# Talk:Phase modulation

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## Old 2005 Q&A

yeah... and can someone create a graphic how phase modulation actually looks like?! I have no clue by the information this article gives me.

thanks, --Abdull 22:08, 17 Jan 2005 (UTC)

Hi!

Let w1, w2 be the frequencies of two oscillators and t be the time. Then for a system where the first oscillator is modulated by the second, you could write phase-modulation as:

``` out[t] = cos(w1 * t + cos(w2 * t));
```

... whereas frequency-modulation would be:

``` out[t] = cos( (w1 + cos(w2 * t)) * t);
```

The famous DX7 and many other socalled FM-synths are all of the phase-modulating kind. The difference shows up for instance when you implement feedback loops:

``` out[t] = cos(w * t + out[t-1]);    // phase-modulated
```
``` out[t] = cos((w + out[t-1]) * t);  // frequency-modulated
```

It should be obvious that letting w == 1, will force the frequency-modulated variety to a full stop when out == -1 (that is to say when cos is passing thru its most negative value.) Phase-modulation will instead continue to oscillate at the desired frequency, because the intermediate result of w * t is never affected by the previous output.

Another even simpler example to show the difference between phase- and frequency modulation would be letting w1 == 1 and w2 == 0. The value of cos(w2 * t) will now always be == 1, which gives us:

``` out[t] = cos(1 * t + 1);    // phase-modulated
```
``` out[t] = cos((1 + 1) * t);  // frequency-modulatede
```

We see here that the frequency-modulated variety will double its frequency, whereas the phase-modulated variety will shift the phase (and then run stable at the desired frequency).

In order to also let the phase-modulated variety double its frequency, we would have to find a function f() such that cos(f()) == t. It might exist, but can by definition only be valid for values of t between 1 and -1.

So to answer Abdulls question: You already know what phase-modulation looks like. For historical reasons (and a programming error) it is well documented disguised as its cousin frequency-modulation. What we need is instead documentation on what frequency-modulation would look like, since it is clearly different.

mvh // Jens M Andreasen

Jens: if you were recommending that information should be added, then please add it - else we should remove it from the discussion page as it did not inspire any discussion! haha
Any one agree? daviddoria (talk) 13:51, 2 October 2008 (UTC)

## What does PM look like?

Picture represents frequency modulation! If there is no suitable image, then it's better to remove it rather to show a wrong one. Don't disinform people.

Nah, the current picture (as of jan 2006) is correct. The carrier slows down when the modulator is in a downward slope. FM would have the carrier slow down when the modulator is near minimum, regardless of direction.
MX44
I am persuaded that MX44 is right. However the depth of phase modulation shown in the picture is great (fast) enough to defeat whole cycles of the carrier, which raises the question of how can one recover (demodulate) the original signal?Cuddlyable3 01:36, 18 February 2007 (UTC)

## Phase modulation is not widely used for transmitting radio waves

This might have been true in the 1959's. Today it's the other way around. PM (in the form of QAM) is used everywhere. Cellphones, satellite communication, xDSL modems, etc. FM is only used for analog broadcasting and some legacy data communication devices. 194.237.220.107 (talk) 06:53, 17 October 2013 (UTC)

I have fixed it...

## Illustrations

The text of the article describes two main applications: data communication and music synthesis. But there are no illustrations for either application.

I could generate graphs for the functions in the text, but I don't know enough about the sort of inputs that would be used to generate graphs that illustrate real usage.

Does anyone have the knowledge and time to add such illustrations? Or the knowledge to add enough text to describe the wave functions as they'd actually be used? — Steve98052 (talk) 06:58, 19 May 2016 (UTC)

Hello. I've made an animation for Phase Modulation. Though it (the animation) has no direct connection to data communication nor music synthesis, I believe it illustrates PM well enough. Potasmic (talk) 21:47, 3 August 2016 (UTC)

That's a nice animation, and as you say, it appears to illustrate phase modulation effectively. It might still be nice to see illustrations that apply to communications and music, but those might be more appropriate to include in articles about those specific applications. Nice work. — Steve98052 (talk) 00:49, 14 June 2017 (UTC)

Hm... Now that I look at it, the animation generalizes to PM of sine waves... Obviously, I could just throw in some other signals and shows how you'd encode data.. I'll think more about this... Ultimately, you'd want something that shows Phase Modulation in general, not just for sine waves. I am currently having another idea to illustrate PM, but this time it'll only work for sine waves... If you could link me to some resource on how things are encoded using PM, I could update the animation. E.g., what kind of signal is it? Is it pulses? Potasmic (talk) 03:13, 16 June 2017 (UTC)

I don't know enough about the subject either; that's one of the reasons I thought an illustration might be useful. But I know that music synthesizers use waves other than sine waves (which have a plain, pure sound), such as triangle waves (which sound a bit more brassy) and square waves (which have a more buzzy sound, though that varies with pitch). With luck, maybe another editor will have more insight. — Steve98052 (talk) 07:14, 23 June 2017 (UTC)