窮人睇concert....之音魂不散

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EFFECTS OF POLARITY AND PHASE ON "REAL" AUDIO SIGNALS

Figure 13: This shows a pink noise signal generated as noted above.

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Figure 14: This shows both the original signal in blue and what happens when an identical
but phase shifted signal is added to it, as shown in red. The red signal is similar to the
combined signal shown in figure 6. Note the increases in signal level and the changes in the
waveform (many glitches). However you can also see the combined signal follows the
original fairly closely.

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Figure 15: This shows both the original signal in blue and what happens when the phase
shifted signal is also reversed in polarity and combined with it, as shown in red. In this case
there are huge differences between the original and combined signal.

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Figure 16: To better understand what is going on, this figure shows an averaged or integrated
version of the pink noise signal in figure 13. This is basically what would you would see if you
graphed the readings from a typical SPL meter for the signal in figure 13.

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Figure 17: This shows the averaged signal from figure 16, in blue, and the averaged
combined signal from figure 14, in red. Note that there are primarily level differences (mostly
increases). Otherwise the two lines look very similar.

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Figure 18: This really shows what is going on in figure 15. The blue line is the averaged
signal from figure 16. The red line is the averaged signal from figure 15. The red line shows
that the out of polarity and phase-shifted signal approaches a straight line. Because you are
looking at a broad frequency range, you are seeing a severe cancellation of the lower
frequencies due to the polarity reversal. However, unlike the low frequencies, the upper
frequencies do not completely cancel due to the phase shift. The red line contains primarily
high frequency energy. In the blue signal the higher frequencies are the small "bumps".
These can be clearly seen in the red signal and most of them correspond to those in the blue
signal.

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Figure 18 is a prime example of what you would hear if you stand exactly between two
speakers playing the same signal (i.e. mono) with one speaker out of polarity. The bass will
disappear. But, there will always be a difference in distance between you and the speakers
due to the spacing of your two ears and probably a slight overall difference in distance
between you and each speaker. A difference in distance means a difference in the time
arrival and thus there will be phase shifts between the sound from the two speakers. The
amount of shift will vary with frequency.

Because of the shorter wavelengths at high frequencies, the phase shifts allow most of the
highs to be heard. They may be out of polarity but the effect is like what is shown in figure 8.
Also, in a room you would also hear sound reflections from the floor, walls, and ceiling. You
would only hear something like the red line in figure 18 outdoors away from any reflective
surfaces or in an anechoic chamber.

The small distance between your ears and any small difference in distance from you to each
speaker do not cause appreciable phase shifts at low frequencies. This is because of the
considerably larger wavelengths. The difference in your distance from each speaker might be
only 1 inch (25 mm). However, the wavelength of even a 1 kHz sound is roughly 1 foot (300
mm) and at 100 Hz roughly 10 feet (3 m). At the lower frequencies the polarity difference
predominates because the phase shifts due to the difference in your distance from the
speakers is very small compared to the wavelengths of the low frequencies. Thus the lower
frequency signals, being nearly in phase but out of polarity, will cancel like in figure 4. The
lower the frequency the less the phase shift between the two speakers and the greater the
cancellation.

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A POLARITY / PHASE FIELD TRIP!!

(As with all physical exercise, check with your doctor first, who might not recommend
you do this for some reason.)





Find two railroad tracks, lie across them, and wait.
Two trains, one on each track, come along. Both are right side up and both hit you at exactly
the same time. The trains are in polarity and in phase.
The same thing happens again and both trains hit you at exactly the same time. However,
this time one train is upside down. That is a polarity reversal.
The third time both trains are right side up but one hits you first and the other hits you shortly
after the first. That is a phase shift.
The last time the second train is upside down and hits you later than the first. That is both a
polarity reversal and a phase shift.

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SUMMARY

So there you have it. Although this has only touched on a few areas concerning phase and
polarity issues, it is hoped you better understand the difference between the two and a few of
the effects of each. Remember that the audio frequency range covers wavelengths of over 30
feet (10 meters) at the lowest frequencies to less than an inch (under 25 mm) at the highest
frequencies. While a reversal of polarity will affect all frequencies identically, a difference in
time arrival between two otherwise identical signals will have very different effects on the
phase between them. The amount of phase shift will be different at different frequencies and
this will depend on how much time difference there is between the arrival of the two signals.

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