Binaural sound localization using a formant-type cascade of resonators and anti-resonators

A method of performing a head related transfer function comprising the step of:

• performing a cascade of at least one resonator and at least one anti-resonator;
• said step of performing at least one resonator includes performing a resonator for each peak in a magnitude spectrum of the head related transfer function having a frequency peak corresponding to said peak in the magnitude spectrum of the head related transfer function and selecting a bandwidth of said resonator to minimize a difference from the magnitude spectrum of the head related transfer function;
• said step of performing at least one anti-resonator includes performing an anti-resonator for each valley in the magnitude spectrum of the head relate transfer function includes performing an anti-resonator for each valley in the magnitude spectrum of the head related transfer function significantly smaller in magnitude than natural valleys between peaks of said resonators and selecting a bandwidth of said anti-resonator to minimize a difference from the magnitude spectrum of the head related transfer function employing the equation:
• y(n)=x(n)+Dx(n−1)+x(n−2)+Ey(n−1)+Fy(n−2)
• where:
• D=−2 cos θ;
• E=2 dcos θ;
• F=−d2;
• and θ=2πF·T;
• d is a constant in the range [0.8,1.0] related to the bandwidth;
• T is the sampling period;
• and F is the anti-resonant frequency in Hertz.

A method of stereo enhancement comprising the steps of:

• providing at least one delay of a left channel input;
• selectively attenuating each at least one delay of the left channel input;
• summing the selectively attenuated at least one delay of the left channel input thereby forming a first sum signal;
• forming a first head related transfer function of the first sum signal relative to a listener's left ear;
• forming a second head related transfer function of the first sum signal relative to a listener's right ear;
• providing at least one delay of a right channel input;
• selectively attenuating each at least one delay of the right channel input;
• summing the selectively attenuated at least one delay of the right channel input thereby forming a second sum signal;
• forming a third head related transfer function of the second sum signal relative to a listener's right ear;
• forming a fourth head related transfer function of the second sum signal relative to a listener's left ear;
• summing said first and fourth head related transfer functions thereby forming a third sum;
• summing said third sum and the left channel input thereby forming a left channel output;
• summing said second and third head related transfer functions thereby forming a fourth sum;
• and
• summing said fourth sum and the right channel input thereby forming a right channel output.