Lindsey and Suter have shown that for many transforms the transform of the convolution of two functions have the same functional form. We explain the origin of this result and derive the condition on the transformation kernel for when this should be the case. In addition we consider the general transform of the inverse and direct scale transform and obtain condition on the kernel so that the transform gives similar functional forms.

Date Published: 4 December 2000
PDF: 4 pages
Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408626

Published in SPIE Proceedings Vol. 4119:
Wavelet Applications in Signal and Image Processing VIII
Akram Aldroubi; Andrew F. Laine; Michael A. Unser, Editor(s)