What are Leslie speaker / "rotary" style of digital audio processors doing?
I think a simple one would model:
But what (more) is there really?
I highly recommend taking a closer look on great book:
Zolzer U. - DAFX Digital Audio Effects
As well as his publication on this specific topic:
Disch S., Zolzer U. - Modulation and Delay Line Based Digital Audio Effects
Leslie (Rotary) speaker can be simulated using tremolo and Doppler effect for both change in signal amplitude and pitch.
Basic signal flow diagram that can be found in the article:
The main idea of the Leslie is the addition of rotation to the sound projector, the speaker. Therefore, from the point of view or rather, the point of audition of a listener, the sound source is being modulated both in phase as well as amplitude.
So, to simply achieve something that sounds like the Leslie speaker, you can combine a phaser and a tremolo that are driven by a sinusoidal LFO that "simulates" the rotary motion and try to tune their parameters.
But, that is not all.
A Leslie speaker is supposed to reproduce a wide spectrum of frequencies and it therefore has woofer and tweeter speakers. Consequently, it also has a crossover filter. An accurate simulator would have to include the effect of this filter on the sound.
The woofer and tweeters are projecting the sound on rotating waveguides (or the speaker itself is rotated) that operate inside a padded cabin.
Therefore, there is a varying geometry between the actual source of the sound and the ear of a listener that needs to be modeled. There are a number of parameters here: Rotating mass has inertia, therefore doesn't start and stop instantly, so there is a transient interval as the effect "comes in" and "goes out". The fact that the speakers rotate inside a cabinet means that the modulation profile is not exactly sinusoidal. The dimensions of the cabinet's openings, the waveguides, the padding of the cabinet and the rotational speed of the motor all contribute to the final result and would need to be modeled to a certain extent.
Here is a Leslie "coming in" and "going out". This video is great overall as well but also you can see many different Leslie designs, different choices would have to be modeled in a "simulator". Finally, one of the most accurately simulated Leslies comes as part of the B4. The amount of detail in that instrument overall is impressive, clicks, distortions, transients are all there (from the original) and of course, the Leslie speaker. Notice at the bottom left the "Rotator" switch as it is turned on and turned off and compare that with the effect it has on the sound.
