## Appendix A: Construction of polynomial transforms

Let , denote a set of polynomials, which satisfies the orthogonality condition:

 (20)

It is known that as polynomials, can be expressed

 (21)

denotes polynomial coefficients. It is natural that can be expressed based on superposition of different polynomials:

 (22)

Based on equations 22 and 23, th polynomial can be expressed as lower-order polynomials

 (23)

Get squares of equation 22 and combine with equation 20, we can obtain

 (24)

and

 (25)

From equations 23 to 25, we can construct the set of polynomials. We first get based on equation 24, and thus , then compute , to construct . In the same way, we can construct all polynomials.

2020-03-27