Wavelet decomposition of harmonizable random processes
- 1 January 1993
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 39 (1) , 7-18
- https://doi.org/10.1109/18.179337
Abstract
The discrete wavelet decomposition of second-order harmonizable random processes is considered. The deterministic wavelet decomposition of a complex exponential function is examined, where its pointwise and bounded convergence to the function is proved. This result is then used for establishing the stochastic wavelet decomposition of harmonizable processes. The similarities and differences between the wavelet decompositions of general harmonizable processes and a subclass of processes having no spectral mass at zero frequency, e.g., those that are wide-sense stationary and have continuous power spectral densities, are also investigated. The relationships between the harmonization of a process and that of its wavelet decomposition are examined. Finally, certain linear operations such as addition, differentiation, and linear filtering on stochastic wavelet decompositions are considered. It is shown that certain linear operations can be performed term by term with the decompositionKeywords
This publication has 15 references indexed in Scilit:
- Wavelet analysis and synthesis of fractional Brownian motionIEEE Transactions on Information Theory, 1992
- The wavelet transform, time-frequency localization and signal analysisIEEE Transactions on Information Theory, 1990
- A Karhunen-Loeve-like expansion for 1/f processes via waveletsIEEE Transactions on Information Theory, 1990
- Regularite locale de la fonction “non-differentiable” de RiemannPublished by Springer Nature ,1990
- Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R)Transactions of the American Mathematical Society, 1989
- A theory for multiresolution signal decomposition: the wavelet representationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1989
- Multifrequency channel decompositions of images and wavelet modelsIEEE Transactions on Acoustics, Speech, and Signal Processing, 1989
- A block spin construction of ondelettes. Part I: Lemarié functionsCommunications in Mathematical Physics, 1987
- Decomposition of Hardy Functions into Square Integrable Wavelets of Constant ShapeSIAM Journal on Mathematical Analysis, 1984
- Spectral representation of a periodic nonstationary random processIEEE Transactions on Information Theory, 1971