We present the windowed Fourier transform and wavelet transform as tools for analyzing persistent signals, such as bounded power signals and almost periodic functions. We establish the analogous Parseval-type identities. We consider discretized versions of these transforms and construct generalized
Wavelet Transform of Periodic Generalized Functions
β Scribed by A.I. Zayed
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 657 KB
- Volume
- 183
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
We investigate expansions of periodic functions with respect to wavelet bases. Direct and inverse theorems for wavelet approximation in C and L p norms are proved. For the functions possessing local regularity we study the rate of pointwise convergence of wavelet Fourier series. We also define and i
## Communicated by C. Benzaken It is shown that, for a function A from (0, 1)" to (0, 1)" whose components form PI symmetric set of threshold functions the repeated application of A, leads either to a fixed point or to a cycle of length two.
In this paper, we investigate a class of nonstationary, orthogonal periodic scaling functions and wavelets generated by continuously differentiable periodic functions with positive Fourier coefficients; such functions are termed periodic basis functions. For this class of wavelets, the decomposition