Talk:Phase modulation

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Contents 1 Headline text 2 Comparing AM and FM 3 ... 4 What does PM look like?

[edit] Headline text

[edit] Comparing AM and FM

hey what is difference between amplitude modulation and frequency modulation

[edit] ...

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)

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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

[edit] 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)