Controlling the spectrum

• A waveshaper with a linear transfer function will not produce distortion, but any deviation from a line will introduce some sort of distortion and change the spectrum of the input.

• To control the maximum harmonic in the spectrum (say, for the purpose of avoiding aliasing), a transfer function is expressed as a polynomial:
  $$F(x) = d_0 + d_1x + d_2x^2 + ... + d_Nx^N$$
  where the order of the polynomial is $N$, and $d_i$ are the polynomial coefficients.

• When driven with a sinusoid, a waveshaper with a transfer function of order $N$ produces no harmonics above the $N^{th}$ harmonic.

• When the driving sinusoid is of unit amplitude, the amplitudes of the various harmonics can be calculated using the right side of Pascal's triangle.