# Phase modulation for binary data - higher frequency harmonics?

I've recently learned about PSK and QAM. I first came across it in this youtube video (timestamped), and my understanding for how it works has remained the same as what is shown in that video. (I also understand that QAM essentially "adds" amplitude modulation to PSK).

To me this all makes sense for BPSK (binary psk, only 2 states), you just do a "vertical flip" of the carrier frequency:

What I can't quite grasp however is "higher-order" PSK, because then from the various states, you can get "jumps" between them, like this:

Having explored a few areas of electronics now, the idea that a "square wave is composed by many sine waves (harmonics)" has been firmly impressed upon me:

So it would follow that those "jumps" in the modulated carrier frequency between phase changes would generate many harmonics.
This seems like it would be very undesireable because it would "polute" above parts of the spectrum, which may even be illegal.

So does PSK work differently in practice than it does in theory? Is there perhaps some mitigating factor to this that I'm not seeing? Or did I just get it wrong from the start? Thank you.

• Clearly you've been to the wiki site. Did you look at SOQPSK? Feb 19 at 13:56
• @periblepsis Not until I read your comment, no. I was having a hard time understanding OQPSK so I hadn't gotten that far. And since there were so many other variants I figured the more general answer wouldn't lay in a specific one of those. But thank you, I would probably only get to it much later on if you hadn't mentioned. Feb 19 at 14:38
• The points made here already tell a story. But SOQPSK just makes sense, too. Give it a moment of consideration. Feb 19 at 14:41

You are correct. The jumps in QPSK do generate high frequency spurious signals, as do the changes of slope that you've shown in BPSK.

The solution is that the signal from a modulator like that is never simply amplified and sent directly to the antenna. it is always bandpass filtered first, to reduce the splatter into adjacent frequency bands.

The specification of filters that can preserve modulation accuracy, while controlling spurious emissions, is a subject in its own right. Often the modulation is specified to use a specific filter.

A very common filter is the Root Raised Cosine filter. A receiver needs a filter as well, to keep adjacent signals and nearby noise out of the demodulator. The same response filter is used on both transmitter and receiver. Their product as seen by the whole channel from modulator to demodulator is a Raised Cosine response, which can be made to have zero intersymbol interference, when its width is chosen correctly for the data rate.

• What problems are caused by the slope changes? With CNCs and 3D printers people limit jerk to avoid unwanted vibrations so I imagine it's analogous, but I don't see how exactly that would apply to electronics. Feb 19 at 14:33
• @TrisT sorry, changing language unnecessarily. Discontinuities in dv/dt cause harmonics just as discontinuities in v do, albeit of less magnitude. Feb 19 at 15:54

Is there perhaps some mitigating factor to this that I'm not seeing?

It's the same with normal modulation like AM or FM; you don't need to take it to a level that is more complicated to see that a square wave modulating a sinewave carrier will produce massive disruptive harmonics. So, what we do is band limit the square wave so that the harmonics caused by the modulation are reasonable and under control. Then we band-pass filter the output and, if necessary we filter even harder.

We may even consider extending a data bit by a small amount to ensure that it "changes" the carrier as it passes through a more benign region like 0 volts. We do what we have to in order to keep down the harmonics in the transmitted signal.

• Thank you for your answer, I accepted Neil's as the answer, but if I could do both I would. The 0v was incredibly insightful. About your first statement, would an abrupt change in frequency cause harmonics as well (provided the voltage didn't instantly change along with it)? Feb 19 at 14:31
• I don't think I understand your supplementary question i.e. an abrupt change in frequency must be matched by an equally abrupt change in voltage. Feb 19 at 14:42
• If frequency B starts at the same voltage frequency A ended, would it? desmos example Feb 19 at 15:00
• Yes it will cause harmonics. Feb 19 at 15:11