Home HomeHenrique S. Malvar, PictureTel Corp. (U.S.A.)
Two new lapped transforms are introduced: the LBT (lapped biorthogonal transform) and the HLBT (hierarchical lapped biorthogonal transform). The LBT has the same computational complexity of the LOT (lapped orthogonal transform), with much less blocking artifacts. The HLBT has a significantly lower computational complexity than the LOT, essentially no blocking artifacts, and less ringing artifacts than the commonly-used DCT (discrete cosine transform). The LBT and HLBT have a transform coding gain that is typically between 0.5 and 2.5 dB higher than that of the DCT. Image coding examples using JPEG and embedded zerotree coders demonstrate the better performance of the LBT and HLBT.
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Jamal Tuqan, Caltech (U.S.A.)
Palghat Vaidyanathan, Caltech (U.S.A.)
In this paper, we statistically optimize a well known class of IIR two channel orthonormal filter banks parameterized by a single coefficient when subband quantizers are present. The optimization procedure is extremely simple and very fast compared for example to the linear programming method used in the FIR case to achieve similar compaction (coding) gains. The special form of the filters assure the existence of a zero at (pi) which can be important for some wavelet applications and eliminate some of the major concerns that arise in the FIR design case. Finally, the compaction gain obtained is high and numerically very close to two (ideal case) for low pass spectra, high pass spectra and certain cases of multiband spectrum. For these cases,the use of higher order IIR filters does not increase the compaction (coding) gain.
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Takayuki Nagai, Keio University (Japan)
Takaaki Futie, Keio University (Japan)
Masaaki Ikehara, Keio University (Japan)
In this research, we propose a direct design method of nonuniform filter banks (NUFBs). This method is based on frequency domain constraints to eliminate the amplitude and the aliasing distortions. Both NUFBs with integer and rational sampling factors can be designed with common procedure. Here, we also consider the design method which requires only to solve linear equations iteratively. In our proposed method, least square error of the perfect reconstruction (PR) constraints is minimized without using the nonlinear programing technique.
ic972429.pdf TOPCormac Herley, HP Lab. (U.S.A.)
We examine the problem of reconstructing a signal from periodic non-uniform samples, i.e. a uniform train from which samples are deleted in some periodic fashion. We develop a condition previously derived by Herley and Wong and examine its implications. We show that this method has a number of advantages over alternative approaches. In particular it gives a condition for achieving the minimum rate rather than approaching it asymptotically. We show that it generally leads to a reconstruction scheme that is simpler than those derived by other strategies. We examine a few special cases in which the minimum rate is precisely achieveable, and cases where design of the reconstruction system is possible without explicitly knowing the signal spectrum.
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Dong-yan Huang, INT (France)
Phillip A. Regalia, INT (France)
This paper compares the eigenstructure and modulation algorithms, which are used for two-channel lossless FIR filter optimization. We study the effects of eigenvalue separation of the input covariance matrix and the step size on their convergence behavior. First, we show that the convergence rate of two algorithms increases as the separation of eigenvalues of the covariance matrix increases. The modulation algorithm (MA) converges more rapidly than the eigenstructure one (EA) because of its better eigenvalue separation. Second, the necessary condition for which the two algorithms converge is derived. Simulations are presented which support th analysis.
ic972437.pdf ic972437.pdf TOPFrank Hartenstein, RWTH Aachen (Germany)
We present a parametrization of discrete finite biorthogonal wavelets with linear phase. Our approach is similar to Zou and Tewfik's for orthogonal wavelets in the way that we utilize a lattice factorization of polyphase matrices of two-channel PR filter banks. However in the biorthogonal case we are faced with the additional possibilitiy of having length differences between the low- and high-pass filters. Our solution to this problem is the introduction of a set of initial polyphase matrices for the lattice product in order to receive the possibility of choosing a certain length difference between the two corresponding filters. This modification of the original lattice product enables us to generate a larger class of discrete wavelets in a systematic way.
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Tanja Karp, Hamburg University of Technology (Germany)
Alfred Mertins, University of Kiel (Germany)
Truong Q. Nguyen, University of Wisconsin (U.S.A.)
