HRTF Models

Researchers have investigated several ways to model HRTF's (see Carlile or Duda). The following general approaches have been explored:
  1. Rational function or pole/zero models. Here the modeling problem is viewed as one of system identification, which has several classical solutions. Unfortunately, the coefficients are usually such complicated functions of azimuth and elevation that they have to be tabulated, which destroys the usefulness of the model.

  2. Series expansions. Fourier-series expansions or Karhunen-Loeve expansions (also known as principal component analysis or PCA) let one represent the HRTF as a weighted sum of simpler basis functions. While this is useful for inspecting the data, the run-time complexity of such models severely limits their usefulness.

  3. Structural models. Here one attempts to craft transfer functions that account for the physical mechanisms -- head shadow, shoulder reflections, etc. This approach, which was developed in depth by Genuit, has some unsolved problems but holds considerable promise.
In the remainder of these notes, we examine a sequence of structural models of increasing sophistication:
  1. ITD model
  2. ILD model (head-shadow model)
  3. Spherical-head model
  4. Monaural pinna model
  5. Combined models

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