A Unified Transform for LTI Systems--Presented as a (Generalized) Frame

We present a set of functions in L2([0,8)) and show it to be a (tight) generalized frame (as presented by G. Kaiser (1994)). The analysis side of the frame operation is called the continuous unified transform. We show that some of the well-known transforms (such as Laplace, Laguerre, Kautz, and Hambo) result by creating different sampling...