A. Tewrik, D. Sinha, and P. Jorensen, "On the optimal choice of a wavelet for signal representation, " IEEE Trans. Inform. Theory, vol. 398, pp. 747--765, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....problem was formulated and solved by Huang and Schultheiss [27] nearly four decades ago. For the case of subband coders various useful cases of the filter bank optimization problem have been considered by a number of authors, for example, by Akansu and Liu [5] Haddad and Uzun [23] Tewfik et al. [55], Gopinath et al. 22] Malvar and Staelin [41] and Dasgupta et al. 15] The optimality of principal component filter banks (PCFB) for certain objectives was observed independently by a number of authors [56, 60, 61, 73] For the unconstrained of orthonormal filter banks the PCFB was ....

A. H. Tewfik, D. Sinha, and P. E. Jorgensen, On the optimal choice of a wavelet for signal representation, IEEE Trans. Inform. Theory. March (1992), 747--765.

.... to the fast Fourier transform (FFT) the discrete wavelet transform (DWT) defines a wavelet representation of the original data which is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters (QMFs) 2] Thus the selection of an appropriate QMF has to be solved [5]. As this selection strongly depends on the characteristics of the input signals heuristic search strategies with high computation time are commonly used to find the optimal QMF. We propose to use a neural net to classify the source signals according to their corresponding optimal QMF by learning ....

Tewfik, A. H.; Sinha, D. and Jorgensen, P.: On the Optimal Choice of a Wavelet for Signal Representation. IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 747-765, 1992.

....hn [ filter, given the constraints of (4) we face a problem of considerable complexity. The optimization of the CQF filter bank is much more tractable if we can express the 2N coefficients in terms of a reduced number of parameters. Several parametrizations have been proposed in the literature [8,9,10,11,12]. Pollen [8] showed that a 2N sequence hn [ satisfying the constraints in (4) is a function of N 1 parameters. For N = 2 the expressions for the 4 coefficients are as follows: h 0 1 8 1 ( cos sin = h 1 1 8 1 ( cos sin = 9.a) h 2 1 8 1 ( cos sin = h 3 1 8 ....

....on Signal Processing Vitor Silva and Lus de S MS Word 6.0 7 which has no particular behaviour at = 3 . The variation with of the signal energy, aliasing energy and cross correlation is shown in Fig. 3 for the case of an AR(1) input model with = 095. V. CONCLUSION It is known [9] that the parametrization = 3 corresponds to the Daubechies D 2 solution of equation (4) which is minimum phase. On the other hand, 3 corresponds to the maximum phase counterpart of the Daubechies D 2 filter. Therefore we conclude that regularity is a desired property for the 4 tap CQF ....

Ahmed H. Tewfik, Deepen Sinha and Paul Jorgensen, "On the optimal choice of a wavelet for signal representation", IEEE Trans. on Information Theory, vol. 38, n. 2, pp. 747-765, March 1992.

....and filter banks. The parameterization of complex filter banks changes the constrained optimization problem to an unconstrained problem, which can be easily solved by numerical algorithms. An appropriate criterion can be chosen and a similar optimization method used in choosing real wavelet bases [28], 29] 30] can be used to choose optimal complex orthogonal wavelet bases and filter banks. Similarly, the method can also be used to select optimal complex wavelet packet bases. DRAFT X. P. ZHANG ETAL, ORTHOGONAL COMPLEX FILTER BANKS AND WAVELETS 14 Appendix A Assume filter h has even length ....

A. H. Tewfik, F. Ainha, and P. Jorgensen, "On the optimal choice of wavelet for signal representation," IEEE Trans. on Info. Theo., vol. 38, no. 2, pp. 747--765, Mar. 1992.

....We develop two new multiscale transforms scale adapted transforms (ScAT) and space adapted transforms (SpAT) The fundamental idea in both cases is to adapt the prediction to minimize a data based error criterion. While other adaptive transform techniques have been proposed in the literature [4, 5, 6], the adaptive transforms developed here are new, particularly in their use of the lifting programme. We also present adaptive redundant transforms, and a lifting interpretation of median filters. We demonstrate the power of these new transforms with applications to signal denoising problems; in ....

....have the equivalent filter h at the top of the Figure. Note that h is a function of both the update coefficients u k and the prediction coefficients p k . 1 p 1 p 2 1 u 2 u 3 u 4 u p 1 p 2 p 1 p 2 p 1 p 2 1 1 1 1 x [0] e x [0] o x [1] e x [1] o x [2] e x [2] o x [3] e x [3] o x [4] e c[2] p u 1 1 u 1 p u p u 1 2 2 1 1 p u p u 2 1 2 3 p u 2 4 u 4 u 2 u 3 p u p u 2 1 3 4 [ d[0] d[3] d[2] d[1] h = T Figure 6: Update filtering. An N = 2 point linear predict followed by an e N = 4 point linear update yields the update vector h shown ....

