Method and apparatus for the compression and decompression of audio files using a chaotic system

Abstract

A system for the compression and decompression of sections of audio files is provided. A library of basic waveforms is produced by applying selected digital initialization codes to a chaotic system. Each basic waveform is in one-to-one correspondence with an initialization code. A weighted sum of the selected basic waveforms is used to approximate a section of audio file. The basic waveforms are then discarded and only the weighting factors and the corresponding initialization codes are stored in a compressed audio file. When the compressed audio file is decompressed for playback, the stored initialization codes are stripped out and applied to a similar chaotic system to regenerate the basic waveforms, which are recombined according to the stored weighting factors to reproduce the original section of audio file.

1 - 9 . (canceled)  
     
     
         10 . A method of compressing a data signal, using a chaotic system, comprising: 
 causing the chaotic system to assume periodic orbits by applying initialization codes to the chaotic system;    generating periodic waveforms for the periodic orbits;    weighting the periodic waveforms to approximate at least a portion of the data signal; and    producing a compressed representation of the at least a portion of the data signal from a combination of at least one initialization code and information representative of the weighting.    
     
     
         11 . The method of  claim 10  further comprising: 
 stabilizing at least one of the periodic orbits.    
     
     
         12 . The method of  claim 10  further comprising: 
 identifying a trend over portions of the data signal; and    defining a relationship between weighting factors in the portions of the data signal.    
     
     
         13 . The method of  claim 12 , wherein the identifying the trend includes determining a mathematical model for the trend.  
     
     
         14 . The method of  claim 12 , wherein the producing includes producing the compressed representation of the at least a portion of the data signal from a combination of the trend, the at least one initialization code, and the information representative of the weighting.  
     
     
         15 . The method of  claim 10 , wherein the data signal comprises audio data.  
     
     
         16 . The method of  claim 10  further comprising: 
 transforming the at least a portion of the data signal and the generated periodic waveforms to a suitable frequency range, wherein the producing includes producing the compressed representation of the at least a portion of the data signal from a combination of the at least one initialization code, the information representative of the weighting, and frequency information representative of the transforming.    
     
     
         17 . The method of  claim 10  further comprising: 
 assigning a weighting of zero to any of the generated periodic waveforms not deemed necessary to approximate sufficiently well the portion of the data signal.    
     
     
         18 . The method of  claim 17  further comprising: 
 removing from the weighted sum of the generated periodic waveforms the initialization code of any periodic waveform having zero weighting.    
     
     
         19 . A computer program product for compressing a data signal, which when executed on a computing device performs the steps of  claim 10 .  
     
     
         20 . A method of decompressing a compressed representation of a first data signal, the compressed representation produced using a first chaotic system and containing a combination of at least one initialization code and at least one representation of a weighting, comprising: 
 receiving at a second chaotic system, substantially identical to the first chaotic system, the combination of the at least one initialization code and the at least one representation of a weighting;    causing the second chaotic system to assume at least one periodic orbit by applying the at least one initialization code from the combination;    generating at least one periodic waveform for the at least one periodic orbit; and    applying to the at least one periodic waveform the at least one representation of a weighting to produce at least a portion of a second data signal substantially identical to at least a portion of the first data signal.    
     
     
         21 . The method of  claim 20  further comprising: 
 stabilizing the at least one periodic orbit.    
     
     
         22 . The method of  claim 20 , wherein the compressed representation includes trend information for the at least a portion of the first data signal.  
     
     
         23 . The method of  claim 22  further comprising: 
 applying the trend information to the second data signal, to substantially reproduce the at least a portion of the first data signal.    
     
     
         24 . The method of  claim 22 , wherein the trend information includes a mathematical model of the trend.  
     
     
         25 . The method of  claim 20 , wherein the first data signal comprises audio data.  
     
     
         26 . The method of  claim 20 , wherein: 
 the causing includes causing the second chaotic system to assume a plurality of periodic orbits by applying a plurality of initialization codes to the second chaotic system;    the generating includes generating a periodic waveform for each of a subset of the plurality of periodic orbits; and    the applying includes applying the at least one representation of a weighting to the generated periodic waveforms to produce the at least a portion of a second data signal substantially identical to the at least a portion of the first data signal.    
     
