The notion of "Intermediate frequency". Conversion of a given frequency to an "intermediate frequency". Frequency translation.

Let us consider the case of a satellite dish receiving a TV signal from a satellite at 11.75 GHz. You cannot use an inexpensive coaxial cable to bring this microwave frequency into the building but instead you would need what is called a "waveguide". Also as mentioned at https://en.wikipedia.org/wiki/Intermediate_frequency, "at very high (gigahertz) frequencies, signal processing circuitry performs poorly. Active devices such as transistors cannot deliver much amplification (gain). Ordinary circuits using capacitors and inductors must be replaced with cumbersome high frequency techniques"

For these reasons, it is necessary to convert a given frequency to a different frequency, an "intermediate frequency" as it is called. For satellite TV the intermediate frequency used is in the range of 950 - 2150 MHz.

The AM radio band is from 535 to 1605 kHz. In other words, the Amplitude Modulated (AM radio) carrier frequencies are in the frequency range 535-1605 kHz. (Note: carrier frequencies of 540 to 1600 kHz are assigned at 10 kHz intervals.) The FM radio band is from 88 to 108 MHz.

The intermediate frequency used in AM radio is 455 kHz. For FM radio it is 10.7 MHz.

Luxembourg effect: Cross-modulation in the ionosphere | Citizen science at HAARP

When one AM radio station wave modulates another in the ionosphere. Mixing of two AM station waves in the ionosphere (in the same volume of plasma).
Experimental demonstration with HAARP. When HAARP broadcasts music in AM.

Dr. Chris Fallen presents theoretically the Luxembourg effect at his presentation https://livestream.com/internetsociety/hope/videos/178070432 at 23min55s (3min talk until 26min29s)
Slide title: "Radio Luxembourg, the first high-power radio modification of the ionosphere"
Reference: Tellegen, B.D.H (1933) "Interaction between Radio-Waves?" Nature 131(840)

How to design such an experiment with HARPP?
Have half the array transmit one radio frequency (or radio broadcast) and the other half transmit another. (We refer to two different channels.)
This is equivalent to having two powerful radio-transmitters. The two frequencies will mix in the ionosphere. Approximately equal mixing at each channel.

Dr. Fallen refers to the experimental demonstration of the Luxembourg effect with HAARP at 42min55s.

1) First audio frequency reproduction of the Luxembourg effect with HAARP (time point: 47min00s) was in 2014. He chose telephone touch tones (DTMF tones) familiar to most. He had written code for wav file generation for a programming teaching course. HAAPR's AM mode could be defined by wav files. This actually makes HAARP like a big radio that can be used "to transmit your play list" with Gigawatts of power.

2) Art students composed two pieces of abstract jazz music for a Luxembourg effect demonstration.

3) In collaboration with Jeff Dumps (KL4IU) he broadcasted a childrens's song "row, row, row your boat" (48min36s)

Dr. Fallen said that amateur radio operator had paid for the experiment with a credit card and that HAARP accepts all major credit cards!

4) Reproduction of the Luxembourg effect with HAARP in 2017. Tweet by @ctfallen on 2018-12-10 https://twitter.com/ctfallen/status/1072103474668728321
Description:
Frequency 1 (F1) is tunded to 2800 KHz in AM mode
Frequency 2 (F2) is tuned to 3300 KHz in AM mode
F1 is at the left audio channel and F2 at the right audio channel.
Use headphones. You hear an F1 tone on the left audio channel followed by an F2 tone on the right audio channel in a sequence.

The protocol has the steps described below. The first, third and fourth have a duration of one minute exactly. The second is 30 seconds.

2min21 Simultaneous tones on each frequency
3min21 No modulation on either frequency
3min51 Continuous tones on each frequency
4min51 Unmodulated CW on each frequency (Term "CW" here means "Continuous Wave")
5min21 Music transmitted in each frequency
6min51 Idem
8min21 Idem - "Note that 3300 KHz appears to have intentional off times in carrier and audio"
9min25 Unmodulated carrier, both frequencies
Followed by 'both frequencies off' and repetition of the set

(Radiofrequency) Mixing - Heterodyning - Non-linear combination

Generation of new frequencies at sum or difference of original ones - Represented mathematically with wave multiplication

What is the result of applying two different voltages (cf. waveforms) on a non-linear electrical circuit element like a diode?

“RF mixing is not like audio mixing where several signals are added together in a linear fashion to give several sounds together. Radio frequency, or RF mixing is a non-linear process that involves the instantaneous level of one signal affecting the level of the other at the output.”

“It is found that if two signals are passed through a non-linear circuit, then additional signals on new frequencies are formed. These appear at frequencies equal to the sum and difference frequencies of the original signals. In other words if signals at frequencies of f1 and f2 enter the mixer, then additional signals at frequencies of (f1+f2) and (f1-f2) will also be seen at the output.”

(1) “If two signals, one at a frequency of 5 MHz and another at a frequency of 6 MHz are mixed together then new signals at frequencies of 11 MHz and 1 MHz are generated.”

“RF mixer mathematics: It is possible to easily represent the action of an RF mixer mathematically. The two input waveforms are represented by simple sine waves, and these are multiplied together.” (cf image of post)

(2) RF Mixer applications: “They are used in circuits from radio receivers and transmitters to radar systems”

"Frequency translation:  The most obvious application for RF mixers is for frequency translation. This technique is used in many areas and in particular in receivers and transmitters to move the frequency of a signal from one band to another."