Thanks Steve for the link and all the information you posted in those threads.
Now I see the subject with more clarity. Several modulator versions use 17500Hz as the carrier, but the patent mentioned only 14500Hz. Is this higher frequency mentioned in other papers, or is it just a way to make the output more silent?
Regarding the FM version of the modulator you posted on the thread https://forum.audacityteam.org/t/modulate-one-waveform-track-with-another-fm-synthesis/19806/1
I have tried it and it works fine for short tracks (like 30s), but when it is longer than 2 minutes the output wave form gets very distorted. It is still possible to use it by splitting the audio track into small segments, modulate them separately using your code and the reassemble them. But this is a bit of bother for long tracks. Can this be accomplished using Nyquist code?
After some digging found this thread, which was also very useful to show me another possible solution https://forum.audacityteam.org/t/nyquist-prompts-for-am-and-fm/29418/1
Based on the code on that page I have used the following modification:
(fmosc (hz-to-step 14500) (mult 6000 (aref s 0)))
Which produced a nice looking FM output without visible waveform distortion. Perhaps you can add some improvements to this code, or just give your opinion whether this will produce any good result related to antialiasing etc. which I did not take into account. Would a band pass filter 300-6000 Hz help improve the quality of FM modulation like in case of AM?
There is a lot of effort invested in making the output “silent”, or inaudible. My opinion on this is that from the point of view of effectiveness it is necessary only to be incomprehensible to the conscious mind. This is necessary to prevent the conscious mind from blocking, criticizing, or interfering with the messages, so that the messages can reach the subconscious and influence it.
If the conscious mind would understand these messages it could reject them by judging them to be impossible, or by doubts etc, thus the subconscious mind listening to the conscious mind would also reject them. Therefore, even if some high pitch chirping is audible, it should not influence the effectiveness of the messages, as long as they are heard and understood by the subconscious. So from psychological point of view this should work, just like hypnotic suggestion do work. The only source of error may be whether the subconscious mind can really hear and understand the hidden messages or not.
The output to be completely inaudible would be an important requirement only if intended to be used on others in a covert manner. But even then a masking song could do the job.
I know it is not the subject of this forum to discuss the effectiveness of the method, but it is still interesting to find out whether this really works, and in what form. I have not tested it yet, but even if this silent subliminal prove to be inefficient, some truth still must be in that subliminal hidden in sound is effective.
For example in this article
they reveal that the KGB used subliminals modulated on white noise which could influence the subjects within short period of time. I suppose the subjects were not eager to be influenced, so the placebo effect is out of question. I wonder whether they used FM or AM on the noise…