This paper presents methods for the efficient realization of prototype filters for modulated filter banks. The implementation is based on the lattice structure of the polyphase filters. The lattice coefficients, representing rotations, are approximated by a small number of simple micro-rotations each of which can be realized by some shift and add operations instead of a multiplication. Since the lattice structure is robust against coefficient quantization we do not loose the perfect reconstruction (PR) property of the filter bank when doing this approximation. Frequency responses of the original and approximated prototype filters are compared in terms of complexity and stopband attenuation.
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Palghat Vaidyanathan, Caltech, Pasadena (U.S.A.)
Ahmet Kirac, Caltech, Pasadena (U.S.A.)
We introduce the fundamentals of cyclic multirate systems and filter banks and present a number of important differences between the cyclic and noncyclic (traditional) cases. Some of the additional freedom offered by cyclic systems is pointed out, and a number of open issues are summarized.
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Helmut Bölcskei, Vienna University of Technology (Austria)
Franz Hlawatsch, Vienna University of Technology (Austria)
We show that oversampled filter banks (FBs) offer more design freedom and less noise sensitivity than critically sampled FBs. We provide a parameterization of all synthesis FBs satisfying perfect reconstruction for a given oversampled analysis FB, and we derive bounds and expressions for the variance of the reconstruction error due to noisy subband signals. Finally, we introduce noise shaping in oversampled FBs and calculate the optimal noise shaping system.
ic972453.pdf ic972453.pdf TOPFrank Heinle, University of Erlangen (Germany)
Filter banks for transform and subband coding are usually designed so as to achieve perfect reconstruction without considering distortions induced by inevitable or even desired effects such as filter implementation, subband quantization, and transmission. Other design algorithms minimize the distortion using more or less realistic models of quantizers. In contrast, we propose a new type of alias compensation based on the reasonable assumption that perfect or even near-perfect reconstruction in general cannot be attained if the subband signals are manipulated in some way. Therefore, a mostly time-invariant behaviour of the overall system seems to be more desirable. The proposed algorithm is capable of designing a compensation filter bank which reduces aliasing while the desired time-invariant part of the original system is preserved as far as possible.
ic972457.pdf ic972457.pdf TOPPeter Rieder, University of Technology Munich (Germany)
In this paper multiwavelets based on two scaling functions are discussed. They exhibit the following properties: compact support, symmetry and orthogonality as well as a good frequency resolution. Lattice structures do not only offer the possibility to implement these multiwavelet transforms, the lattice rotation angles also can be used in order to parameterize all multiwavelets of a certain length. Here we search for optimal multiwavelets with respect to regularity, vanishing moments, frequency behavior (stopband attenuation) and also take a simple implementation into consideration.
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Ricardo de Queiroz, Xerox Corp. (U.S.A.)
Reiner Eschbach, Xerox Corp. (U.S.A.)
Compressed images may be decompressed for devices using different resolutions. Full decompression and rescaling in space domain is a very expensive method. We studied downscaled inverses where the image is decompressed partially and a reduced inverse transform is used to recover the image. We studied the design of fast inverses, for a given forward transform. General solutions are presented for M-channel FIR filter banks of which block and lapped transforms are a subset.
ic972465.pdf ic972465.pdf TOPGerald Schuller, University of Hannover (Germany)
A new filter structure and design method for time-varying cosine modulated FIR filter banks with critical sampling, perfect reconstruction, and an efficient implementation is presented. The proposed filter banks have an arbitrary system delay which can be chosen in the design process and is independent of the arbitrary filter length, hence making a low system delay possible. The time variation includes changing the number of bands and/or filters during signal processing while maintaining critical sampling and perfect reconstruction. The transition windows can be overlapping, which improves the frequency responses. It is based on a factorization of the polyphase matrices into a cascade of 2 types of simple matrices.
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Jerome Lebrun, EPFL (Switzerland)
Martin Vetterli, EPFL (Switzerland)
This paper deals with multiwavelets which are a recent generalization of wavelets in the context of multirate filter banks and their applications to signal processing and especially compression. By their inherent structure, multiwavelets are fit for processing multi-channel signals. First, we will recall some general results on multiwavelets and the convergence of the iterated matrix product. Then, we will define under what conditions we can apply systems based on multiwavelets to one-dimensional signals in a simple way. That means we will give some natural and simple conditions that should help in the design of new multiwavelets for signal processing. Finally, we will provide some tools in order to construct multiwavelets with the required properties, the so-called `balanced multiwavelets'.
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