Matching a Spectrum Using Chebyshev Polynomials

A spectrum containing several harmonics can be matched by combining the appropriate Chebyshev polynomial for each harmonic into a single transfer function.

Let $h_j$ be the amplitude of the $j^{\mbox{th}}$ harmonic, and $N$ be the highest harmonic in the spectrum. The transfer function is then given by:

$$F(x) = h_0T_0(x) + h_1T_1(x) + h_2T_2(x) + \cdots + h_NT_N(x).$$