Head related transfer function (HRTF) enhancement for improved vertical-polar localization in spatial audio systems

A spatial audio system with lateral and vertical localization of an audio signal comprising a left audio signal and a right audio signal, the spatial audio system comprising:

• a receiver system having left and right earpieces;
• a look-up table of measured head-related transfer functions, each of the transfer functions defining a left measured frequency-dependent gain for the left audio signal, a right measured frequency-dependent gain for the right audio signal, and a measured interaural time delay for a plurality of source directions,
• a signal splicer configured to provide (i) the left audio signal with the left measured frequency-dependent gain and a left time delay to the left earpiece and (ii) the right audio signal with the right measured frequency-dependency gain and a right time delay to the right earpiece;
• first and second filters between the signal splicer and the left earpiece and, together, configured to create a left signal output, the first filter configured to add a first lateral magnitude head-related transfer function to the left audio signal and the second filter configured to add a first vertical magnitude head-related transfer function scaled by a first enhancement factor to the left audio signal;
• third and fourth filters between the signal splicer and the right earpiece and, together, configured to create a right signal output, the third filter configured to add a second lateral head-related magnitude transfer function to the right audio signal and the fourth filter configured to add a second vertical head-related magnitude transfer function scaled by a second enhancement factor to the right audio signal;
• and
• the left signal output and right signal output delivered to the respective left and right earpieces to provide a virtual sound, the virtual sound having a desired apparent source location and a desired level of spatial enhancement, the desired apparent source location having a desired apparent lateral angle with respect to a lateral dimension and a desired apparent vertical angle with respect to a vertical dimension,
• wherein the first lateral magnitude head-related transfer function is configured to output a first log lateral frequency-dependent gain equal to a median log frequency-dependent gain across all left measured frequency-dependent gains having the desired apparent lateral angle,
• the first vertical magnitude head-related transfer function is configured to output a first log vertical frequency-dependent gain equal to the first enhancement factor multiplied by a difference between the left measured frequency dependent gain at the desired apparent source location and the first lateral magnitude head-related transfer function,
• the second lateral magnitude head-related transfer function is configured to output a second log lateral frequency-dependent gain equal to a median log frequency-dependent gain across all the right measured frequency-dependent gains having the desired apparent lateral angle, and
• the second vertical magnitude head-related transfer function is configured to output a second log vertical frequency-dependent gain equal to the second enhancement factor multiplied by a difference between the right measured frequency dependent gain at the desired apparent source location and the second lateral magnitude head-related transfer function.