  In this paper, the generic uncertainty relation (UR) for kernel-based
transformations (KT) of signals is derived. Instead of using the statistics
approach as shown in the literature before, here we employ quantum mechanical
operator approach for directly deriving the UR for KT's. We are able to do this
because we have found the quantum operator realization of KT. Our new method is
concise and applicable to any kinds of KT's with continuous and discrete
parameters and variables. An explicit result of UR for a family of KT's
including FrFT, generalized fractional transformation (GFrT) and linear
canonical transformation (LCT) is provided as an application of our new method.