     
         27 . The method of  claim 26 , wherein the applying includes applying, to a first portion of the second data signal, a predetermined correlation between data in the at least a portion of the first data signal and data in at least one other portion of the first data signal, to produce at least one other portion of the second data signal substantially identical to the at least one other portion of the first data signal.  
     
     
         28 . A computer program product for decompressing a compressed representation of a first data signal, which when executed on a computing device performs the steps of  claim 20 .  
     
     
         29 . A data signal compressor for compressing a data signal using a chaotic system, comprising: 
 means for causing the chaotic system to assume periodic orbits by applying initialization codes to the chaotic system;    means for generating periodic waveforms for the periodic orbits;    means for weighting the periodic waveforms to approximate at least a portion of the data signal; and    means for producing a compressed representation of the portion of the data signal from a combination of at least one initialization code and information representative of the weighting.    
     
     
         30 . The data signal compressor of  claim 29  further comprising: 
 means for stabilizing at least one of the periodic orbits.    
     
     
         31 . The data signal compressor of  claim 29  further comprising: 
 means for identifying a trend over portions of the data signal; and    means for defining a relationship between weighting factors in the portions of the data signal.    
     
     
         32 . The data signal compressor of  claim 31 , wherein the means for identifying the trend includes means for determining a mathematical model for the trend.  
     
     
         33 . The data signal compressor of  claim 31 , wherein the means for producing includes means for producing the compressed representation of the at least a portion of the data signal from a combination of the trend, the at least one initialization code, and the information representative of the weighting.  
     
     
         34 . The data signal compressor of  claim 29 , wherein the data signal comprises audio data.  
     
     
         35 . The data signal compressor of  claim 29  further comprising: 
 means for transforming the at least a portion of the data signal and the generated periodic waveforms to a suitable frequency range, wherein the means for producing includes means for producing the compressed representation of the at least a portion of the data signal from a combination of the at least one initialization code, the information representative of the weighting, and frequency information representative of the transforming.    
     
     
         36 . The data signal compressor of  claim 29  further comprising: 
 means for assigning a weighting of zero to any of the generated periodic waveforms not deemed necessary to approximate sufficiently well the portion of the data signal.    
     
     
         37 . The data signal compressor of  claim 36  further comprising: 
 means for removing from the weighted sum of the generated periodic waveforms the initialization code of any periodic waveform having zero weighting.    
     
     
         38 . A signal decompressor operable on a compressed representation of a first data signal, the compressed representation produced using a first chaotic system and containing a combination of at least one initialization code and at least one representation of a weighting, comprising: 
 means for receiving at a second chaotic system, substantially identical to the first chaotic system, the combination of the at least one initialization code and the at least one representation of a weighting;    means for causing the second chaotic system to assume at least one periodic orbit by applying the at least one initialization code from the combination;    means for generating at least one periodic waveform for the at least one periodic orbit; and    means for applying to the at least one periodic waveform the at least one representation of a weighting to produce at least a portion of a second data signal substantially identical to at least a portion of the first data signal.    
     
     
         39 . The signal decompressor of  claim 38  further comprising: 
 means for stabilizing the at least one periodic orbit.    
     
     
         40 . The signal decompressor of  claim 38 , wherein the compressed representation includes trend information for the at least a portion of the first data signal.  
     
     
         41 . The signal decompressor of  claim 40  further comprising: 
 means for applying the trend information to the second data signal, to substantially reproduce the at least a portion of the first data signal.    
     
     
         42 . The signal decompressor of  claim 40 , wherein the trend information includes a mathematical model of the trend.  
     
     
         43 . The signal decompressor of  claim 38 , wherein the first data signal comprises audio data.  
     
     
         44 . The signal decompressor of  claim 38 , wherein: 
 the means for causing includes means for causing the second chaotic system to assume a plurality of periodic orbits by applying a plurality of initialization codes to the second chaotic system;    the means for generating includes means for generating a periodic waveform for each of a subset of the plurality of periodic orbits; and    the means for applying includes means for applying the at least one representation of a weighting to the generated periodic waveforms to produce the at least a portion of a second data signal substantially identical to the at least a portion of the first data signal.    
     
     
         45 . The signal decompressor of  claim 44 , wherein the means for applying includes means for applying, to a first portion of the second data signal, a predetermined correlation between data in the at least a portion of the first data signal and data in at least one other portion of the first data signal, to produce at least one other portion of the second data signal substantially identical to the at least one other portion of the first data signal.