An Analytical Pascal Matrix Transform for$s$-to-$z$Domain Transfer Functions

An analytical Pascal matrix transform is proposed for conversions of transfer functions between
$s$
- and
$z$
-domains. The transform is formulated uniformly for first-order
$s$
-to-
$z$
transforms, and its Pascal matrix is derived logically and analytically. The inverse transform is then formed in terms of its forward transform matrices without computing the matrix inverses. Computation examples show that the presented Pascal matrix transform works simply and efficiently.