[Article contains additional citation context not shown here]

A. Tewrik, D. Sinha, and P. Jorensen, "On the optimal choice of a wavelet for signal representation, " IEEE Trans. Inform. Theory, vol. 398, pp. 747--765, 1992.

....cutoff frequency of the passband. A second special case occurs when one seeks optimal sub sampled approximations to a signal [6, 10] Finally, since orthonormal wavelets are generated by iterated QMF banks, we see that our problem is closely related to the signal adapted wavelet design problem [14, 15]. The latter problem is clearly more involved than the previous special cases, due to the coupling of successive stages in the filter bank decomposition. While a discrete wavelet transform constrains the filter bank to be the same in each stage [16] the approach presented in this paper yields ....

A. H. Tewfik, D. Sinha and P. Jorgensen, "On the Optimal Choice of a Wavelet for Signal Representation," IEEE Trans. on Info. Theory, Vol. 38, No. 2, pp. 747---765, Mar. 1992.

....We develop two new multiscale analysis techniques scale adapted transforms and space adapted transforms. The fundamental idea in both cases is to adapt the prediction to minimize a data based error criterion. While other adaptive transform techniques have been proposed in the literature [4, 5, 6], the adaptive transforms developed here are new, particularly in their use of the lifting programme. The paper is organized as follows. In Section 2, we review the basic lifting construction and describe a variant of the basic scheme. In Section 3, we develop the two new adaptive DWTs using the ....

....we have the equivalent filter h at the top of the Figure. Note that h is a function of both the update coefficients uk and the prediction coefficients pk . 1 p 1 p 2 1 u 2 u 3 u 4 u p 1 p 2 p 1 p 2 p 1 p 2 1 1 1 1 x [0] e x [0] o x [1] e x [1] o x [2] e x [2] o x [3] e x [3] o x [4] e c[2] p u 1 1 u 1 p u p u 1 2 2 1 1 p u p u 2 1 2 3 p u 2 4 u 4 u 2 u 3 p u p u 2 1 3 4 [ d[0] d[3] d[2] d[1] Figure 3: Update filtering. An N = 2 point linear predict followed by an e N = 4 point linear update yields the update vector h shown across the ....

A. H. Tewfik, D. Sinha, and P. Jorgensen, "On the optimal choice of a wavelet for signal representation," IEEE Trans. Inform. Theory, vol. IT--38, pp. 747--765, Mar. 1992.

....over such as: i ) error measure, ii ) type of transform (2 band [6] M band [39] wavelet packets [4] multiwavelets [40] etc. iii ) properties of the wavelet filters (vanishing moments [6, 25] splines [3] smoothness [23, 24] stopband attenuation [33] signal dependent optimal filters [19, 41], etc. iv) number of levels to threshold in the wavelet coefficient domain. Although it is infeasible to optimize over all of these parameter one needs to consider each of these parameters since they might contribute to improving the noise reducing capabilities for an application. Often one will ....

A. H. Tewfik, D. Sinha, and P. Jorgensen. On the optimal choice of a wavelet for signal representation. IEEE Trans. Inform. Theory, 38(2):747--765, March 1992.

....that minimizes the worst case approximation error among all the signals in the class M , J and the support size of the wavelets are fixed as in the previous problem. The class of signals considered are the frequency domain L p class. Problem 1 has been addressed by Tewfik, Sinha and Jorgensen [29] for the special case M = 2 (i.e. for Daubechies orthonormal wavelet bases) Since the expression for the exact approximation error is unwieldy and complicated, the approach in [29] is to obtain upper and lower bounds on the approximation error, and devise a numerical scheme to minimize the ....

....considered are the frequency domain L p class. Problem 1 has been addressed by Tewfik, Sinha and Jorgensen [29] for the special case M = 2 (i.e. for Daubechies orthonormal wavelet bases) Since the expression for the exact approximation error is unwieldy and complicated, the approach in [29] is to obtain upper and lower bounds on the approximation error, and devise a numerical scheme to minimize the upper bound. This gives a sub optimal solution to the approximation problem that is relatively efficient to implement. Our approach to Problem 1 is based on the following crucial ....

[Article contains additional citation context not shown here]

A. H. Tewfik, D. Sinha, and P. Jorgensen. On the optimal choice of a wavelet for signal representation. IEEE Trans. Inform. Theory, 38(2):747--765, March 1992.

