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Chapter 5: The Transformation of Sound by Computer
Section 5.3: Localization/Spatialization
Humans have a pretty complicated system for perceptually locating sounds, involving, among other factors, the relative loudness of the sound in each ear, the time difference between the sounds arrival in each ear, and the difference in frequency content of the sound as heard by each ear. How would a "cyclaural" (the equivalent of a "cyclops") hear? Most attempts at spatializing, or localizing, recorded sounds make use of some combination of factors involving the two ears on either side of the head.
Simulating Sound Placement
Simulating a loudness difference is pretty simpleif someone standing to your right says your name, their voice is going to sound louder in your right ear than in your left. The simplest way to simulate this volume difference is to increase the volume of the signal in one channel while lowering it in the otheryouve probably used the pan or balance knob on a car stereo or boombox, which does exactly this. Panning is a fast, cheap, and fairly effective means of localizing a signal, although it can often sound artificial.
Interaural Time Delay (ITD)
Simulating a time difference is a little trickier, but it adds a lot to the realism of the localization. Why would a sound reach your ears at different times? After all, arent our ears pretty close together? Were generally not even aware that this is true: snap your finger on one side of your head, and youll think that you hear the sound in both ears at exactly the same time.
But you dont. Sound moves at a specific speed, and its not all that fast (compared to light, anyway): about 345 meters/second. Since your fingers are closer to one ear than the other, the sound waves will arrive at your ears at different times, if only by a small fraction of a second. Since most of us have ears that are quite close together, the time difference is very slighttoo small for us to consciously "perceive."
Lets say your head is a bit wide: roughly 250 cm, or a quarter of a meter. It takes sound around 1/345 of a second to go 1 meter, which is approximately 0.003 second (3 thousandths of a second). It takes about a quarter of that time to get from one ear of your wide head to the other, which is about 0.0007 second (0.7 thousandths of a second). Thats a pretty small amount of time! Do you believe that our brains perceive that tiny interval and use the difference to help us localize the sound? We hope so, because if theres a frisbee coming at you, it would be nice to know which direction its coming from! In fact, though, the delay is even smaller because your heads smaller than 0.25 meter (we just rounded it off for simplicity). The technical name for this delay is interaural time delay (ITD).
To simulate ITD by computer, we simply need to add a delay to one channel of the sound. The longer the delay, the more the sound will seem to be panned to one side or the other (depending on which channel is delayed). The delays must be kept very short so that, as in nature, we dont consciously perceive them as delays, just as location cues. Our brains take over and use them to calculate the position of the sound. Wow!
Modeling Our Ears and Our Heads
That the ears perceive and respond to a difference in volume and arrival time of a sound seems pretty straightforward, albeit amazing. But whats this about a difference in the frequency content of the sound? How could the position of a bird change the spectral makeup of its song? The answer: your head!
Imagine someone speaking to you from another room. What does the voice sound like? Its probably a bit muffled or hard to understand. Thats because the wall through which the sound is travelingbesides simply cutting down the loudness of the soundacts like a low-pass filter. It lets the low frequencies in the voice pass through while attenuating or muffling the higher ones.
Your head does the same thing. When a sound comes from your right, it must first pass through, or go around, your head in order to reach your left ear. In the process, your head absorbs, or blocks, some of the high-frequency energy in the sound. Since the sound didnt have to pass through your head to get to your right ear, there is a difference in the spectral makeup of the sound that each ear hears. As with ITD, this is a subtle effect, although if youre in a quiet room and you turn your head from side to side while listening to a steady sound, you may start to perceive it.
Modeling this by computer is easy, provided you know something about how the head filters sounds (what frequencies are attenuated and by how much). If youre interested in the frequency response of the human head, there are a number of published sources available for the data, since they are used by, among others, the government for all sorts of things (like flight simulators, for example). Researcher and author Durand Begault has been a leading pioneer in the design and implementation of what are called head transfer functionsfrequency response curves for different locations of sound.
What Are Head-Related Transfer Functions (HRTFs)?
Not surprisingly, humans are extremely adept at locating sounds in two dimensions, or the plane. Were great at figuring out the source direction of a sound, but not the height. When a lion is coming at us, its nice of evolution to have provided us with the ability to know, quickly and without much thought, which way to run. Its perhaps more of a surprise that were less adept at locating sounds in the third dimension, or more accurately, in the "up/down" axis. But we dont really need this ability. We cant jump high enough for that perception to do us much good. Barn owls, on the other hand, have little filters on their cheeks, making them extraordinarily good at sensing their sonic altitude distances. You would be good at sensing your sonic altitude distance, too, if you had to catch and eat, from the air, rapidly running field mice. So if its not a frisbee heading at you more or less in the two-dimensional plane, but a softball headed straight down toward your head, wed suggest a helmet!
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