Digital audio precompensation

• US 20040125487A9
• Filed: 04/17/2002
• Published: 07/01/2004
• Est. Priority Date: 04/17/2002
• Status: Active Grant

• Current Assignee: Dirac Research AB
• Original Assignee: Dirac Research AB
• Inventors: Ahlen, Anders, Sternad, Mikael
• Granted Patent: US 7,215,787 B2
• Time in Patent Office: Days
• US Class Current: 360/65
• CPC Class Codes: H04R 29/007 for public address systems public address systems per se H04R27/00
• CPC Class Codes: H04R 3/04 for correcting frequency response
• CPC Class Codes: H04S 7/307 Frequency adjustment, e.g. tone control H04S7/301 takes precedence

Abstract

The invention concerns digital audio precompensation, and particularly the design of digital precompensation filters. The invention proposes an audio precompensation filter design scheme that uses a novel class of design criteria. Briefly, filter parameters are determined based on a weighting between, on one hand, approximating the precompensation filter to a fixed, non-zero filter component and, on the other hand, approximating the precompensated model response to a reference system response. For design purposes, the precompensation filter is preferably regarded as being additively decomposed into a fixed, non-zero component and an adjustable compensator component. The fixed component is normally configured by the filter designer, whereas the adjustable compensator component is determined by optimizing a criterion function involving the above weighting. The weighting can be made frequency- and/or channel-dependent to provide a very powerful tool for effectively controlling the extent and amount of compensation to be performed in different frequency regions and/or in different channels.

Claims

1. A method for designing a precompensation filter based on a model of the response of an associated sound generating system, said method comprising the step of determining filter parameters of said precompensation filter based on a given weighting between, on one hand, approximating the precompensation filter to a fixed, non-zero filter component and, on the other hand, approximating the precompensated model response to a reference system response.

2. The method according to claim 1, wherein said precompensation filter, for design purposes, is regarded as being additively decomposed into said fixed filter component and an adjustable compensator component, said method further comprising the step of determining said adjustable compensator component of said precompensation filter by optimizing a criterion function including said weighting, and wherein said filter parameters of said precompensation filter are determined based on said fixed filter component and said determined compensator component.

3. The method according to claim 1, further comprising the steps of configuring said fixed filter component and configuring said weighting.

4. The system according to claim 1, wherein said fixed filter component includes a by-pass component with at least one selectable delay element.

5. The method according to claim 1, wherein said model of the response of the sound generating system is a linear dynamic model and said precompensation filter is a linear dynamic filter.

6. The method according to claim 1, wherein said weighting includes a frequency-dependent weighting function.

7. The method according to claim 6, wherein said frequency-dependent weighting function is configured to enable different degrees of compensation in different frequency regions within the frequency range described by said model.

8. The method according to claim 6, wherein said frequency-dependent weighting function is configured such that the compensated model response approximates the reference system response in a set of user-specified frequency ranges, while the compensated model response approximates the by-passed model response in another set of user-specified frequency ranges.

9. The method according to claim 8, wherein the degree of approximation is measured by any appropriate norm for dynamic systems.

10. The method according to claim 1, wherein said sound generating system is a multi-channel system, and said precompensation filter includes multiple filters, each of which, for design purposes, has an individual non-zero by-pass component and an individual compensator component.

11. The method according to claim 10, wherein said weighting includes a channel-dependent weighting function.

12. The method according to claim 11, wherein said channel-dependent weighting function is configured to enable different types of compensation in different channels of said multi-channel system.

13. The method according to claim 1, wherein said step of optimizing said criterion function is performed on-line by using recursive optimization or adaptive filtering.

14. The method according to claim 1, wherein said step of optimizing said criterion function is performed as a model-based off-line design.

15. The method according to claim 2, wherein said step of determining said compensator component comprises the step of minimizing said weighted criterion function with respect to adjustable filter parameters in said compensator component.

16. The method according to claim 15, wherein said criterion function is defined as:

J=E|V(HR−

D)w(t)|²+E|WCw(t)|²,

where H is a representation of said model, R is a representation of said precompensation filter, D is a representation of said reference system, C is a representation of said adjustable compensator component, W is a weighting function representing said weighting, and V is a further optional weighting function, both of said weighting functions being linear and stable transfer function matrices, w(t) is an input signal to said precompensation filter, and E( ) denotes the expectation with respect to said input signal w(t).

