Methods, apparatus, systems, and articles of manufacture to implement a third-order signal scrambler are disclosed. An example apparatus includes a controlled scramble generator to generate a controlled random sequence based on one or more subcarriers and a random pulse sequence, the random pulse sequence based on an output of a random number generator processed by a multi-order sinusoidal noise function. The example apparatus further includes a sequence modifier to form an output sequence by combining a source sequence with the controlled random sequence, the controlled random sequence to modify a characteristic of the source sequence in a frequency domain.