Construction of orthogonal matrices from orthogonal polynomials

Question

Let $\{P_n\}_{0\le n\le N}$ be the family of orthogonal polynomials associated with the following inner product: $$ \langle f, g \rangle_{1} = \sum_{k=0}^{N}{f(k)g(k)w_1(k)} $$ where $ w_1(\cdot)$ is the weight function and $N$ is a non-negative integer. Then, we can construct an orthogonal matrix $A = (a_{ij})_{0 \leq i, j \leq N}$ defined by $$ a_{ij} = P_i(j)\sqrt{\frac{w(j)}{\|P_i\|_1^2}}\qquad \text{and} \qquad -1 \leq a_{ij} \leq 1 $$ Now, consider the following inner product: $$ \langle f, g \rangle_{2} =\langle f, g \rangle_{1} + \sum_{k=0}^{N}{f'(k)g'(k)w_2(k)} $$ where $w_2(\cdot)$ is the weight function and $f'$ denotes the derivative of $f$. Let $\{Q_n\}_{n}$ be a family of orthogonal polynomials associated with $\langle . \rangle_2$. My problem is how can I construct an orthogonal matrix $B=(b_{ij})_{0\le i,j\le N}$ such that $ -1 \leq b_{ij} \leq 1$.