17. The method according to claim 16, wherein said precompensation filter is implemented as a state-space realization of a stable IIR filter, and is based on the minimization of said criterion function by linear quadratic state-space tools.

18. The method according to claim 16, wherein said precompensation filter is implemented in the form of a stable IIR Wiener filter, where the fixed, non-zero by-pass component, represented by F, is configured as an FIR filter so that:

F(q<sup>−

1</sup>)=q<sup>−

d+k</sup>F(q<sup>−

1</sup>),

where q<sup>−

x</sup> is the standard backward shift operator with x steps, while q^x is the standard forward shift operator with x steps and said adjustable compensator component C is a stable recursive filter defined as;

β

(q<sup>−

1</sup>)N(q<sup>−

1</sup>)G(q<sup>−

1</sup>)C(q<sup>−

1</sup>)=Q(q<sup>−

1</sup>)V(q<sup>−

1</sup>),

where the polynomial Q(q<sup>−

1</sup>) is, together with an anti-causal FIR filter L*(q), given by the unique solution to the linear scalar Diophantine polynomial equation;

z<sup>−

d+k</sup>[D(q<sup>−

1</sup>)A(q<sup>−

1</sup>)−

F(q<sup>−

1</sup>)B(q<sup>−

1</sup>)N(q <sup>−

1</sup>)]G(q<sup>−

1</sup>)V*(q)B*(q)=Q(q<sup>−

1</sup>)rβ

*(q)−

A(q<sup>−

1</sup>)N(q<sup>−

1</sup>)H(q<sup>−

1</sup>)qL*(q),

while the monic polynomial β

(q<sup>−

1</sup>) is, together with a scalar r, given by the unique stable solution to the polynomial spectral factorization;

rβ

(q<sup>−

1</sup>)β

*(q)=V(q<sup>−

1</sup>)V*(q)B(q<sup>−

1</sup>)B*(q)+W(q<sup>−

1</sup>)W*(q)A(q<sup>−

1</sup>)A*(q),

where A, B, G, L, N are auxiliary polynomials.

19. The method according to claim 1, wherein said model of the response of the sound generating system is a non-linear dynamic model and said precompensation filter is a non-linear dynamic filter.

42. A precompensation filter designed by using the method according to claim 1.

43. An audio system comprising a sound generating system and a precompensation filter in the input path to said sound generating system, wherein said precompensation filter is designed by using the method according to claim 1.

44. A digital audio signal generated by a precompensation filter designed by the method according to claim 1.

45. The digital audio signal according to claim 44, wherein said digital signal is encoded on a medium readable by a sound generating system.

20. A system for designing a precompensation filter based on a model of the response of an associated sound generating system, said system comprising means for determining filter parameters of said precompensation filter based on a given weighting between, on one hand, approximating the precompensation filter to a fixed, non-zero filter component and, on the other hand, approximating the precompensated model response to a reference system response.

21. The system according to claim 20, wherein said precompensation filter, for design purposes, is regarded as being additively decomposed into said fixed filter component and an adjustable compensator component, said system further comprising means for determining said adjustable compensator component of said precompensation filter by optimization of a criterion function that is based on said weighting, and wherein said means for determining filter parameters is operable for determining said filter parameters based on said fixed filter component and said determined compensator component.

22. The system according to claim 20, further comprising means for configuring said fixed filter component and means for configuring said weighting.

23. The system according to claim 20, wherein said fixed filter component includes a by-pass component with at least one selectable delay element.

24. The system according to claim 20, wherein said model of the response of the sound generating system is a linear dynamic model and said precompensation filter is a linear dynamic filter.

25. The system according to claim 20, wherein said weighting includes a frequency-dependent weighting function.

26. The system according to claim 25, wherein said frequency-dependent weighting function is configured to enable different degrees of compensation in different frequency regions within the frequency range described by said model.

27. The system according to claim 25, wherein said frequency-dependent weighting function is configured such that the compensated model response approximates the reference system response in a set of user-specified frequency ranges, while the compensated model response approximates the by-passed model response in another set of user-specified frequency ranges.

28. The system according to claim 27, wherein the degree of approximation is measured by any appropriate norm for dynamic systems.

