Le traitement du signal et l'analyse mathématique
Annales de l'Institut Fourier, Volume 50 (2000) no. 2, p. 593-632

The interaction between signal processing and functional analysis is discussed on some relevant examples.

Nous étudons sur des exemples significatifs l’intersection entre le traitement du signal et l’analyse fonctionnelle.

@article{AIF_2000__50_2_593_0,
     author = {Meyer, Yves},
     title = {Le traitement du signal et l'analyse math\'ematique},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {50},
     number = {2},
     year = {2000},
     pages = {593-632},
     doi = {10.5802/aif.1766},
     zbl = {0986.42016},
     mrnumber = {2001m:94013},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2000__50_2_593_0}
}
Meyer, Yves. Le traitement du signal et l'analyse mathématique. Annales de l'Institut Fourier, Volume 50 (2000) no. 2, pp. 593-632. doi : 10.5802/aif.1766. http://www.numdam.org/item/AIF_2000__50_2_593_0/

[1] A. Cohen, R. Ryan, Wavelets and multiscale signal processing., Appl. Math & Math. Comp., Chapman & Hall ed., 11 (1995). | MR 97k:42048 | Zbl 0848.42021

[2] I. Daubechies, Ten lectures on wavelets, SIAM, Philadelphia, 1992. | MR 93e:42045 | Zbl 0776.42018

[3] S. Mallat, A wavelet tour of signal processing, Academic Press, 1988. | Zbl 0937.94001

[4] M. Vetterli, J. Kovacevic, Wavelets and subband coding, Prentice Hall PTR, Englewood Cliffs, NJ 07632, 1995. | Zbl 0885.94002

[5] Y. Meyer, Wavelets and operators, Vol. 1,2 and 3, Cambridge University Press, 1992. | Zbl 0776.42019

[6] H.J. Landau, Sampling, data transmission and the Nyquist rate, Proceedings of the IEEE, vol. 55, 10 (1967).

[7] J. Gerver, The differentiability of the Riemann's function at certain rational multiples of π, Amer. J. Math., 92 (1970), 33-35 et 93 (1971), 33-41. | MR 42 #434 | Zbl 0203.05904

[8] M. Holschneider, Ph. Tchamitchian, Pointwise analysis of Riemann's ‘non differentiable’ function, Inventiones Mathematicae, 105 (1991), 157-176. | Zbl 0741.26004

[9] S. Itatsu, Differentiability of Riemann's function, Proc. Japan Acad., Ser. A. Math. Sci, 57, vol. 10 (1981), 492-495. | MR 83e:42006 | Zbl 0501.26004

[10] S. Jaffard, The spectrum of singularities of the Riemann's function, Rev. Math. Iberoamericana, 12 (1996), 441-490. | MR 97g:26006 | Zbl 0889.26005

[11] S. Jaffard, Y. Meyer, Wavelets methods for pointwise regularity and local oscillations of functions, Memoirs of the AMS, 123 (1996). | Zbl 0873.42019