The red diagram is called a lissajous and all the changes are in the X direction (time). I use these functions all the time in motion control. Our products are defined by perfect lissajous!
Salute the Lissajous!
I've always known a Lissajous curve as graphing the phase relationship between two different sines, like on an analog oscilloscope. But never mind that, we'll just confuse people even more if we get into that. And I plan on confusing enough with the rest of this post
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But you're right, MCI, the red part of that diagram is key. It's key to understanding phase and to the ability to shift phase without shifting time. I'm going to try and explain it a little here.
WARNING: This subject quickly pushes my graphical creation skills to their breaking point. The pictures will not be real pretty or mathematically exact in many cases, and will often be borrowed from sources on the net that I could find without spending hours searching for "just the right one". So bear with me here, gang, and try to understand the general concept at least, if not the exact details.
Phase is nothing more than a property of a waveform. Just as amplitude, frequency and duration are all properties. It's just that we are used to only looking at or graphing two of those properties at the same time; amplitude and duration (time). These are the y(vertical) and x(horizontal) axises in our DAW timelines.
(We sometimes look at amplitude and frequency in the form of an FFT spectrogram from our frequency analyzer, but that's another animal altogether. Let's stick to our DAW timeline displays.)
We use the two x and y axis to show two properties of amplitude and time simultaneously. If we want to look at a third property - such as our old friend phase - we can plot that in the third dimension, or z axis. If x is length an y is height, z would be depth.
On the above image, the axies have been rotated a bit to expose the z axis, but on our DAW timeline, we'd be looking the z axis head on, and it would just look like a point where the x and y axies meet.
Now, we have decided to use the third dimension, or z axis, to represent phase. But because phase is a special property mathematically equal to the 360 degrees on a circle, such a circle can be drawn (or imagined) as being on the z axis. The center of the circle is centered on the x axis (if the circle were a wheel, the x axis would be the axle).
(NOTE:, if there is DC offset, then the center would shift upwards to match the amount of offset.)
This circle, marked with its phase values in degrees, is what we see in red on this diagram:
Now here's where my graphical skills fall a bit short and your imaginations have to take over for a bit to fill the gap. If we take a standard sine wave that just keeps going up and down, up and down, at a fixed frequency, what is happening is the values is actually circling around that circle at a fixed rate.
As we move through time - i.e. move down the x axis, this movement which looks like a sine wave on our 2D timeline actually looks like a spiral in the three dimensions of our "phase space" (as it would be called in math and physics). The sine wave is really little more than the 2-dimensional (amplitude and time) shadow of the spiral in the three dimensions of amplitude, time and phase.
Take a look at this photo of a typical spring, which is basically a spiral coil.
Or take one out of your ball point pen there at your desk. Notice how if you look at the sping side on, it pretty much looks like a sine wave (the lower left of the picture). If you look at it edge on (through the middle, right down the x axis, with the z axis now going left-right), it just looks like a circle.
Now, we can easily take that spiral spring and spin it around. Like a drill bit, it spins around, and the lines of the 3D spiral or 2D sine wave appear to move. Yet the actual spring is not going anywhere, it is just rotating in place.
This is phase change in action. There is no shifting in time or movement along the x axis; the spring is not moving back or forth. It is simply rotating in place along the z circle, with the 2D shadow of sine wave shifting in phase as we rotate along, but without moving up or down the timeline.
G.
. I guess what it comes down to is that there are a few subjects that our hobby/vocation touches upon where the answers can be a bit more difficult than the questions, and require a decent grounding in advanced math and science topics like trigonometry, physics or information theory to truly understand the actual fundamentals behind them.
. If you could get your mic to the other side of the living room, pointed away from the PC, and preferably pointed towards drapes or padded furniture, to reduce the amount of fan sound reflecting off the back wall back into the mic, if possible. Yeah it may be a little of a pain to have to walk across the room every time you hit record, but you get used to such things.
