Frequency extension of harmonic signals

• US 20060293016A1
• Filed: 06/28/2005
• Published: 12/28/2006
• Est. Priority Date: 06/28/2005
• Status: Active Grant

• Current Assignee: Blackberry Limited
• Original Assignee: Harman Becker Automotive Systems GmbH (Samsung Group)
• Inventors: Li, Xueman, Giesbrecht, David, Hetherington, Phillip
• Granted Patent: US 8,311,840 B2
• Time in Patent Office: Days
• US Class Current: 455/308
• CPC Class Codes: G10L 21/038 using band spreading techniques

Abstract

A system and methods are provided for extending the frequency bandwidth of a harmonic signal. Harmonic content of a band-limited signal is extended to frequencies outside the signal'"'"'s passband by performing a non-linear transformation on the complex spectrum of the band-limited signal in the frequency domain. The non-linear transformation may be accomplishes by a linear convolution of the complex spectrum with itself. A system for extending the frequency bandwidth of a harmonic signal includes a signal processor with a forward transform module for transforming a time domain signal into the frequency domain, a non-linear transform module for performing the non-linear transformation on the complex spectrum of the harmonic signal, and a reverse transform module for transforming the extended spectrum of the harmonic signal back into the time domain.

Claims

1. A method of extending harmonics of a band-limited harmonic signal, the method comprising:

transforming a band-limited harmonic signal from the time domain to the frequency domain to obtain a complex spectrum of the band-limited harmonic signal;

performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal in the frequency domain to extend harmonic content of the band-limited harmonic signal to frequencies outside the limited frequency band of the band-limited harmonics signal; and

inverse transforming the extended complex spectrum of the band-limited harmonic signal back into the time domain.

2. The method of claim 1 wherein the step of transforming a band-limited harmonic signal from the time domain to the frequency domain comprises performing a Fast Fourrier Transform (FFT) on the band-limited harmonics signal.

3. The method of claim 2 wherein the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal comprises performing a linear convolution on the complex spectrum of the band-limited harmonics signal with itself.

4. The method of claim 3 wherein the linear convolution is performed according to the formula

Y(k)=X(k)*X(k) k=0 . . . N/2

where * denotes a linear convolution operation, k is the frequency index and N is the length of the FFT used in transforming the band-limited harmonic signal from the time domain to the frequency domain.

5. The method of claim 2 wherein the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal comprises performing a linear convolution on the complex spectrum of the band-limited harmonic signal with a mirrored complex conjugate of the complex spectrum of the band-limited harmonic signal.

6. The method of claim 2 wherein the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal comprises performing a linear convolution on the spectrum of the band-limited harmonic signal weighted by a first weighting factor and the complex spectrum of the band-limited harmonic signal weighted by a second weighting factor.

7. The method of claim 2 wherein the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal comprises performing a linear convolution of a portion of the complex spectrum of the band-limited harmonic signal with a portion of the complex spectrum of the band-limited harmonic signal.

8. The method of claim 1 wherein in the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal in the frequency domain, the non-linear transformation is selected such that harmonic energy is added to at least one harmonic frequency above an upper frequency limit of the band-limited harmonic signal.

9. The method of claim 1 a wherein in the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal in the frequency domain, the non-linear transformation is selected such that harmonic energy is added to at least one harmonic frequency below a lower frequency limit of the band-limited harmonic signal.

10. The method of claim 1 wherein the step of transforming a band-limited harmonic signal from the time domain to the frequency domain comprises employing one of:

a Discrete Fourrier Transform (DFT);

a Discrete Cosine Transform (DCT);

a filter bank;

or a wavelet transform.

15. The method of claim 2 wherein the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal comprises performing a linear convolution on the complex spectrum of the band-limited harmonic signal with a mirrored complex conjugate of the complex spectrum of the band-limited harmonic signal.

11. A harmonic extension method comprising:

receiving a band-limited harmonic signal having significant signal energies at regular frequency intervals within a limited frequency band defined by a passband lower frequency limit and a passband upper frequency limit;

transforming the band-limited harmonic signal from the time domain to the frequency domain to obtain a complex spectrum of the received band-limited harmonic signal;

performing a non-linear transformation of the complex spectrum of the received band-limited harmonic signal in the frequency domain to generate an extended spectrum having harmonic energy at at least one harmonic frequency at which harmonic energy was absent in the received band limited harmonic signal; and

transforming the extended spectrum into the time domain.

12. The harmonic extension method of claim 11 wherein the step of transforming the band-limited harmonic signal from the time domain to the frequency domain comprises performing a Fast Fourrier Transform on the band-limited harmonic signal.

13. The method of claim 12 wherein the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal comprises performing a linear convolution on the complex spectrum of the band-limited harmonics signal with itself.