29. The system according to claim 20, wherein said sound generating system is a multi-channel system, and said precompensation filter includes multiple filters, each of which, for design purposes, has an individual non-zero by-pass component and an individual compensator component.

30. The system according to claim 29, wherein said weighting includes a channel-dependent weighting function.

31. The system according to claim 30, wherein said channel-dependent weighting function is configured to enable different types of compensation in different channels of said multi-channel system.

32. The system according to claim 20, wherein said optimization of said criterion function is performed on-line by means of recursive optimization or adaptive filtering.

33. The system according to claim 20, wherein said optimization of said criterion function is performed as a model-based off-line design.

34. The system according claim 21, wherein said means for determining said compensator component comprises means for minimizing said weighted criterion function with respect to adjustable filter parameters in said compensator component.

35. The system according to claim 34, wherein said criterion function is defined as:

J=E|V(HR−

D)w(t)|²+E|WCw(t)|²,

where H is a representation of said model, R is a representation of said precompensation filter, D is a representation of said reference system, C is a representation of said adjustable compensator component, W is a weighting function representing said weighting, and V is a further optional weighting function, both of said weighting functions being linear and stable transfer function matrices, w(t) is an input signal to said precompensation filter, and E( ) denotes the expectation with respect to said input signal w(t).

36. The system according to claim 35, wherein said precompensation filter is implemented as a state-space realization of a stable IIR filter, and is based on the minimization of said criterion function by linear quadratic state-space tools.

37. The system according to claim 35, wherein said precompensation filter is implemented in the form of a stable IIR Wiener filter, where the fixed, non-zero by-pass component, represented by F, is configured as an FIR filter so that:

F(q<sup>−

1</sup>)=q<sup>−

d+k</sup>F(q<sup>−

1</sup>),

where q<sup>−

x</sup> is the standard backward shift operator with x steps, while q^x is the standard forward shift operator with x steps, and said adjustable compensator component C is a stable recursive filter defined as;

β

(q<sup>−

1</sup>)N(q<sup>−

1</sup>)G(q<sup>−

1</sup>)C(q<sup>−

1</sup>)=Q(q<sup>−

1</sup>)V(q<sup>−

1</sup>),

where the polynomial Q(q<sup>−

1</sup>) is, together with an anti-causal FIR filter L*(q), given by the unique solution to the linear scalar Diophantine polynomial equation;

z<sup>−

d+k</sup>[D(q<sup>−

1</sup>)A(q<sup>−

1</sup>)−

F(q<sup>−

1</sup>)B(q<sup>−

1</sup>)N(q <sup>−

1</sup>)]G(q<sup>−

1</sup>)V*(q)B*(q)=Q(q<sup>−

1</sup>)rβ

*(q)−

A(q<sup>−

1</sup>)N(q<sup>−

1</sup>)H(q<sup>−

1</sup>)qL*(q),

while the monic polynomial β

(q<sup>−

1</sup>) is, together with a scalar r, given by the unique stable solution to the polynomial spectral factorization;

rβ

(q<sup>−

1</sup>)β

*(q)=V(q<sup>−

1</sup>)V*(q)B(q<sup>−

1</sup>)B*(q)+W(q<sup>−

1</sup>)W*(q)A(q<sup>−

1</sup>)A*(q),

where A, B, G, L, N are auxiliary polynomials.

38. The system according to claim 20, wherein said model of the response of the sound generating system is a non-linear dynamic model and said precompensation filter is a non-linear dynamic filter.

39. A computer program product for designing, when running on a computer, a precompensation filter based on a model of the response of an associated sound generating system, said computer program comprising:

program means for configuring a fixed, non-zero component of said precompensation filter;

program means for configuring a weighting between, on one hand, approximating the precompensation filter to said fixed component and, on the other hand, approximating the precompensated model response to a reference system response;

program means for determining an adjustable compensator component of said precompensation filter by optimization of a criterion function that is based on said weighting; and

program means for determining filter parameters of said precompensation filter based on said configured fixed filter component and said determined compensator component.

40. The computer program product according to claim 39, wherein said fixed filter component includes a by-pass component with at least one selectable delay element.

41. The computer program product according to claim 39, wherein said computer program product is encoded on a computer-readable medium.