Figure 8: This is what happens when the two signals are combined. The picture is similar to
figure 6 with two important differences. First the "glitch" at the point where the second signal
starts is different. This is the point where the line turns black. Second is that the entire
waveform is shifted by 45 degrees again but this time to the left of the original signal.
The glitches in figures 6 and 8 give an indication of what happens during the onset of a
signal. While the so-called steady state portion of the combined signal (shown by the black
portion of the lines) looks the same except for the amplitude change, these glitches will affect
the transient attack of sounds. This is not to say that either will sound horrible, but a phase
shift between otherwise identical replicas of a sound WILL make a difference in the sound of
the initial transient attacks, depending on the frequency and amount of phase shift.
This is exactly the kind of phenomena that can occur in the crossover region of a speaker.
This is because the distance from each driver to the listener is usually different and the
crossover itself shifts the phase of the signal between the drivers. Speaker designers are
often faced with a choice between something like what you see in figures 6 and 8. Neither is
"correct" so a designer can only choose the one that "listens" better. Just looking at these
two, I would bet the waveform in figure 8 might sound better and the choice would be to
reverse the polarity of one of the drivers. These crossover "glitches" occur only over a small
range of frequencies where both drivers reproduce the sound. It is well accepted by
designers that this kind of "improvement" is sonically more significant than the fact that
frequencies above and below the crossover point may be out of polarity.
This is where many get into trouble in thinking that phase and polarity are the same thing,
meaning that it is often assumed that a 180 degree phase shift and reversing the polarity are
the same.
Figure 9: In this figure each sine wave lasts for only 2-1/2 cycles. The second sine wave,
shown in red, is shifted in phase 180 degrees from the first shown in blue. This is what would
happen if the speaker reproducing the red sine wave were about 6.8 inches (170 mm) further
away from you than the one reproducing the blue sine wave. You can see that between the
180 and 900 degrees the signals LOOK like they are simply out of polarity but they are NOT.
It is VERY important to note that if you could not see the beginning or the end of these
signals you could not tell whether they were out of polarity or 180 degrees out of phase. Too
often this is what causes confusion between a polarity reverse and a 180 degree phase shift.
Figure 10: This is the result of combing the two signals. Unlike figure 4 where the signals are
simply out of polarity, and completely cancel, there are clearly two positive halves of a sine
wave visible before and after the two signals cancel along the black line between 180 and
900 degrees. The first is from the blue sine wave in figure 9 that occurs before the start of the
red sine wave. The second is from the red sine wave in figure 9 that continues after the blue
sine wave stopped.
Figure 12: This is the two signals in figure 11 combined. Between the 180 and 900 degrees,
the signals add much like in figure 2. However there are significant differences in the overall
90 to 1080 degree signal. The first 1/2 sine wave of this signal is only from the blue sine
wave from figure 11. The last 1/2 sine wave is only from the red sine wave in figure 11. You
can clearly see that both of these 1/2 sine waves are only 1 volt at the peaks. This is a clear
difference from figure 2 where all the peaks reach 2 volts.
The reason is that the two signals in figure 11, even though identical, are offset by 180
degrees. They add together only between 180 and 900 degrees when both are being heard.
More importantly, during this time period DIFFERENT parts of the same signal have added
together. For example you can see that between 180 and 360 degrees it is the second 1/2 of
the blue signal's first complete sine wave that adds to the first 1/2 of the red signal's first
complete sine wave.
Sine waves are easy to look at to dramatically show the difference between polarity and
phase. Armed with this knowledge you can look at figures 13 through 18 that show something
like a real audio signal where the effects of polarity and phase are more difficult to see.
The signal shown in these figures was a generated by a mathematical algorithm that
produces something close to a pink noise signal. Pink noise contains all frequencies with an
equal amount of energy in each octave band. Real audio signals don't look much different
than pink noise (but one would hope they sound better!). The scales on these graphs are
arbitrary. You can look at the vertical scales as +/-3 volts if you like. However, because of the
way the signal was generated, there was no way to define absolute time or degrees along the
horizontal scales. Suffice it to say that the phase-shifted signal used in these figures was
shifted by one data point out of the 240 data points that make up the signal lines.
There is one important thing to understand about phase shift. The amount of time one signal
is delayed from another will have different effects at different frequencies. Assume there is a
1 millisecond time difference between two identical signals. At 500 Hz the result will be as
shown in figure 10 because at 500 Hz the 1 millisecond time difference is a phase shift of
180 degrees. The signals are offset by 1/2 a cycle. At 1 kHz the signals will be offset by 1
complete cycle. In other words you would hear one cycle from the first signal then both
combine then you'd hear the one cycle from the second signal after the first stopped. This is
similar to what is shown in figure 12 (which shows only 1/2 cycle) but is not the result of the
same conditions that were used to make figure 12. At 250 Hz the effect would be as shown in
figure 6 because a 1 millisecond time difference corresponds to a 90 degree phase shift at
250 Hz or an offset of 1/4 cycle. At lower frequencies the phase shift would be even less and
the signals would tend to add as in figure 2, approaching but never quite reaching the 6 dB
increase shown in that figure.
Contrary to phase, polarity affects all frequencies the same way. It makes the positive
portions negative and the negative portions positive. Put another way, it simply flips the
signal over the same way at all frequencies.
With these things in mind, examine figures 13 through 18
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樓主
發表於 2012-6-9 08:24
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