Sound synthesis for data sonification employing a human auditory perception eigenfunction model in Hilbert space

A method for data sonification optimized for human auditory perception for use in conjunction with human hearing, the method comprising:

• using a processing device for retrieving a plurality of approximations, each approximation corresponding with one of a plurality of eigenfunctions previously calculated, each approximation having resulted from approximating an eigenfunction equation representing a model of human hearing, wherein the model comprises a bandpass operation with a bandwidth including the frequency range of human hearing and a time-limiting operation approximating the time duration correlation window of human hearing;
• receiving incoming coefficient information determined by underlying data;
• and
• using the approximation to each of the plurality of eigenfunctions to produce outgoing associated audio information by mathematically processing the incoming coefficient information together with each of the retrieved approximations to compute the value of an additive component to an outgoing audio information associated with an interval of time, the result comprising a plurality of coefficient values associated with the calculation time,
• wherein the eigenfunction equation is a Slepian's bandpass-kernel integral equation;
• wherein the plurality of coefficient values is used to produce at least a portion of the outgoing audio information for an interval of time;
• wherein the outgoing audio information associated with each of the plurality of eigenfunctions are summed to produce a composite synthesized signal;
• and
• wherein the composite synthesized signal is rendered as at least one audio signal representing the underlying data with synthesized sound.