Example of Spectral Matching

Given the following spectrum, what would be the transfer function?

Figure 11: A steady state spectrum.

The spectrum contains the first, second, fourth, and fifth harmonics, with amplitudes 5, 1, 4, 3, respectively.

The transfer function is given by

$$F(x) = 5T_1(x) + T_2(x) + 4T_4(x) + 3T_5(x)$$

$$= 5x + (2x^2 - 1) + 4(8x^4-8x^2 + 1)$$

$$+ 3(16x^5 - 20x^3 + 5x)$$

$$= 48x^5 + 32x^4 - 60x^3 -30x^2+20x+3.$$

Figure 12: The steady state plotted in Matlab.