Hey all,
Here's my answer to Jabco's question.
http://johnlsayers.com/phpBB2/viewtopic.php?p=1189#1189
I read through Skippy's and Light's explanations and they do give very good information. Let me just supplement these with another graphic explaining the difference between phase and polarity.
Like Skippy said, the confusion between phase and polarity usually results because sine waves are so often used in these discussions. Continuous sine, triangle, and square waves are examples of special types of waveforms that have directional symmetry. Looking at the sine wave in the picture you can see if we flip the polarity then translate the phase (in time) we wind up with the exact same waveform with the voltage rising and falling in the exact same way at all times as the original waveform.
The sawtooth, however, shows us that translating the phase after reversing the polarity does not always result in the same waveform. In the original sawtooth the voltage rises gradually then falls sharply. In the reverse polarity waveform the voltage rises sharply then falls gradually and no amount of phase translation can get it to act like the original.
So lets try to come up with some good definitions of phase and polarity.
Polarity is fairly simple. It only has to do with the direction in which the current, air, water, or whatever flows. It doesn't depend on any translation of the waveform in time.
Phase is in part the position of a waveform relative to a fixed point in time. It does have to do with time. But, there's an extra component. The term phase is only really meaningful when talking about a continuous or at least semi-continuous waveform. If you translate a transient waveform (like a kick) in time, you can't consider this a phase shift - at least not when considering the waveform as a whole. This is a "delay". It only makes sense to talk about phase when there are exact repeats of the waveform ready to slide into place when we make the time shift.
So here now are our definitions:
Polarity - the direction of flow of a wave at any fixed point in time. Reversing the polarity reverses the direction of flow.
Delay - the position of any waveform relative to a fixed point in time.
Phase - the position of a
continuous and periodic waveform relative to a fixed point in time.
Just a couple extra notes:
Even though the sawtooth wave does not have directional symmetry like the sine wave, if it's continuous and shifted in time, this is still considered a phase shift.
Fourier analysis does provide us a way to consider the "phase" characteristics of transient waveforms. The Fourier Theorem states that any arbitrary waveform, be it continuous or a pulse, can be built up from a group of continuous sine waves having various amplitude, wavelength, and phase relationships. So, in this sense we can think of shifting a kick drum waveform in time as being the same as shifting the phase of all its constituent sine waves. And in this terminology the time shift of the entire waveform would be viewed as a "group delay".
Thomas