On the evaluation of double square integral in the (s1, s2) complex biplane

In this correspondence, a method of evaluating the double square integral
\int\min{0}\max{\infin}\int\min{0}\max{\infin} [h(t_{1}, t_{2})]^{2} dt_{1} dt_{2}
= \frac{1}{(2\pij)^{2}} \int\min{-j\infin}\max{j\infin}\int\min{-j\infin}\max{j\infin} H(-s_{1}, -s_{2}) ds_{1} ds_{2}
where
h(t_{1}, t_{2}) = L^{-1} [H(s_{1}, s_{2})]
is discussed. The method of evaluation is based on using the double bilinear transformation (DBT)
s_{k} = (1 - z_{k})/(1 + z_{k}), k = 1, 2
to reduce the above complex integral to a double integral in the complex (
z_{1}, z_{2}
) bidisk,
\sum\min{m=0}\max{\infin}\sum\min{n=0}\max{\infin}[a(m, n)]^{2} =\frac{1}{(2\pij)^{2}} \oint\min{|z1| = 1} \oint\min{|z2| = 1} A(z_{1}, z_{2})
\cdot A(Z_{1}^{-1}, Z_{2}^{-1}) \frac{dz_{1}}{z_{1}}\frac{dz_{1}}{z_{2}}
. There exist several methods for evaluating the above double integral. In this correspondence, we mention one promising method. Also, a matrix method is proposed for applying the "DBT" to a quotient of two-dimensional (2-D) polynomials.