Click here to purchase the entire book in PDF format. Head Related Transfer Functions (HRTF's) We have already seen that anything that changes a signal can be called a filter - this could mean a device that we normally call a filter (like a high pass filter or a low pass filter) or it could be the result of the combination of an acoustic signal with a reflection, or reverberation. We have also seen that the filter can be described by its transfer function - this doesn't tell us how a filter does something, but it at least tells us what it does. Let's pretend that we have a perfect loudspeaker and a perfect microphone in a perfectly anechoic room exactly 1 m apart. If we do an impulse response measurement of this system, we'll see a perfect impulse at the output of our microphone, meaning that it and the loudspeaker have perfectly flat frequency and phase responses. Now, we'll take away the microphone and put you in its place so that you are facing the loudspeaker and that your eardrum is exactly where the microphone diaphragm used to be. If we could magically get an electrical output directly from your eardrum proportional to its excursion, then we could make another impulse response measurement of the signal that arrives at your eardrum. If we could do that, we would see a measurement that looks something very similar to Figure 5.6 Figure 5.6: An example of the impulse response of a sound source directly in front of you, measured at the eardrum [Gardner and Martin, 1995]. You will notice that this is not a perfect impulse, and there are a number of reasons for this. Remember that in between the sound source and your eardrum there are a number of obstructions that cause reflections and absorption. These obstructions include shadowing and boundary effects of the head, reflections off the the pinna and shoulders, and resonance in the ear canal. The signal that reaches your eardrum includes all of the effects caused by these components and more. The combination of these effects changes with different locations of the sound source (measured by its rotation and its azimuth) and different orientations of the head. The result is that your physical body creates different filter effects for different relationships between the location of the sound source and your two ears. Also, remember that, unless the sound source is on the median plane (see Figure 5.7), then the signals arriving at your two ears will be different. Figure 5.7: The horzintal, median and frontal planes. If we consider the effect of the body on the signal arriving from a given direction and with a given head rotation as a filter, then we can measure the transfer function of that filter. This measurement is called a head-related transfer function or HRTF. Note that typically, an HRTF typically includes the effects of reflections off the shoulders and body and therefore are not just the transfer function of the effects of the head itself.