72 research outputs found
The S-Transform From a Wavelet Point of View
Abstract—The -transform is becoming popular for time-frequency
analysis and data-adaptive filtering thanks to its simplicity.
While this transform works well in the continuous domain, its discrete
version may fail to achieve accurate results. This paper compares
and contrasts this transform with the better known continuous
wavelet transform, and defines a relation between both. This
connection allows a better understanding of the -transform, and
makes it possible to employ the wavelet reconstruction formula as
a new inverse -transform and to propose several methods to solve
some of the main limitations of the discrete -transform, such as
its restriction to linear frequency sampling.This work was supported by the projects SigSensual
ref. CTM2004-04510-C03-02 and NEAREST CE-037110. The work of
M. Schimmel was supported through the Ramon y Cajal and the Consolider-Ingenio
2010 Nr. CSD2006-00041 program.Peer reviewe
Low-complexity wavelet filter design for image compression
Image compression algorithms based on the wavelet transform are an increasingly attractive and flexible alternative to other algorithms based on block orthogonal transforms. While the design of orthogonal wavelet filters has been studied in significant depth, the design of nonorthogonal wavelet filters, such as linear-phase (LP) filters, has not yet reached that point. Of particular interest are wavelet transforms with low complexity at the encoder. In this article, we present known and new parameterizations of the two families of LP perfect reconstruction (PR) filters. The first family is that of all PR LP filters with finite impulse response (FIR), with equal complexity at the encoder and decoder. The second family is one of LP PR filters, which are FIR at the encoder and infinite impulse response (IIR) at the decoder, i.e., with controllable encoder complexity. These parameterizations are used to optimize the subband/wavelet transform coding gain, as defined for nonorthogonal wavelet transforms. Optimal LP wavelet filters are given for low levels of encoder complexity, as well as their corresponding integer approximations, to allow for applications limited to using integer arithmetic. These optimal LP filters yield larger coding gains than orthogonal filters with an equivalent complexity. The parameterizations described in this article can be used for the optimization of any other appropriate objective function
Role of anticausal inverses in multirate filter-banks. II. The FIR case, factorizations, and biorthogonal lapped transforms
For pt. I see ibid., vol.43, no.5, p.1090, 1990. In part I we studied the system-theoretic properties of discrete time transfer matrices in the context of inversion, and classified them according to the types of inverses they had. In particular, we outlined the role of causal FIR matrices with anticausal FIR inverses (abbreviated cafacafi) in the characterization of FIR perfect reconstruction (PR) filter banks. Essentially all FIR PR filter banks can be characterized by causal FIR polyphase matrices having anticausal FIR inverses. In this paper, we introduce the most general degree-one cafacafi building block, and consider the problem of factorizing cafacafi systems into these building blocks. Factorizability conditions are developed. A special class of cafacafi systems called the biorthogonal lapped transform (BOLT) is developed, and shown to be factorizable. This is a generalization of the well-known lapped orthogonal transform (LOT). Examples of unfactorizable cafacafi systems are also demonstrated. Finally it is shown that any causal FIR matrix with FIR inverse can be written as a product of a factorizable cafacafi system and a unimodular matrix
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Image compression using the W-transform
The authors present the W-transform for a multiresolution signal decomposition. One of the differences between the wavelet transform and W-transform is that the W-transform leads to a nonorthogonal signal decomposition. Another difference between the two is the manner in which the W-transform handles the endpoints (boundaries) of the signal. This approach does not restrict the length of the signal to be a power of two. Furthermore, it does not call for the extension of the signal thus, the W-transform is a convenient tool for image compression. They present the basic theory behind the W-transform and include experimental simulations to demonstrate its capabilities
Nullspaces and frames
In this paper we give new characterizations of Riesz and conditional Riesz
frames in terms of the properties of the nullspace of their synthesis
operators. On the other hand, we also study the oblique dual frames whose
coefficients in the reconstruction formula minimize different weighted norms.Comment: 16 page
On-Line Robust Modal Stability Prediction using Wavelet Processing
Wavelet analysis for filtering and system identification has been used to improve the estimation of aeroservoelastic stability margins. The conservatism of the robust stability margins is reduced with parametric and nonparametric time- frequency analysis of flight data in the model validation process. Nonparametric wavelet processing of data is used to reduce the effects of external disturbances and unmodeled dynamics. Parametric estimates of modal stability are also extracted using the wavelet transform. Computation of robust stability margins for stability boundary prediction depends on uncertainty descriptions derived from the data for model validation. The F-18 High Alpha Research Vehicle aeroservoelastic flight test data demonstrates improved robust stability prediction by extension of the stability boundary beyond the flight regime. Guidelines and computation times are presented to show the efficiency and practical aspects of these procedures for on-line implementation. Feasibility of the method is shown for processing flight data from time- varying nonstationary test points
Weighted projections and Riesz frames
Let be a (separable) Hilbert space and a
fixed orthonormal basis of . Motivated by many papers on scaled
projections, angles of subspaces and oblique projections, we define and study
the notion of compatibility between a subspace and the abelian algebra of
diagonal operators in the given basis. This is used to refine previous work on
scaled projections, and to obtain a new characterization of Riesz frames.Comment: 23 pages, to appear in Linear Algebra and its Application
Frame Theory for Signal Processing in Psychoacoustics
This review chapter aims to strengthen the link between frame theory and
signal processing tasks in psychoacoustics. On the one side, the basic concepts
of frame theory are presented and some proofs are provided to explain those
concepts in some detail. The goal is to reveal to hearing scientists how this
mathematical theory could be relevant for their research. In particular, we
focus on frame theory in a filter bank approach, which is probably the most
relevant view-point for audio signal processing. On the other side, basic
psychoacoustic concepts are presented to stimulate mathematicians to apply
their knowledge in this field
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