R. A. Altes, "Wideband, proportional-bandwidth Wigner-Ville analysis," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1005--1012, June 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... proportional bandwidth analysis tools based on the concept of scale have been developed, including the Mellin transform [5] the joint time scale wavelet transform and wavelet orthonormal bases and frames [3] and bilinear wavelet generalizations such as the Altes Marinovich distribution [6, 7], the affine Wigner distributions of the Bertrands [8 10] the affine class [11, 12] the time frequency scale classes of Cohen [13] and the hyperbolic and power classes of Papandreou, Hlawatsch, and Boudreaux Bartels [14,15] A further generalization of the time frequency and time scale ....

....system from a T invariant one. The fundamental transform for the system PU is the e T Fourier transform F e T = FU . This transform measures in time signals the physical quantity associated with the new operator e F . As a simple example, consider the unitary warping operator 8 [6, 14] (U log s) x) def = e x=2 s (e x ) 28) that takes functions in L 2 (IR ) and stretches them into functions in L 2 (IR) This transformation maps the unitary time operator to the scale operator U Gamma1 log T t U log = D t (29) on L 2 (IR ) and, therefore, converts linear ....

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R. A. Altes, "Wideband, proportional-bandwidth Wigner-Ville analysis," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1005--1012, June 1990.

....transform it. The scale transform, the short time scale transform and the general class of joint time scale, frequency scale and time frequency scale distributions have been recently introduced and discussed by Cohen [4] 5] While particular members of the general class have been studied (e.g. [1]) to date, the question of how to generate the positive members of this class has not been addressed. Indeed, the theory of positive joint distributions involving scale has yet to be considered. In this paper, we introduce the class of positive joint scale distributions and give a general method ....

....yet to be considered. In this paper, we introduce the class of positive joint scale distributions and give a general method for computing them for any signal. 2. Background Some of the first to consider joint distributions involving scale were Marinovich [7] 10] the Bertrands [2] and Altes [1]. Others have also considered the issue, offering a variety of approaches, interpretations and generalizations (e.g. 4] 5] 13] 14] In this paper, we consider the approach of Cohen [5] One formulation of the general class of joint time scale distributions is [5] 1 (1) where the kernel ....

R. Altes, "Wide-band, proportional-bandwidth Wigner-Ville Analysis," IEEE Trans. Acoust., Speech and Sig. Proc., vol. 38, no. 6, pp.1005-1012, 1990.

....(30) and (31) it can be easily seen that the ST transform is the usual Fourier transform IF defined in (11) which is invariant to time shifts, and the SF transform is the identity transform I, which is invariant to frequency shifts. Similarly, SD : L 2 (IR ) L 2 (IR) is the Mellin transform [37, 38, 34] defined by (SD s) c) M(c) Z IR s(t) e Gammai2 c ln(t) p t dt (35) which is invariant to dilations (D oe ) and the SQ transform is given by (SQ s) r) p jf o j jrj S(f o =r) p jf o j jrj (IFs) f o =r) 36) which is invariant to the Q operator; that is, to changes in the ....

R. A. Altes, "Wide-band proportional-bandwidth Wigner-Ville analysis", IEEE Trans. Acoust., Speech Signal Processing, vol. 38, pp. 1005--1012, June 1990.

....form js(t)j 2 . The T IED vs. D IED distributions have Fourier and Mellin marginals. We will work with continuous time analytic signals whose Fourier transforms live in L 2 (IR ) The Altes Q distribution results from (16) with the ordering D 0 d=2 T t D 0 d=2 , with t 2 IR, d 2 IR [42]. The ordering T d Gamma1 log d t D 0 d [6] yields the Bertrand tomographic distribution [5] which has also been obtained by Shenoy and Parks [6] and by Cohen [1, p. 257] The Q distribution is covariant to scale changes, but not to time shifts. The Bertrand distribution is covariant to both ....

....changes, but not to time shifts. The Bertrand distribution is covariant to both scale changes and time shifts. The T CED vs. D IED distributions have time and Mellin marginals. The ordering D 0 d=2 F f D 0 d=2 yields the time scale distribution of Eichmann and Marinovich [43] and Altes [42] for single sided signals in L 2 (IR ) Time A: For analyzing time signals, joint distributions with a time marginal are fundamental. Joint distributions of T and A measure joint time and A content. For the distributed ordering A a Gamma1 =2 F Gamma A a Gamma1 =2 , 5 T CED vs. A IED ....

R. A. Altes, "Wideband, proportional-bandwidth Wigner-Ville analysis," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1005--1012, June 1990.

