Further details on the frequency shifter all-pass filter network:

If one was only dealing with two (sine) frequencies it would be possible to use a single all-pass filter and adjust the cutoff point accordingly. However given that ring modulation typically produces multiple frequencies (especially when applied to a complex input signal) a network of filters is needed to cover the entire audible frequency range.

My first searches on the web brought me across Hordijk’s Frequency Shifting patch for the Nord G2 Modular, as well as Jürgen Haible’s descriptions and schematic drawings which filled in a little more detail on the Hilbert transform filter network. Fortunately I also came across an article on Analog Wide Band Audio Phase Shift Networks with a diagram (see fig. 4) and a table of frequencies that I could use as a point of departure.

Via Don Tillman’s collection of Moog Patents I could download a PDF of the Bode Frequency Shifter that Moog produced in the early 70s. That helped fill in the final pieces of the puzzle, showing how the sine/cosine oscillator (which I’d already encountered in Hordijk’s Harmonic Oscillator) connects up with the Hilbert filter network (or ‘Dome Filter’ in Moog parlance) to enable the ring modulation and phase cancellations.

I’ve uploaded a few demos to the Audulus Forum.

Here’s my first take at putting together a Frequency Shifter in Audulus. Once again, one of Rob Hordijk’s NOVARS tutorials has provided the inspiration and point of departure.

Hordijk describes the frequency shifter as kind of luxury ring modulator – with the added feature that it’s possible to split the upper and lower sidebands and achieve some special transformations through that. In essence it’s a ring modulator and an all-pass filter network, with the filters making it possible to remove one of the sidebands through phase cancellations.

The all-pass filter is something that Hordijk covers succinctly in his video on the Physics of Sound, and I’d already made one on the basis of his description while putting together an Audulus version of his Dual Phaser. While Hordijk provides a good explanation of the principles behind the frequency shifter and a thorough demonstration of his own module, I needed to do a little detective work before I could figure out what was going on with the filter network.