N. J. Munch. Noise reduction in tight Weyl-Heisenberg frames. IEEE Trans. Inform. Theory, 38(2):608--616, March 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....also a paraunitary FB corresponds to a tight frame expansion, its 1=K behavior does not come as a surprise. A 1=K behavior has furthermore been observed for tight frames in nite dimensional spaces [21, 29] and for reconstruction from a nite set of Weyl Heisenberg (Gabor) or wavelet coecients [21, 30]. Under additional conditions, a 1=K 2 behavior has been demonstrated for Weyl Heisenberg frames in [30] In [5, 31, 32, 33, 34] based on a deterministic quantization noise model, a nonlinear set theoretic estimation method is used to achieve a 1=K 2 behavior for frames of sinc functions (A D ....

.... A 1=K behavior has furthermore been observed for tight frames in nite dimensional spaces [21, 29] and for reconstruction from a nite set of Weyl Heisenberg (Gabor) or wavelet coecients [21, 30] Under additional conditions, a 1=K 2 behavior has been demonstrated for Weyl Heisenberg frames in [30]. In [5, 31, 32, 33, 34] based on a deterministic quantization noise model, a nonlinear set theoretic estimation method is used to achieve a 1=K 2 behavior for frames of sinc functions (A D conversion) and for Weyl Heisenberg frames. In Sections 3 and 4, we shall propose oversampled predictive ....

N. J. Munch, \Noise reduction in tight Weyl-Heisenberg frames," IEEE Trans. Inf. Theory, vol. 38, pp. 608-616, March 1992.

.... been exploited for noise reduction by means of noise shaping [6, 7, 13] We show that predictive quantization in oversampled FBs yields better noise reduction (at the cost of increased bit rate) than the best methods previously proposed for noise reduction in overcomplete representations [14] [16]. Oversampled predictive subband coders allow to trade bit rate for quantizer accuracy, and they are therefore well suited for subband coding applications where for technological or other reasons quantizers with low accuracy (even single bit) have to be used. The practical advantages of using ....

N. J. Munch, \Noise reduction in tight Weyl-Heisenberg frames," IEEE Trans. Inf. Theory, vol. 38, pp. 608-616, March 1992.

....which means that more oversampling entails more noise reduction. Such a 1=K behavior has previously been observed for oversampled A D conversion [11] for tight frames in nite dimensional spaces [10, 12] and for reconstruction from a nite set of Weyl Heisenberg (Gabor) or wavelet coe cients [10, 13]. Recently, under additional conditions, a 1=K 2 behavior has been demonstrated for Weyl Heisenberg frames [13, 14] In Section 4, we shall propose noise shaping techniques which can do even better than 1=K 2 . Noise reduction versus design freedom. Let us now consider an oversampled FB with ....

.... for oversampled A D conversion [11] for tight frames in nite dimensional spaces [10, 12] and for reconstruction from a nite set of Weyl Heisenberg (Gabor) or wavelet coe cients [10, 13] Recently, under additional conditions, a 1=K 2 behavior has been demonstrated for Weyl Heisenberg frames [13, 14]. In Section 4, we shall propose noise shaping techniques which can do even better than 1=K 2 . Noise reduction versus design freedom. Let us now consider an oversampled FB with R(z) chosen according to (2) i.e. R(z) R(z) U(z) IN E(z) R(z) such that PR is guaranteed. Inserting ....

N. J. Munch, \Noise reduction in tight Weyl-Heisenberg frames," IEEE Trans. Inf. Theory, vol. 38, pp. 608-616, March 1992.

....framework for understanding non orthogonal transforms. Frames were introduced by Duffin and Schaeffer [10] in the context of non harmonic Fourier series. Recent interest in frames has been spurred by its utility in analyzing discrete wavelet transforms [5, 6, 15] and timefrequency decompositions [22]. We are motivated by a desire to understand quantization effects and efficient representations in a general framework. To put this chapter in context, we will give a particular interpretation of Fourier analysis and discuss a sense in which it can be generalized. Since we are limiting our ....

....known frame coefficients. The remainder of the section gives new results on reconstruction from quantized frame coefficients. Most previous work on frame expansions is predicated either on exact knowledge of coefficients or on coefficient degradation by white additive noise. For example, Munch [22] considered a particular type of frame and assumed the coefficients were subject to a stationary noise. This report, on the other hand, is in the same spirit as [4, 32, 33, 35] in that it utilizes the deterministic qualities of quantization. 2.1 Frames 2.1.1 Definitions and Basics The material ....

N. J. Munch, "Noise Reduction In Tight Weyl-Heisenberg Frames," IEEE Transactions on Information Theory, Vol. 38, No. 2, March 1992, pp. 608--616.

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N. J. Munch. Noise reduction in tight Weyl-Heisenberg frames. IEEE Trans. Inform. Theory, 38(2):608--616, March 1992.

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N. J. Munch, "Noise Reduction In Tight Weyl-Heisenberg Frames," IEEE Transactions on Information Theory, Vol. 38, No. 2, March 1992, pp. 608--616.

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N. J. Munch, "Noise reduction in tight Weyl--Heisenberg frames," IEEE Trans. Inform. Theory, vol. 38, pp. 608--616, Mar. 1992.

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N. Munch, "Noise reduction in tight Weyl-Heisenberg frames," IEEE Trans. Info. Theory 38(2/II), pp. 608--616, 1992.

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N. J. Munch. Noise reduction in tight Weyl-Heisenberg frames. IEEE Trans. Inform. Theory, 38(2):608--616, March 1992.

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