Transfer Functions with Multiple Terms

If the transfer function has multiple terms, then the output will be the sum of the contributions of each term.

For example, the transfer function

$$F(x) = x + x^2 + x^3 + x^4 + x^5$$

produces an output spectrum with the following harmonic amplitudes:

$$h_0 = \frac{1}{2}(2) + \frac{1}{8}(6) = 1.75$$

$$h_1 = 1 + \frac{1}{4}(3) + \frac{1}{16}(10) = 2.375$$

$$h_2 = \frac{1}{2}(1) + \frac{1}{8}(4) = 1.0$$

$$h_3 = \frac{1}{4}(1) + \frac{1}{16}(5) = 0.5625$$

$$h_4 = \frac{1}{8}(1) = 0.125$$

$$h_5 = \frac{1}{16}(1) = 0.0625$$

Figure 10: Output spectrum of the transfer function $y = x+x^2+x^3+x^4+x^5$, where $x$ is a unit amplitude sinusoid at a frequency of 220 Hz.