Aliasing reduction using complex-exponential modulated filterbanks

• US 20030016772A1
• Filed: 04/02/2002
• Published: 01/23/2003
• Est. Priority Date: 04/02/2001
• Status: Active Grant

• Current Assignee: Dolby International AB (Dolby Laboratories Incorporated)
• Original Assignee: Coding Technologies AB
• Inventors: Ekstrand, Per
• Granted Patent: US 7,242,710 B2
• Time in Patent Office: Days
• US Class Current: 375/350
• CPC Class Codes: H03H 17/0266 Filter banks

Abstract

The present invention proposes a new method and apparatus for the improvement of digital filterbanks, by a complex extension of cosine modulated digital filterbanks. The invention employs complex-exponential modulation of a low-pass prototype filter and a new method for optimizing the characteristics of this filter. The invention substantially reduces artifacts due to aliasing emerging from independent modifications of subband signals, for example when using a filterbank as an spectra equalizer. The invention is preferably implemented in software, running on a standard PC or a digital signal processor (DSP), but can also be hardcoded on a custom chip. The invention offers essential improvements for various types of digital equalizers, adaptive filters, multiband companders and spectral envelope adjusting filterbanks used in high frequency reconstruction (HFR) systems.

Claims

1. A method for estimation of energy measures of coefficients or subband signals obtained from a digital filterbank, characterized by:

optimizing a symmetric low-pass prototype filter p₀(n), having filter order N, not constrained to have the perfect reconstruction property;

building an M-channel analysis filterbank by complex-exponential modulation of said prototype filter;

where said filterbank has filter coefficients as

$h_k<br><br>\left(n\right)=p_0<br><br>\left(n\right)<br><br>\exp <br><br>\left\{\mathrm{<br><br>}<br><br>\frac{\mathrm{\pi <br><br>}}{2<br><br>M}<br><br>\left(2<br><br>k+1\right)<br><br>\left(n-\frac{N}{2}\right)\right\},$

 

and n=0, 1, . . . , N, and k=0,1, . . . , M−

1;

filtering a real-valued time domain signal through said filterbank; and

calculating the squared absolute values of the complex-valued subband signals obtained from said filtering.

2. A method according to claim 1, characterized in that said analysis filterbank is used to estimate average energy measures as

4. A method according to claims 1-3, characterized in that said low-pass prototype filter has a filter order N that is higher than 2M−

1, where M is the number of channels in said digital filterbank.

5. A method according to claims 1-4, characterized in that said optimization of said low-pass prototype filter is accomplished by minimizing a composite objective function ε

_tot(α

) as

ε

_tot(α

)=α

ε

_t+(1−

α

)ε

_α

where α

is a weighting constant;

ε

_t is the passband error and ε

_α

is the aliasing error.

6. A method according to claim 5, characterized in that said passband error ε

_t is calculated as

7. A method according to claim 6, characterized in that said alias gain terms are calculated using gain adjusted versions of said analysis and synthesis filters according to

h_k^(eq)(n)=g_kh_k(n) and f_k^(eq)(n)=g_kf_k(n),

where g_k represents randomized or deterministic real-valued gainfactors, n=0 . . . N, and k=0 . . . M−

1.

8. A method according to claims 5-7, characterized in that said low-pass prototype filter has a filter order of at least a number N, where N is chosen so that said composite objective function is smaller than a predefined value.

9. A method according to claims 1-2, characterized in that said analysis filterbank is used for the estimation of energy measures in a high frequency reconstruction system.

3. A method for reduction of aliasing emerging from modifications of the coefficients or subband signals obtained from a digital filterbank, characterized by:

optimizing a symmetric low-pass prototype filter p₀(n), having filter order N, not constrained to have the perfect reconstruction property;

building an M-channel filterbank by complex-exponential modulation of said prototype filter;

where said filterbank has analysis and synthesis filter coefficients as

$h_k<br><br>\left(n\right)=f_k<br><br>\left(n\right)=p_0<br><br>\left(n\right)<br><br>\exp <br><br>\left\{\mathrm{<br><br>}<br><br>\frac{\mathrm{\pi <br><br>}}{2<br><br>M}<br><br>\left(2<br><br>k+1\right)<br><br>\left(n-\frac{N}{2}\right)\right\},$

 

and n=0 . . . N, and k=0 . . . M−

1;

filtering a real-valued time domain signal through the analysis part of said filterbank;

modifying the complex-valued subband signals obtained from said filtering;

filtering said modified complex-valued subband signals through the synthesis part of said filterbank; and

taking the real part of the complex-valued time domain output signal, where said output signal is the sum of the signals obtained from said synthesis filtering.

10. A method according to claims 3-8, characterized in that said complex-exponential modulated filterbank is used as the envelope adjusting filterbank in a high frequency reconstruction system.

11. A method according to claims 3-8, characterized in that said complex-exponential modulated filterbank is used as the filters in a digital equalizing system.

12. A method according to claims 3-8, characterized in that said complex-exponential modulated filterbank is used in an adaptive filtering system.

13. A method according to claims 3-8, characterized in that said complex-exponential modulated filterbank is used in a multiband compander system.

14. An apparatus for estimation of energy measures of coefficients or subband signals obtained from a digital filterbank, characterized by:

means for optimizing a symmetric low-pass prototype filter p₀(n), having filter order N, not constrained to have the perfect reconstruction property;

means for building an M-channel analysis filterbank by complex-exponential modulation of said prototype filter;

where said filterbank has filter coefficients as

$h_k<br><br>\left(n\right)=p_0<br><br>\left(n\right)<br><br>\exp <br><br>\left\{\mathrm{<br><br>}<br><br>\frac{\mathrm{\pi <br><br>}}{2<br><br>M}<br><br>\left(2<br><br>k+1\right)<br><br>\left(n-\frac{N}{2}\right)\right\},$

 

and n=0, 1, . . . , N, and k=0,1, . . . , M−

1;

means for filtering a real-valued time domain signal through said filterbank; and

means for calculation of the squared absolute values of the complex-valued subband signals obtained from said filtering.

15. An apparatus for reduction of aliasing emerging from modifications of the coefficients or subband signals obtained from a digital filterbank, characterized by:

means for optimizing a symmetric low-pass prototype filter p₀(n), having filter order N, not constrained to have the perfect reconstruction property;

means for building an M-channel filterbank by complex-exponential modulation of said prototype filter;

where said filterbank has analysis and synthesis filter coefficients as

$h_k<br><br>\left(n\right)=f_k<br><br>\left(n\right)=p_0<br><br>\left(n\right)<br><br>\exp <br><br>\left\{\mathrm{<br><br>}<br><br>\frac{\mathrm{\pi <br><br>}}{2<br><br>M}<br><br>\left(2<br><br>k+1\right)<br><br>\left(n-\frac{N}{2}\right)\right\},$

 

and n=0, 1, . . . , N and k=0,1, . . . , M−

1;

means for filtering a real-valued time domain signal through the analysis part of said filterbank;

means for modifying the complex-valued subband signals obtained from said filtering;

means for filtering said modified complex-valued subband signals through the synthesis part of said filterbank; and

means for taking the real part of the complex-valued time domain output signal, where said output signal is the sum of the signals obtained from said synthesis filtering.