Cross product enhanced harmonic transposition

1. A system for generating a high frequency component of an audio signal from a low frequency component of the audio signal, comprising:

an analysis filter bank providing a plurality of analysis subband signals of the low frequency component of the audio signal;

a non-linear processing unit to generate a synthesis subband signal with a synthesis frequency by multiplying the phase of a first and a second of the plurality of analysis subband signals and by combining the phase-multiplied analysis subband signals; and

a synthesis filter bank for generating the high frequency component of the audio signal from the synthesis subband signal;

wherein

the non-linear processing unit comprises a multiple-input-single-output unit of a first and second transposition order generating the synthesis subband signal from the first and the second analysis subband signals with a first analysis frequency ω and a second analysis frequency (ω+Ω), respectively;

the first analysis subband signal is phase-multiplied by the first transposition order (T-r);

the second analysis subband signal is phase-multiplied by the second transposition order r;

T>1; 1≦r<T; and

the synthesis frequency is (T−r)·ω+r·(ω+Ω).

2. The system according to claim 1 , further comprising:

a gain unit for multiplying the synthesis subband signal by a gain parameter.

3. The system according to claim 1 , further comprising

a plurality of multiple-input-single-output units and/or a plurality of non-linear processing units which generate a plurality of partial synthesis subband signals with the synthesis frequency; and

a subband summing unit for combining the plurality of partial synthesis subband signals.

4. The system according to claim 1 , wherein the non-linear processing unit further comprises:

a direct processing unit for generating a further synthesis subband signal from a third of the plurality of analysis subband signals; and

a subband summing unit for combining synthesis subband signals with the synthesis frequency.

5. The system according to claim 4 , wherein

the subband summing unit ignores the synthesis subband signals generated in the multiple-input-single-output units if the minimum of the magnitude of the first and second analysis subband signals is smaller than a pre-defined fraction of the magnitude of the signal.

6. The system according to claim 4 , wherein the direct processing unit comprises:

a single-input-single-output unit of a third transposition order T′, generating the synthesis subband signal from the third analysis subband signal exhibiting a third analysis frequency, wherein

the third analysis subband signal is phase-modified by the third transposition order T′;

T′ is greater than one; and

the synthesis frequency corresponds to the third analysis frequency multiplied by the third transposition order.

7. The system according to claim 1 , wherein

the signal comprises a fundamental frequency; and

the analysis filter bank exhibits a frequency spacing which is associated with the fundamental frequency of the signal.

8. The system according to claim 1 , wherein

the analysis filter bank has N analysis subbands at a constant subband spacing of Δω;

an analysis subband is associated with an analysis subband index n, with nε{1, . . . , N};

the synthesis filter bank has a synthesis subband;

the synthesis subband is associated with a synthesis subband index n; and

the synthesis subband and the analysis subband with index n each comprise frequency ranges which relate to each other through the factor T.

9. The system according to claim 8 , wherein

the synthesis subband signal is associated with the synthesis subband with index n;

the first analysis subband signal is associated with an analysis subband with index n−p 1 ;

the second analysis subband signal is associated with an analysis subband with index n+p 2 ; and

the system further comprises an index selection unit for selecting p 1 and p 2 .

10. The system according to claim 9 , wherein

the index selection unit is operable to select the index shifts p 1 and p 2 from a limited list of pairs (p 1 , p 2 ) stored in an index storing unit; and

the index selection unit is operable to select the pair (p 1 , p 2 ) such that the minimum value of a set comprising the magnitude of the first analysis subband signal and the magnitude of the second analysis subband signal is maximized.

11. The system according to claim 9 , wherein the index selection unit is operable to determine a limited list of pairs (p 1 , p 2 ) such that

the index shift p 1 =r·l;

the index shift p 2 =(T−r)·l; and

−l is a positive integer; and

wherein the index selection unit is operable to select the parameters l and r such that the minimum value of the set comprising the magnitude of the first analysis subband signal and the magnitude of the second analysis subband signal is maximized.

12. The system according to claim 9 , wherein the index selection unit is operable to select the index shifts p 1 and p 2 based on a characteristic of the signal.

13. The system according to claim 12 , wherein

the signal comprises a fundamental frequency Ω;

the index selection unit is operable to select the index shifts p 1 and p 2 such that

their sum of the index shifts p 1 +p 2 approximates the fraction Ω/Δω; and

their fraction p 1 /p 2 is a multiple of r/(T−r).

14. The system according to claim 12 , wherein

the signal comprises a fundamental frequency Ω;

the index selection unit is operable to select the index shifts p 1 and p 2 such that

their sum of the index shifts p 1 +p 2 approximates the fraction Ω/Δω; and

the fraction p 1 /p 2 equals r/(T−r).

15. The system according to claim 1 , further comprising:

a core decoder for decoding the low frequency component of the signal;

an upsampler for performing an upsampling of the low frequency component to yield an upsampled low frequency component;

an envelope adjuster to shape the high frequency component; and

a component summing unit to determine the decoded signal as the sum of the upsampled low frequency component and the adjusted high frequency component.

16. The system according to claim 15 , further comprising

a subband selection reception unit for receiving information which allows the selection of the first and second analysis subband signals from which the synthesis subband signal is to be generated.

17. A method for performing high frequency reconstruction of a high frequency component from a low frequency component of an audio signal, comprising:

providing a first subband signal of the low frequency component with a first frequency ω and a second subband signal of the low frequency component with a second frequency (ω+Ω);

multiplying a phase of the first subband signal with a first transposition factor (T−r) to yield a first transposed subband signal;

multiplying a phase of the second subband signal with a second transposition factor r to yield a second transposed subband signal; wherein T>1; and 1≦r<T; and

combining the first and second transposed subband signals to yield a high frequency component with a high frequency (T−r)·ω+r·(ω+Ω).

18. The method according to claim 17 , wherein the combining step comprises:

multiplying the first and the second transposed subband signals to yield a high subband signal; and

inputting the high subband signal into a synthesis filter bank to generate the high frequency component.

19. The method according to claim 17 further comprising:

decoding an encoded audio signal to yield the low frequency component of the audio signal, wherein the encoded signal is derived from an original audio signal, and represents only a portion of frequency subbands of the original signal below a cross-over frequency.