Continuous and discrete wavelet transforms
SIAM Review
A friendly guide to wavelets
Filtering and deconvolution by the wavelet transform
Signal Processing
Digital image processing
Joint time-frequency analysis: methods and applications
Joint time-frequency analysis: methods and applications
Behaviour of image degradation model in multiresolution
Signal Processing
Continuous wavelet transform with arbitrary scales and O(N) complexity
Signal Processing
Multiscale Kalman Filtering of Fractal Signals Using Wavelet Transform
WAA '01 Proceedings of the Second International Conference on Wavelet Analysis and Its Applications
Speech Signal Deconvolution Using Wavelet Filter Banks
WAA '01 Proceedings of the Second International Conference on Wavelet Analysis and Its Applications
Fast continuous wavelet transform
ICASSP '95 Proceedings of the Acoustics, Speech, and Signal Processing, 1995. on International Conference - Volume 02
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Eigentransformation-based face super-resolution in the wavelet domain
Pattern Recognition Letters
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We study the application of the continuous wavelet transform to perform signal filtering processes. We first show that the convolution and correlation of two wavelet functions satisfy the required admissibility and regularity conditions. By using these new wavelet functions to analyze both convolutions and correlations, respectively, we derive convolution and correlation theorems for the continuous wavelet transform and show them to be similar to that of other joint spatial/spatial-frequency or time/frequency representations. We then investigate the effect of multiplying the continuous wavelet transform of a given signal by a related transfer function and show how to perform spatially variant filtering operations in the wavelet domain. Finally, we present numerical examples showing the usefulness of applying the convolution theorem for the continuous wavelet transform to perform signal restoration in the presence of additive noise.