# 0.2 Finding directional hrtfs

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Finding directional transfer functions by means of in-ear signal sampling.

## Directional signal sampling

In order to find directional HRTFs for our test subject, we first had to make recordings of the signals as heard by the test subject coming from different directions. In order to do this, we placed our microphone in the ear to be tested, as shown below.

We then played our chirp signal at the test subject from various directions with the speaker at the same distance as in the initial channel characterization. As in the initial channel characterization, we sampled twice for each direction and averaged the two results. After sampling for that particular ear, we then switched the microphone to the other ear and sampled the same directions for the other ear.

## Hrtf calculation

In the initial channel characterization, the transfer function ${H}_{\text{Channel}}\left(\omega \right)$ was the only thing acting on the chirp signal. Now, with the microphone situated in the test subject’s ear, both ${H}_{\text{Channel}}\left(\omega \right)$ and the directional HRTF for that particular ear ${H}_{\text{Directional}}\left(\omega \right)$ act on the chirp signal. In other words:

${H}_{\text{Channel}}\left(\omega \right)\cdot \text{IN}\left(\omega \right)\cdot {H}_{\text{Directional}}\left(\omega \right)=\text{OUT}\left(\omega \right)$

Since we already calculated ${H}_{\text{Channel}}\left(\omega \right)$ and $\text{IN}\left(\omega \right)$ during the initial channel characterization, and we can find $\text{OUT}\left(\omega \right)$ for each particular ear/direction combination by taking the fft of our recorded outputs, we can therefore calculate ${H}_{\text{Directional}}\left(\omega \right)$ using the equation:

${H}_{\text{Directional}}\left(\omega \right)=\text{OUT}\left(\omega \right)/\left[{H}_{\text{Channel}}\left(\omega \right)\cdot \text{IN}\left(\omega \right)\right]$

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I think
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