....rather than fully transparent quality. Because the WP transform can provide a non uniform decomposition of the signal into frequency bands approximating the critical band divisions, several new WP transform based algorithms which try to overcome the shortcomings of [6] have been produced [4, 5, 7, 8, 9]. The audio coder in [4, 5] offers improved reconstructed audio signal quality at 60 70kbps but without much reduction in delay. In contrast, the methods of [7, 8, 9] focus mainly on reducing computational effort to achieve real time implementation, but offer poorer quality reconstruction than the ....

....band divisions, several new WP transform based algorithms which try to overcome the shortcomings of [6] have been produced [4, 5, 7, 8, 9] The audio coder in [4, 5] offers improved reconstructed audio signal quality at 60 70kbps but without much reduction in delay. In contrast, the methods of [7, 8, 9] focus mainly on reducing computational effort to achieve real time implementation, but offer poorer quality reconstruction than the method of [6] In this paper, we propose an algorithm which aims not only to keep high quality but also to achieve reasonable delay when applied in real time. ....

A. H. Tewfik Deepen Sinha, Paul Jorgensen "On the Optimal Choice of a Wavelet for Signal Representation" IEEE Trans. on Info. Theory. Vol. 38, No. 2, March 1992.

.... combination of adaptive wavelets which can be used as a wavelet by itself [3] These super wavelets would allow the flexibility of adaptively changing the fundamental shape of the wavelet for a given application rather than just changing the parameters of a fixed shape wavelet as in the case of [4]. From speech applications point of view, the adaptive wavelets and super wavelets would be useful in overcoming the problems associated with variability in speaker s speaking rate and inter and intra speaker variability in speech characteristics. The application of wavelets for signal ....

A. Tewfik, D. Sinha and P. Jorgensen, "On the optimal choice of a wavelet for signal representation," IEEE Trans. on Inf. Theory, Vol. 38, pp. 747-765, March 1992.

....a wavelet by itself is referred to as super wavelet . The main advantage of super wavelets is that it would allow the flexibility of adaptively changing the fundamental shape of the wavelet for a given application rather than just changing the parameters of a fixed shape wavelet as in the case of [16, 17, 18, 19]. From speech applications point of view, the adaptive wavelets and super wavelets would be useful in overcoming the problems associated with variability in speaker s speaking rate and inter speaker variability in speech characteristics. The approximation equation mentioned above (Eq. 1) can be ....

A. Tewfik, D. Sinha and P. Jorgensen, "On the optimal choice of a wavelet for signal representation, " IEEE Trans. on Inf. Theory, Vol. 38, pp. 747-765, March 1992.

....for predicting the performance [14] but its relevance to signal processing has not yet been strongly established [20] The correlation between the reconstructed SNR and the regularity of the filter is not very strong either. Some researchers have emphasized orthogonality as a selection criterion [4, 17], but this might conflict with other desirable characteristics. Others have characterized wavelet filter banks in terms of their associated continuous scaling functions and wavelets derived under iteration [21] Daubechies 4 tap filter was the choice for all the simulation results discussed ....

A. H. Tewfik, D. Sinha, and P. Jorgensen, "On the Optimal Choice of a Wavelet for Signal Representation," IEEE Tran. on Information Theory, vol. 38, pp. 747 -- 765, 1992.

....to segment high dimensional objects. Progress needs to be made to extend these algorithms to higher dimensions. In this chapter, we only consider the structure of the wavelet systems. It is also meaningful and possible to design the wavelets themselves in order to further improve the performance [36, 75, 50]. There are many types of wavelets systems, e.g. M band wavelets [73] Cos Modulated wavelets [35] and others [31] Generalization of the best basis idea to other types of wavelets is also possible. 58 Chapter 4 Applications of Orthonormal Wavelet Transform 4.1 Introduction In the previous ....

A. H. Tewfik, D. Sinha, and P. Jorgensen. On the optimal choice of a wavelet for signal representation. IEEE Trans. Inform. Theory, 38(2):747--765, March 1992.

....cutoff frequency of the passband. A second special case occurs when one seeks optimal sub sampled approximations to a signal [6, 10] Finally, since orthonormal wavelets are generated by iterated QMF banks, we see that our problem is closely related to the signal adapted wavelet design problem [14, 15]. The latter problem is clearly more involved than the previous special cases, due to the coupling of successive stages in the filter bank decomposition. Generally speaking, a discrete wavelet transform constrains the filter bank to be the same in each stage [16] but the approach presented in ....

A. H. Tewfik, D. Sinha and P. Jorgensen, "On the Optimal Choice of a Wavelet for Signal Representation," IEEE Trans. on Info. Theory, Vol. 38, No. 2, pp. 747---765, Mar. 1992.

