Celebratio Mathematica — Daubechies

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R. Balan, I. Daubechies, and V. Vaishampayan: “The analysis and design of windowed Fourier frame based multiple description source coding schemes,” IEEE Trans. Inform. Theory 46 : 7 (2000), pp. 2491–2536. MR 1806816 Zbl 0998.94011 article

In this paper the windowed Fourier encoding-decoding scheme applied to the multiple description compression problem is analyzed. In the general case, four window functions are needed to define the encoder and decoder, although this number can be reduced to three or two by using time-shift or frequency-shift division schemes. The encoding coefficients are next divided into two groups according to the eveness of either the modulation or translation index. The distortion on each channel is analyzed using the Zak transform. For the optimal windows, explicit representation formulas are obtained and nonlocalization results are proved. Asymptotic formulas of the total distortion and transmission rate are established and the redundancy is shown to trade off between these two.

Radu Victor Balan	Related
Vinay A. Vaishampayan	Related

R. Balan and I. Daubechies: “Optimal stochastic encoding and approximation schemes using Weyl–Heisenberg sets,” Chapter 11, pp. 259–320 in Advances in Gabor analysis. Edited by H. G. Feichtinger and T. Strohmer. Applied and Numerical Harmonic Analysis. Birkhäuser (Boston), 2003. MR 1955939 Zbl 1033.94001 incollection

Thomas Strohmer	Related
Radu Victor Balan	Related
Hans Georg Feichtinger	Related