If you want to check up on the harmonics and their relative strengths derived from full-wave rectification, check this site:

http://www.falstad.com/fourier/e-fullrect.htmlIt shows the DC value is 0.63662 times the input

2nd (desired) harmonic = 0.42442 = -7.44db

4th harmonic = 0.08489 = -21.42db

6th harmonic = 0.03638 = -28.78db

8th harmonic = 0.02021 = -33.89db

There are no odd harmonics, but the harmonics above 2nd are usually undesirable. The waveform coming into the device will behave this way if it is a pure sine wave - other waveforms may just become a fuzzy mess. The site quoted above will show what happens in fullwave rectification of a triangular sawtooth function under the "next" link on that page. In order to avoid this, it may be best to split the signal into frequency bands and rectify the signals in each band separately before recombining them.

A better way to generate an octave up would be to square it (multiply the signal linearly by itself) using the trig identity that:

cos (F) * cos (F) = 0.5 + 0.5 * cos(2F)

This has the advantage that only the second harmonic is generated. Once again, it may be best to split the signal into frequency bands and square the signals in each band separately before recombining them. Linear multiplication can be done in an MC1496 (readily available) or MC1495 (rare - I last used one in the early 1970's).