Published May 19, 2017
| Version v1
Publication
The convolution theorem for the continuous wavelet tranform
Contributors
Description
We study the application of the continuous wavelet transform to perform signal 1ltering processes. We 1rst 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 e5ect of multiplying the continuous wavelet transform of a given
signal by a related transfer function and show how to perform spatially variant 1ltering 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.
Additional details
Identifiers
- URL
- https://idus.us.es/handle/11441/60082
- URN
- urn:oai:idus.us.es:11441/60082