14. The method of claim 13 wherein the linear convolution is performed according to the formula

Y(k)=X(k)*X(k) k=0 . . . N/2

where * denotes a linear convolution operation, k is the frequency index and N is the length of the FFT used in transforming the band-limited harmonic signal from the time domain to the frequency domain.

16. The method of claim 12 wherein the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal comprises performing a linear convolution on the spectrum of the band-limited harmonic signal weighted by a first weighting factor and the complex spectrum of the band-limited harmonic signal weighted by a second weighting factor.

17. The method of claim 12 wherein the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal comprises performing a linear convolution of a portion of the complex spectrum of the band-limited harmonic signal with a portion of the complex spectrum of the band-limited harmonic signal.

18. The method of claim 11 wherein in the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal in the frequency domain, the non-linear transformation is selected such that harmonic energy is added to at least one harmonic frequency above an upper frequency limit of the band-limited harmonics signal.

19. The method of claim 11 a wherein in the step of performing a non-linear transformation on the complex spectrum of the band-limited harmonic signal in the frequency domain, the non-linear transformation is selected such that harmonic energy is added to at least one harmonic frequency below a lower frequency limit of the band-limited harmonic signal.

20. The method of claim 11 wherein the step of transforming a band-limited harmonic signal from the time domain to the frequency domain comprises employing one of:

a Discrete Fourier Transform (DFT);

a Discrete Cosine Transform (DCT);

a digital filter bank;

or a wavelet transform.

21. A system for extending harmonics of a band-limited harmonic signal, the system comprising:

means for receiving a band-limited harmonic signal; and

a signal processor having a forward transform module for transforming the received band-limited harmonic signal from the time domain to the frequency domain to generate a complex spectrum of the band-limited signal; and

a harmonic generation module for performing a non-linear transformation of the complex spectrum of the band-limited signal in the frequency domain to create a harmonically extended spectrum of the band-limited harmonics signal; and

a reverse transform module for transforming the harmonically extended spectrum of the band-limited harmonics signal back to the time domain.

22. The system of claim 21 wherein the for transform employ is one of a Discrete Fourier Transform (FFT);

the Discrete Fourier transform (DFT);

a Discrete Cosine Transform (DCT);

a digital filter bank;

or a wavelet transforms to transform the band-limited harmonic signal into the frequency domain.

23. The system of claim 21 wherein the non-linear transformation module employs linear convolution in the frequency domain to create the harmonically extended spectrum of the band-limited harmonic signal.

24. The system of claim 23 wherein the linear convolution is performed on the complex spectrum of the band-limited harmonics signal with itself.

25. The system of claim 23 wherein the linear convolution is performed on the complex spectrum of the band-limited harmonic signal in the mirrored complex conjugate of the complex spectrum of the band-limited harmonic signal.

26. The system of claim 23 wherein the linear convolution is performed on the complex spectrum of the band-limited harmonics signal weighted by a first weighting factor, with the complex spectrum of the band-limited harmonic signal weighted by a second weighting factor.

27. A system for extending harmonics and spectral envelope of a band-limited harmonic signal and combining the extended signal with the original band-limited signal, the system comprising:

means for receiving a band-limited harmonic signal; and

a signal processor having a forward transform module for transforming the received band-limited harmonic signal from the time domain to the frequency domain to generate a complex spectrum of the band-limited signal; and

a harmonic generation module for performing a non-linear transformation of the complex spectrum of the band-limited signal in the frequency domain to create a harmonically extended spectrum of the band-limited harmonics signal; and

a spectral envelope extender module to ensure the spectral envelope of the extended harmonics is complimentary to that of the original band-limited signal; and

a combiner module to combine the harmonic extended spectrum with the original band-limited spectrum; and

a reverse transform module for transforming the final frequency extended harmonic spectrum back to the time domain.

28. The system of claim 27 wherein the for transform employ is one of a Discrete Fourier Transform (FFT);

the Discrete Fourier transform (DFT);

a Discrete Cosine Transform (DCT);

a digital filter bank;

or a wavelet transforms to transform the band-limited harmonic signal into the frequency domain.

29. The system of claim 27 wherein the non-linear transformation module employs linear convolution in the frequency domain to create the harmonically extended spectrum of the band-limited harmonic signal.

30. The system of claim 29 wherein the linear convolution is performed on the complex spectrum of the band-limited harmonics signal with itself.

31. The system of claim 29 wherein the linear convolution is performed on the complex spectrum of the band-limited harmonic signal in the mirrored complex conjugate of the complex spectrum of the band-limited harmonic signal.

32. The system of claim 29 wherein the linear convolution is performed on the complex spectrum of the band-limited harmonics signal weighted by a first weighting factor, with the complex spectrum of the band-limited harmonic signal weighted by a second weighting factor.