....= IR ; Theta) where IR = 0; 1) and Theta denotes multiplication. One characterization of the dual group is ( Gamma; ffi) IR; with the characters given by (k; j e j2 ln(k) In this case d G (k) dk=k and d Gamma ( d. The group Fourier transform is the Mellin transform [24, 25] (IF IR s) j Z 1 0 s(k)e Gammaj 2 ln(k) dk=k : 16) 2.2 Cohen s Approach Let a and b be two variables of interest; they could be time and scale, for example. In Cohen s approach, the variables a and b are associated with appropriate Hermitian operators A and B, respectively. The ....

.... marginals or the T IED, D IED marginals are trivial [16] T a 0 and D k 0 , represented in the same signal space, are identical Working in the L 2 (IR ; dk=k) space, the symmetric Wigner like representation corresponding to T CED, D IED marginals yields exactly the Q distribution of Altes [25]. The corresponding representation in Cohen s method, using Theorem 2, is the Wigner distribution 25 Which is associated with scale in [16, 17] WD) W , corresponding to the variables time and frequency; that is, Qs) e t ; f) WT Gamma1 s) t; f ) where (T Gamma1 s) t) s(e ....

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R. A. Altes, "Wide-band proportional-bandwidth Wigner-Ville analysis", IEEE Trans. Acoust., Speech Signal Processing, vol. 38, pp. 1005--1012, June 1990.

.... noise implements the optimal quadratic detector T by correlating the Wigner distribution W x of the observed signal x with a two dimensional time frequency function S based on the statistics [13] T (x) Z Z W x (t; f)S(t; f)dtdf : 1) A similar formulation in terms of the Altes distribution [14] is given in [15] and detection schemes based on the spectrogram are considered in [16] In [17] and [15, 18] maximum likelihood detectors for detecting noncoherent linear and hyperbolic chirps, respectively, with unknown chirp parameters, are implemented equivalently by integrating certain TFRs ....

R. A. Altes, "Wide-band proportional-bandwidth Wigner-Ville analysis", IEEE Trans. Acoust., Speech Signal Processing, vol. 38, pp. 1005--1012, June 1990.

.... proportional bandwidth analysis tools based on the concept of scale have been developed, including the Mellin transform [6,7] the joint time scale wavelet transform and wavelet orthonormal bases and frames [4] and bilinear wavelet generalizations such as the Altes Marinovich distribution [8, 9], the affine Wigner distributions of the Bertrands [10 12] the affine class [13 15] the time frequency scale classes of Cohen [2, 3] and the hyperbolic and power classes of Papandreou, Hlawatsch, and Boudreaux Bartels [16, 17] Further generalizations of the time frequency and time scale ....

....arguments such as in [28] it is simple to show that unitary equivalence can construct LTI based, A invariant systems for all physical quantities a taking on values isomorphic to the real number system IR. Example: Logarithmic time axis warping. Consider the unitary warping operator 10 [8, 16] (U log s) x) j e x=2 s (e x ) 26) 9 Time covariant is a more accuarte term. 10 Strictly speaking, 26) is inaccurate in terms of dimensional analysis: The index x in the exponentials of (26) must be dimensionless, yet the function s expects an index with units of seconds. Correct ....

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R. A. Altes, "Wideband, proportional-bandwidth Wigner-Ville analysis," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1005--1012, June 1990.

.... Gamma1 to the log time axis of the log time versus Mellin distribution remaps that axis back to true time. The resulting distributions lie in Cohen s class of time Mellin distributions (time scale in his terminology) 1, 9] This class contains the Marinovich Altes (warped Wigner) distribution [7, 10]. It is important to note that this class is unattainable by either signal or axis warping alone. In Figure 1 we show two distributions of a signal consisting of two components concentrated along composite linear sinusoidal instantaneous frequencies. Since the Wigner time frequency distribution ....

R. A. Altes, "Wideband, proportional-bandwidth Wigner-Ville analysis," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1005--1012, June 1990.

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R. A. Altes, "Wideband, proportional-bandwidth Wigner-Ville analysis," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1005--1012, June 1990.

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R. A. Altes, "Wideband, proportional-bandwidth WignerVille analysis," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1005--1012, June 1990.

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R. A. Altes, "Wide-band proportional-bandwidth Wigner-Ville analysis", IEEE Trans. Acoust., Speech Signal Processing, vol. 38, pp. 1005--1012, June 1990.

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R. A. Altes, "Wideband, proportional-bandwidth Wigner-Ville analysis," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1005--1012, June 1990.

No context found.

R. A. Altes, "Wideband, proportional-bandwidth Wigner-Ville analysis," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1005--1012, June 1990.

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R. A. Altes, "Wide-band proportional-bandwidth Wigner-Ville analysis", IEEE Trans. Acoust., Speech Signal Processing, vol. 38, pp. 1005--1012, June 1990.

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R. A. Altes, "Wideband, proportional-bandwidth WignerVille analysis," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1005--1012, June 1990.

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