# Constellation diagram of FSK

I am learning digital modulation basics and I have question about frequency shift keying — how the constellation diagram of M-ary FSK looks like? I can somehow figure how binary FSK diagram looks (it is similar to PSK), but I cannot imagine M-ary FSK diagram.

EDIT: And ome more question. Do you know any nice applet/online-tool where I can play with different modulations and their parameters?

• What do you mean play with different modulations and their parameters? Do you want to be able to adjust these and see different constellations or do you want to see things like data rates, bit error rates, etc? Commented Nov 22, 2011 at 17:19
• I’d like to adjust parameters of different (digital) modulations and see their constellation, output signal, etc. Commented Nov 22, 2011 at 17:23
• I am not sure of any web applet that will do that. I would be interested to know if anyone else knows though. Commented Nov 22, 2011 at 17:55

FSK is difficult to visualize as you increase in order. The reason for this is when you are using FSK, you have orthogonal frequencies that essentially add an extra dimension to your plane. You can visualize up to 3d (3 frequencies) as shown below (pardon the hand paint drawing), but once you get greater then that FSK just can't be represented this way. However, just because we aren't able to plot it on a graph, the matrix math still applies equally the same, just with added dimensions.

• Thank you for good answer. In your picture, I not sure if I understand what are these [0,1,1], [1,1,0], [1,1,1] and [1,0,1] symbols? You wrote every frequency add an extra dimension. So very symbol should be right on axes, with the same amplitude and phase. Am I right? Commented Nov 23, 2011 at 16:24
• The [0,1,1] is there to help show what frequencies are on vs off. It follows [f1,f2,f3], so the [0,1,1] dot is f1 has no energy buy f2 and f3 have 1 unit of energy. Your FSK scheme could then interpret that to mean any symbol you want. If you go to a 4 frequency FSK, you are no longer able to visualize it since it falls into a 4d plane that can't be drawn. Commented Nov 23, 2011 at 17:14
• Is this analogous to the I/Q constellations usually used for PSK and whatnot? If I'm understanding correctly, the [1,0,0] point represents one frequency being present, and the [0,1,0] represents some other frequency being present. But were this an I/Q constellation diagram, those two points would represent the same frequency, but with a 90 degree phase shift. Commented Apr 26, 2016 at 13:16
• This is a strange answer. The question is about M-ary FSK, in which a single carrier is shifted to one of several different frequencies, but the answer appears to be talking about multi-carrier system in which multiple frequencies are turned on or off (amplitude modulated) independently. I wonder why it was accepted so readily. Commented Apr 26, 2016 at 13:53

In terms of an I/Q constellation diagram (i.e. a phasor or real/imaginary diagram), any frequency deviation from the center frequency would result in the IQ vector rotating around in a circle, with the speed of rotation being proportional to the frequency deviation. Essentially, the phase offset relative to your carrier/local oscillator would be continuously changing (because two waves of slightly different frequencies drift out of phase over time). The amplitude would be constant throughout this.

So, FSK would simply modulate the speed of the IQ vector's rotation. For 4-FSK, there would be four distinct speeds of rotation that you would observe over time.

This article has a good visualization of this near the bottom, under FM-modulation in IQ (this is essentially 2FSK):

Also, for a demonstration of why frequency offsets result in rotating phasors, check out this great video by w2aew.