IF) data input, for both carriers, to produce spectrally shaped inphase and quadrature baseband signals using only one decimate-by-two 58-tap multiplexed finite-impulse-response (FIR) filter. A 15.36-MHz multiplexed FIR filter has been designed from a high-level description of the filter characteristics using a technology-independent, silicon generator approach. The 58-tap FIR filter achieves the 17% excess bandwidth and the 40-dB attenuation required by the AD-HDTV system. It also achieves an intersymbol interference of 29 dB. The interleaving, all-digital spread-spectrum quadrature amplitude modulation (SS-QAM) demodulator chip is fabricated in a 1.0-/spl mu/m CMOS N-well process, contains 48 K transistors, and has a die area of 34 mm/sup 2/ and an estimated 359-mW power dissipation with a 5-V power supply. This architecture makes possible a single-chip, low-cost demodulator.