....problem, especially when trying to study a class of signals, is to find the wavelet that minimize the worst case approximation error over all signals in a class. This wavelet, if it exist, will be referred to as the robust wavelet . The former problem has been addressed by Tewfik and Jorgensen [7]. In the paper they derive upper bonds on the L 2 and L 1 approximation error of a given signal up to any desired finite scale. The problem of obtaining robust wavelets was considered by Gopinath [8] In this case the error can be modeled as the output of an error operator acting on the ....

....k 6=0 0 2 M J k M J 3 5 : 24) Now using this in Eqn. 20 we have fl fl fl c Qf fl fl fl p p = 1 2 Z IR fi fi fi f( fi fi fi p g( d : 25) and trivially all impulse trains are included by the definition of essentially scale limited signals. Tewfik and Jorgensen [7] provided upper bounds for design of optimal wavelets for representation of a signal. We can do better than that, and in the special case of L 2;2 (IR) an explicit formula can be obtained for the error. This is suited for numerical optimization to obtain the best wavelet for representing a given ....

A. H. Tewfik and P. E. Jorgensen. On the optimal choice of a wavelet for signal representation. Preprint, 1991.

....vary from person to person. The variability in the acoustic characteristics of different phonemes are being exploited in representing and classifying phonemes. Wavelets have been used for both signal (or image) representation and classification. They have been used for signal representation in [1, 2, 3, 4, 5, 6]. The problems of representation and classification can be viewed as feature extraction problems, in which the goal is to find a set of daughter wavelets (dilations and shifts of a mother wavelet) which either best represent the signal or best separate various signal classes in the resulting ....

A. Tewfik, D. Singha and P. Jorgensen, "On the optimal choice of a wavelet for signal representation," IEEE Trans. on Inf. Theory, Vol. 38, pp. 747-765, March 1992.

.... by AFOSR under grant 90 0334 funded by DARPA and Bell Northern Research 1 Introduction Recently orthonormal bases of compactly supported wavelets have received considerable attention in the signal processing community, both as a tool for signal analysis ( 5, 6, 7, 8] and signal representation ([9, 10, 11, 12, 13, 14]) Several authors have tried to use wavelets for image compression [10, 15] It is well known that image coding using wavelets is a special case of subband coding using particular sets of filters called scaling and wavelet vectors. However, this specialization and the mathematical theory of ....

....WTFs, one can pick a tight frame that is suited to any particular application. This involves choosing the scaling function, and then the wavelets. In the wavelet literature there has been some recent work on the choice of optimal and robust scaling function or equivalently the scaling vector [12, 13, 11]. The scaling vector is generically of length N = MK, and determined by (M Gamma 1) K Gamma 1) parameters. All properties of the multiresolution analysis is determined by the scaling function. However, when M 2, to get a WTF one has to design the wavelets too. For large M the design of the WTF ....

A. H. Tewfik, D. Sinha, and P. Jorgensen. On the optimal choice of a wavelet for signal representation. IEEE Trans. Inform. Theory, 38(2):747--765, March 1992.

No context found.

A. Tewrik, D. Sinha, and P. Jorensen, "On the optimal choice of a wavelet for signal representation, " IEEE Trans. Inform. Theory, vol. 398, pp. 747--765, 1992.

No context found.

A. H. Tewfik and P. E. Jorgensen. On the optimal choice of a wavelet for signal representation. Preprint, 1991.

No context found.

Ahmed H. Tewfik, Deepen Sinha, and Paul Jorgensen, "On the Optimal Choice of a Wavelet for Signal Representation, " IEEE Transactions on Information Theory, Vol. 38, No. 2, pp.747-765, Marc h 1992.

No context found.

Tewfik, A.H.; Sinha, D.; Jorgensen, P., "On the Optimal Choice of a Wavelet for Signal Representation", IEEE Transactions on Information Theory, vol. 38(2), March 1992.

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Tewfik, A., Sinha, D. and Jorgensen, P. (1992). On the optimal choice of a wavelet for signal representation. IEEE Transactions on Information Theory, 38, No 2, 747-765.

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Tewfik, A., Sinha, D. and Jorgensen, P. (1992). On the optimal choice of a wavelet for signal representation. IEEE Transactions on Information Theory 38 No 2, 747-765.

No context found.

A. H. Tewfik, D. Sinha and P. Jorgensen, "On the Optimal Choice of a Wavelet for Signal Representation," IEEE Trans. on Info. Theory, vol. 38, no. 2, pp 747--765, March 1992.

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