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The head related transfer function (HRTF) describes sound arriving from a specific point in space on the spherical head surface. These values, taken as an inverse filter, can be used to convolve a given signal with various positions of a virtual sphere, while optimizing it to perceive as if it comes from the given position.
The HRTF is used by gamers to enhance the experience of playing FPS (first person shooter) games with lots of weapon fire coming from behind them or to widen the cone of surround voice in noisy computer rooms, such as by using surround speakers for a PC.

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This statement is a bit misleading for two reasons.

First, what we are seeing is the slow, steady decline of the “super delegates” that would prevent a brokered convention. I recently wrote a post detailing the demise of super delegates, and it looks as though the momentum is gathering speed.

Second, it’s also incorrect to say that the only way for a brokered convention would be for the super delegates to override the will of the people. They simply don’t

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The HRTFs contain all the information of the real sound.
The spatial coordinates the source is in and the elevations of the source.

The Elevations in the HRTFs are measured in 10m steps.
It is more or less standardized in 30, 45 and 60 degrees.
If you get a HRTF with more than 60 degrees you can translate the sound at the borders of the sphere to get it back to a 60 degree HRTF.
For the elevation you will get a relative elevation.
You can ofcourse change the elevation or the angle of the egressions also.
Last but not least you can change the source position.

How to use the HRTF:
So the question is how to use the HRTFs in a computer program.
We will make a few assumptions which is justified in my opinion.

The sound source is static and the HRTF will adapt to the moving source.
We assume that the HRTFs we use are adjusted to our ears.

Thus the position of the source is defined in a Cartesian coordinate system.
The soundfield positions that we want to adapt are then defined with the source in a 3D sphere of radius R.
The soundfield of a sound coming from position (x,y,z) has egressions that are in a vertical plane that contains the vector (x,y,z).
The position of that plane is (x,y,z).
The length of that plane is 2*R*tan(elevation).
The vector of that plane is (-x,-y,-z).
The elevation is the angle between the vector and the (x,y,z) vector.

Thus the sphere to be simulated has this coordinate system:

(x,y,z) – is the position of the source in the sample
(R,elevation) – defines the size of the sphere
(-x,-y,-z) – defines the position of the points of the sphere to simulate the sound
(-x,-y,-z) – represents the plane that contains the x,y and z axis
The length of the vector is 2*R*tan(elevation)

An example would be a sphere of radius 10m with the elevation angle at 45 degrees.

A RTS Tutorial:
The following tutorial is about creating a RTS game, but is also useful for the HRTF Simulation.

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The HRTF 3D is suitable for stereo and surround-sound applications, such as a virtual-reality environment. This simulation feature is often referred to as spatialization. It was developed by Souheil Belhassen, and it is capable of creating the illusion of hearing the sound from any position. The application uses both the directions of the sound and the structure of the head and ears to simulate sound as if it came from anywhere in space, i.e., from any virtual position within the sound field. This feature creates a realistic experience of sound objects within a surround-sound environment. HRTF 3D uses the HRTF to convolute a given signal with the head related transfer function. The latter is a function that specifies the amount of attenuation of a sound at a given point, versus the amount of attenuation that a sound receives as it moves in the panorama of the sphere. To use this feature, click on the HRTF 3D button. The simulation consists of two parts; the first part offers the user the ability to specify where the head and ear are to be placed, while the second part proposes to convolute any given signal with the head related transfer function for a given position.
The simulation will display a picture of the head in the center of the display window. Two virtual points may be labeled as the left and right end of the head. By positioning the head in a 3D environment, the sound will be measured at these two virtual points.

To enable HRTF 3D:

Position the mouse over the Start button and then click on HRTF 3D (in the Sound Edit menu). This will open a file selection dialog box.

Select one of the many available.WAV files. (Select HRTF 3D_3D_3D_44.WAV for HRTF 3D with 3D surround sound.)

Select which plane of the 3D scene you would like to listen to the sound. (Depending on your Windows version, it may be necessary to select other 3D scenes in the Sound Editor 3D. Various applications may be specified, e.g.,
Microsoft Flight Simulator 3D, where there are no sound objects in the default scenes.)

Confirm that the source is a 1D or 2D sound file.

Click on the Start button to initiate the process.

See the Picture of the Head (in the lower right of the Sound Editor) to see the position of the virtual head,

What’s New In HRTF 3D?

The Head Related Transfer Function (HRTF) describes the spatial filtering effect of the three-dimensional head and pinna on human hearing. It was first analyzed and measured by Williams in 1959 (Williams, 1959) for use in binaural recording and speech reproduction. Figure 1 gives the basic idea of the HRTF. The location of the virtual source, determined by a variable position X, is placed at a distance L from the listener and the listener’s head is located at angle θ with respect to the source’s direction. Figure 2 shows the head and pinna in more detail.
HRTFs have gained popularity as a method for spatialization and as virtualization tools for musicians (see e.g., Gibson & Housard, 1997; Fujimoto, Hasegawa, & Karino, 1990).

Here’s an example of how to use it in a music application:
Inverse HRTF
The frequency inverts and the order of the frequencies also gets inverted (figure 3), but the spatial perception is the same as the original:

Sample code
At a quick glance, the code looks like this:
HRTF[x, θ, L, f] := Module[{fmod, hr, y},
fmod = N[f];
hr = DirichletGamma[1 – 4 (L/fmod)^2];
y = N[
Table[s =
{Sin[2 π (f m) (d] Cos[2 π θ (f m)] –
Cos[2 π (f m) (d] Sin[2 π θ (f m)])}, {d, 0, L}], {f m, f,

2 π (
(f/fmod) θ (d + f/fmod L) – f x)];
If[HRTF[x, θ, L, f] > 0, -y, y] ]

Repetition for all x and positions
Repetition is very important to get better quality, too.
HRTF[x_, θ_, L_

System Requirements For HRTF 3D:

Windows 10 64bit
OS: Windows 10 64bit
CPU: Intel Core i7 or AMD equivalent
Memory: 2 GB
Hard disk: 2 GB
Additional Notes:
Mac: Mac OS 10.10.2 or later
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