The ability of a normal human listener to recognize objects in the environment from only the sounds they produce is extraordinarily robust with regard to characteristics of the acoustic environment and of other competing sound sources. In contrast, computer systems designed to recognize sound sources function precariously, breaking down whenever the target sound is degraded by reverberation, noise, or competing sounds. Robust listening requires extensive contextual knowledge, but the potential contribution of sound-source recognition to the process of auditory scene analysis has largely been neglected by researchers building computational models of the scene analysis process. This thesis proposes a theory of sound-source recognition, casting recognition as a process of gathering information to enable the listener to make inferences about

In a previous paper, we proposed a general Fourier method that provides an accurate prediction of the approximation error, irrespective of the scaling properties of the approximating functions. Here, we apply our results when these functions satisfy the usual two-scale relation encountered in dyadic multiresolution analysis. As a consequence of this additional constraint, the quantities introduced in our previous paper can be computed explicitly as a function of the refinement filter. This is, in particular, true for the asymptotic expansion of the approximation error for biorthonormal wavelets as the scale tends to zero. One of the contributions of this paper is the computation of sharp, asymptotically optimal upper bounds for the least-squares approximation error. Another contribution is the application of these results to B-splines and Daubechies scaling functions, which yields explicit asymptotic developments and upper bounds. Thanks to these explicit expressions, we can quantify ...

This paper presents a chronological overview of the developments in interpolation theory, from the earliest times to the present date. It brings out the connections between the results obtained in different ages, thereby putting the techniques currently used in signal and image processing into historical perspective. A summary of the insights and recommendations that follow from relatively recent theoretical as well as experimental studies concludes the presentation. Keywords—Approximation, convolution-based interpolation, history, image processing, polynomial interpolation, signal processing, splines. “It is an extremely useful thing to have knowledge of the true origins of memorable discoveries, especially those that have been found not by accident but by dint of meditation. It is not so much that thereby history may attribute to each man his own discoveries and others should be encouraged to earn like commendation, as that the art of making discoveries should be extended by considering noteworthy examples of it. ” 1 I.

This paper considers the design of pairs of wavelet bases where the wavelets form a Hilbert transform pair. The derivation is based on the limit functions defined by the infinite product formula. It is found that the scaling filters should be offset from one another by a half sample. This gives an alternative derivation and explanation for the result by Kingsbury, that the dual-tree DWT is (nearly) shift-invariant when the scaling filters satisfy the same offset.

Several authors have demonstrated that significant improvements can be obtained in wavelet-based signal processing by utilizing a pair of wavelet transforms where the wavelets form a Hilbert transform pair. This paper describes design procedures, based on spectral factorization, for the design of pairs of dyadic wavelet bases where the two wavelets form an approximate Hilbert transform pair. Both orthogonal and biorthogonal FIR solutions are presented, as well as IIR solutions. In each case, the solution depends on an allpass filter having a flat delay response. The design procedure allows for an arbitrary number of vanishing wavelet moments to be specified. A Matlab program for the procedure is given, and examples are also given to illustrate the results.

Abstract — The TDOA-based acoustic source localization approach is a powerful and widely-used method which can be applied for one source in several dimensions or several sources in one dimension. However the localization turns out to be more challenging when multiple sound sources should be localized in multiple dimensions, due to a spatial ambiguity phenomenon which requires to perform an intermediate step after the TDOA estimation and before the calculation of the geometrical source positions. In order to obtain the required set of TDOA estimates for the multidimensional localization of multiple sound sources, we apply a recently presented TDOA estimation method based on blind adaptive multiple-input-multiple-output (MIMO) system identification. We demonstrate that this localization method also provides valuable side information which allows us to resolve the spatial ambiguity without any prior knowledge about the source positions. Furthermore we show that the blind adaptive MIMO system identification allows a high spatial resolution. Experimental results for the localization of two sources in a two-dimensional plane show the effectiveness of the proposed scheme. I.

This paper introduces the double-density dual-tree discrete wavelet transform (DWT), which is a DWT that combines the double-density DWT and the dual-tree DWT, each of which has its own characteristics and advantages. The transform corresponds to a new family of dyadic wavelet tight frames based on two scaling functions and four distinct wavelets. One pair of the four wavelets are designed to be offset from the other pair of wavelets so that the integer translates of one wavelet pair fall midway between the integer translates of the other pair. Simultaneously, one pair of wavelets are designed to be approximate Hilbert transforms of the other pair of wavelets so that two complex (approximately analytic) wavelets can be formed. Therefore, they can be used to implement complex and directional wavelet transforms. The paper develops a design procedure to obtain finite impulse response (FIR) filters that satisfy the numerous constraints imposed. This design procedure employs a fractional-delay allpass filter, spectral factorization, and filterbank completion. The solutions have vanishing moments, compact support, a high degree of smoothness, and are nearly shift-invariant.

This paper describes a new class of nonsymmetric maximally flat lowpass FIR filters. By subjecting the magnitude and group delay responses (individually) to differing numbers of flatness constraints, the new filters are obtained. It is found that these filters achieve a smaller delay than symmetric filters while maintaining relatively constant group delay around ! = 0, with no degradation of the frequency response magnitude. The design of these filters is initially investigated using Grobner bases. An analytic design technique, applicable to a subset of the forgoing filters, is provided that does not depend on Grobner basis computations.

This paper introduces an approximately shift invariant redundant dyadic wavelet transform- the phaselet transform- that includes the popular dual-tree complex wavelet transform of Kingsbury [1] as a special case. The main idea is to use a finite set of wavelets that are related to each other in a special way- and hence called phaselets-to achieve approximate shift-redundancy; bigger the set better the approximation. A sufficient condition on the associated scaling filters to achieve this is that they are frac-tional shifts of each other. Algorithms for the design of phaselets with a fixed number vanishing moments is presented- building upon the work of Selesnick [2] for the design of wavelet pairs for Kingsbury’s dual-tree complex wavelet transform. Construction of 2-dimensional directional bases from tensor products of 1-d phaselets is also described. Phaselets as a new approach to redundant wavelet transforms and their construction are both novel and should be interesting to the reader independently of the approximate shift invariance property that this paper argues they possess. 1

A bandlimited signal can be recovered from its periodic nonuniformly spaced samples provided the average sampling rate is at least the Nyquist rate. A multirate filter bank structure is used to both model this nonuniform sampling (through the analysis bank) and reconstruct a uniformly sampled sequence (through the synthesis bank). Several techniques for modelling the nonuniform sampling are presented for various cases of sampling. Conditions on the filter bank structure are used to accurately reconstruct uniform samples of the input signal at the Nyquist rate. Several examples and simulation results are presented, with emphasis on forms of nonuniform sampling that may be useful in mixed-signal integrated circuits.