How are discontinuities in quadrature modulated signal QAM physically produced?

In quadrature modulated signals, for instance:

I am unclear how the "discontinuities" in the waveform at the junction of each data point can be physically produced?

Taking a speaker as an example, how is it possible to produce this "discontinuity" in the sound wave by using the speaker cone's mechanism?

I am unclear how the "discontinuities" in the waveform at the junction of each data point can be physically produced?

They can't, exactly. In the real world you may come close, but everything is a low-pass process, so even if you "order" the electronics or whatever to make a sharp discontinuity, the actual generated waveform will be continuous, with a "sharpness" dependent on bandwidth.

The way you approach this, in 2022, is to generate the waveform digitally and then apply it to a digital to analog converter. The way you would have approached this in 1975 would have been to generate a sine wave in analog circuitry that had inphase and quadrature components available, then, depending on the code, switch in the inphase, quadrature, negative inphase, or negative quadrature.

Note: in actual practice you want to bandpass filter this, but there's a science to getting that filtering right. For now, concentrate on understanding the theory; when you're ready you can start learning about proper filtering.

Taking a speaker as an example, how is it possible to produce this "discontinuity" in the sound wave by using the speaker cone's mechanism?

Use the highest bandwidth speaker you can, and feed it with the highest-bandwidth version of the QAM signal that you can. Or, bandpass filter the signal properly, and feed it to the (ultimately, much happier) speaker.

• thank you, that clears things up for me! As for decoding analog QAM wave signal back to digital, after we ascertain the precise cutoff points for each signal symbol, could we then pass this through 4 parallel channels each chanting repeatedly the symbol patterns for each of 00, 01, 10, 11... and pick the highest amplified output as the decoded "answer" to this particular wave slice? Oct 14, 2022 at 17:45
• Not sure what you mean by "chanting repeatedly...". I suggest you dig around on the Internet for a while to see if you can find an article on decoding QAM -- or find a good book on communications systems. Then if there's something you don't understand, ask another question to clarify. Oct 14, 2022 at 18:01
• thank you. I found youtube.com/watch?v=xxWVaU1Vkg4 which shows the software steps for decoding QAM signals. Oct 14, 2022 at 18:17
• In practice, instead of rectangular pulse shapes, we use root-raised cosine half-sin type filters which are of no discontinuous behaviour in time domain Dec 7, 2022 at 17:58