In-place transformation of generalized and complex spectra through algebraic decision diagrams

This paper presents an extension of the symbolic computational technique for the calculation of both real and complex valued generalized multi-polarity transforms. The new formulation uses the standard Kronecker products of the elementary polarity 0 and 1 matrices, to efficiently generate the algebraic decision diagrams (ADDs) of the spectra for various generalized transforms. To further exploit the power of symbolic algorithms, a new operator on matrices called the pseudo Kronecker product is introduced. It is shown that the in place recursive paradigm can be elegantly expressed as an iterative if-then-else construct on the ADD. By means of the if-then-else constructs of this new operator, many spectra which could not be calculated previously by efficient symbolic algorithms due to the lack of recursive standard Kronecker product representations for their transformation, have now become attainable.