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93
Quantitative Fourier Analysis of Approximation Techniques: Part II  Wavelets
 IEEE Trans. Signal Processing
, 1999
"... 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 twoscale relation encountered in dyadic ..."
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Cited by 97 (38 self)
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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 twoscale 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 leastsquares approximation error. Another contribution is the application of these results to Bsplines and Daubechies scaling functions, which yields explicit asymptotic developments and upper bounds. Thanks to these explicit expressions, we can quantify ...
SoundSource Recognition: A Theory and Computational Model
, 1999
"... 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 source ..."
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Cited by 95 (0 self)
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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 soundsource 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 soundsource recognition, casting recognition as a process of gathering information to enable the listener to make inferences about
A chronology of interpolation: From ancient astronomy to modern signal and image processing
 Proceedings of the IEEE
, 2002
"... 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 histo ..."
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Cited by 88 (0 self)
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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, convolutionbased 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.
Hilbert Transform Pairs of Wavelet Bases
, 2001
"... 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 a ..."
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Cited by 75 (10 self)
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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 dualtree DWT is (nearly) shiftinvariant when the scaling filters satisfy the same offset.
The Design of Approximate Hilbert Transform Pairs of Wavelet Bases
, 2002
"... Several authors have demonstrated that significant improvements can be obtained in waveletbased 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 p ..."
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Cited by 50 (9 self)
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Several authors have demonstrated that significant improvements can be obtained in waveletbased 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.
Simultaneous localization of multiple sound sources using blind adaptive MIMO filtering
 In IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP
, 2005
"... Abstract — The TDOAbased acoustic source localization approach is a powerful and widelyused 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 localize ..."
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Cited by 35 (17 self)
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Abstract — The TDOAbased acoustic source localization approach is a powerful and widelyused 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 multipleinputmultipleoutput (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 twodimensional plane show the effectiveness of the proposed scheme. I.
Reconstruction of nonuniformly sampled bandlimited signals by means of digital fractional delay filters
 IEEE Trans. Signal Processing
, 2002
"... Abstract – This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The points of departures are that the signal is slightly oversampled as to the average sampling frequency and that the sampling instances are know ..."
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Cited by 33 (7 self)
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Abstract – This paper deals with reconstruction of nonuniformly sampled bandlimited continuoustime signals using timevarying discretetime FIR filters. The points of departures are that the signal is slightly oversampled as to the average sampling frequency and that the sampling instances are known. Under these assumptions, a representation of the reconstructed sequence is derived that utilizes a timefrequency function. This representation enables a proper utilization of the oversampling and reduces the reconstruction problem to a design problem that resembles an ordinary filter design problem. Furthermore, for an important special case, corresponding to a certain type of periodic nonuniform sampling, it is shown that the reconstruction problem can be posed as a filterbank design problem, thus with requirements on a distortion transfer function and a number of aliasing transfer functions. 1.
The DoubleDensity DualTree DWT
, 2004
"... This paper introduces the doubledensity dualtree discrete wavelet transform (DWT), which is a DWT that combines the doubledensity DWT and the dualtree DWT, each of which has its own characteristics and advantages. The transform corresponds to a new family of dyadic wavelet tight frames based on ..."
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Cited by 25 (1 self)
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This paper introduces the doubledensity dualtree discrete wavelet transform (DWT), which is a DWT that combines the doubledensity DWT and the dualtree 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 fractionaldelay allpass filter, spectral factorization, and filterbank completion. The solutions have vanishing moments, compact support, a high degree of smoothness, and are nearly shiftinvariant.
Reconstruction of Bandlimited Periodic Nonuniformly Sampled Signals through Multirate Filter Banks
 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS–I: REGULAR PAPERS
, 2003
"... 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 sequen ..."
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Cited by 21 (1 self)
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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 mixedsignal integrated circuits.
Statistical properties of STFT ratios for two channel systems and applications to blind source separation
 in Proc. ICABSS
, 2000
"... The ratio of the short time Fourier transform (STFT) coecients of signals received at two sensors can factor out the role of the power spectrum of emitting sources, under an assumption called disjoint orthogonality. Thus, it can reveal parameters specic to the mixing scenario and serve as a basis fo ..."
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Cited by 17 (8 self)
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The ratio of the short time Fourier transform (STFT) coecients of signals received at two sensors can factor out the role of the power spectrum of emitting sources, under an assumption called disjoint orthogonality. Thus, it can reveal parameters specic to the mixing scenario and serve as a basis for channel estimation techniques. In this paper we analyze and extend a source separation method based on the use of STFT ratios of two sensor inputs, called DUET. We generalize the problem formulation in DUET, and prove that considerably weaker assumptions about the classes of input signals are sucient to apply the derived techniques. The analysis centers on the notion of ratioestimator and a novel stochastic model that enabled us to derive the maximum likelihood ratioestimator. Derived techniques can be eectively applied to source separation, source localization, signal enhancement, and noise reduction when using a twin microphone system, both in echoic environments and degenerate situations. 1 1.