1. 2005/11/101 KOZ Scalable Audio Speaker: 陳繼大 An Introduction

2. 2005/11/10P 22 References  K. M. Short et al, "An Introduction to the KOZ Scalable Audio Compression Technology", AES 118th Convention Paper, Barcelona, May 2005, Preprint 6446  M. K. Johnson, "Controlled Chaos and Other Sound Synthesis Techniques," Thesis for the Degree of Bachelor of Science, University of New Hampshire, May 2000  Douglas J. Nelson, and Kevin M. Short, “A channelized cross spectral method for improved frequency resolution.”, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time- Scale Analysis. IEEE Press, October 1998.

3. 2005/11/10P 33 References (cont.)  “KOZ scalable audio compression” SO/IEC JTC 1/SC 29/WG11 M12253

4. 2005/11/10P 44 Outline  Introduction  Double-scroll oscillator  High Freq. Resolution Analysis  Unified Domain  KOZ Scalable Audio  Results  Conclusions

5. 2005/11/10P 55 Introduction  Traditional transform/subband based codecs encode data by quantizing the coefficients according to psychoacoustic model  Parametric coding is another way for coding – it records the parameters of models, rather than coefficients.  KOZ scalable audio belongs to parametric coding methods  KOZ scalable audio takes Chaos system as the model  The Chaotic system is a nonlinear system

6. 2005/11/10P 66 Introduction (cont.)  Features of the KOZ codec Flexibility over a wide range of bitrates Both small-step and large-step scalability High resolution objects allows easy decoder-side post-processing Integrated Digital Rights Management

7. 2005/11/10P 77 Double-scroll oscillator  Chaotic system: nonlinear dynamical systems deterministic mathematical object sensitive dependence on initial conditions predictable over a short period of time unpredictable in terms of long-term behavior

8. 2005/11/10P 88 Double-scroll oscillator (cont.)  Cupolets: Output periodic waveforms of Chaotic system control process requires only on the order of 16 bits of information but the cupolets can be as simple as a sine wave or so complex that they have more than 200 harmonics in their spectrum

9. 2005/11/10P 99 Double-scroll oscillator (cont.)  A chaotic system will settle down onto a complicated structure called an attractor – settle down onto the same attractor no matter what initial conditions are used  A chaotic system in its natural state is aperiodic.  To stabilize these orbits – simply perturbing the state of the system in certain fixed locations by a tiny amount.

10. 2005/11/10P 1010 Double-scroll oscillator (cont.)  Double-scroll oscillator: One kind of chaotic system Nonlinear differential equations

11. 2005/11/10P 1111 Double-scroll oscillator (cont.) where Parameters:  C, L, G, m, B

12. 2005/11/10P 1212 Double-scroll oscillator (cont.)

13. 2005/11/10P 1313 Double-scroll oscillator (cont.)  Double-scroll attractor can be controlled in such a way that the trajectories around it become periodic.  Control perturbing: a bit string, generally of 16 bits applied at an intersection with the control line  periodic orbits are in one-to-one correspondence with the control string used, independent of the initial state of the system

14. 2005/11/10P 1414 Double-scroll oscillator (cont.)

15. 2005/11/10P 1515 High Freq. Resolution Analysis  Detect (the accurate freq.) of tones  IF-based methods Differentiation of the signal phase fail completely if the signal environment consists of more than one sinusoid  CPS (Cross Power Spectral) Time-averaged IF method Phase differentiation is applied to a time- varying Fourier transform Fourier transform is used to “channelize” the signal isolating the tones

16. 2005/11/10P 1616 High Freq. Resolution Analysis (cont.)  Improved (channelized) CPS estimator CPS can not detect and estimate tones which are not well separated Employ a second Fourier transform  TVFT: Time varying Fourier transform

17. 2005/11/10P 1717 High Freq. Resolution Analysis (cont.)  Channelized CPS if f(t) is tone 

18. 2005/11/10P 1818 High Freq. Resolution Analysis (cont.)

19. 2005/11/10P 1919 Unified Domain  Convert the multiple channels into Special unitary group  Special unitary group group of n×n unitary matrices subgroup of the unitary group SU(2)

20. 2005/11/10P 2020 KOZ Scalable Audio

21. 2005/11/10P 2121 KOZ Scalable Audio (cont.)  Prioritize the components Psychoacoustics are used in order of perceptual importance  Classes of objects are then sorted in order of their “perceptual relevance”  Objects are segregated and written to the floating-point.CCA file format.  Scalability of KOZ is fulfilled by sorting.

22. 2005/11/10P 2222 KOZ Scalable Audio (cont.)

23. 2005/11/10P 2323 KOZ Scalable Audio (cont.)

24. 2005/11/10P 2424 Results

25. 2005/11/10P 2525 Conclusions  KOZ scalable audio takes chaotic system to model audio signal  CPS is applied to find tones and their accurate freq.  Scalability is fulfilled by sorting classes of objects with order of their “perceptual relevance”