Phase Generation

The following schemes are used to generate tone phases of multitone signals:

• Varying the phase difference between adjacent frequency tones linearly from 0 to 360 degrees
• Varying the tone phases randomly

Varying the phase difference between adjacent frequency tones linearly from 0 to 360 degrees allows the creation of multitone signals with very low crest factors. However, the resulting multitone signals have the following potentially negative characteristics:

• The multitone signal is very sensitive to phase distortion. If in the course of generating the multitone signal the hardware or signal path induces non-linear phase distortion, the crest factor might vary considerably.
• The multitone signal might display some repetitive time-domain characteristics, as shown in the multitone signal in the following figure.

The signal in the previous figure resembles a chirp signal in that its frequency appears to decrease from left to right. The apparent decrease in frequency from left to right is characteristic of multitone signals generated by linearly varying the phase difference between adjacent frequency tones. You might want a signal that is more noise-like than the signal in the previous figure.

Varying the tone phases randomly results in a multitone signal whose amplitudes are nearly Gaussian in distribution as the number of tones increases. The following figure shows a signal created by varying the tone phases randomly.

In addition to being more noise-like, the signal in the previous figure also is much less sensitive to phase distortion. Multitone signals with the sort of phase relationship shown in the previous figure generally achieve a crest factor between 10 dB and 11 dB.