Adaptive post-filtering technique based on the Modified Yule-Walker filter

• US 6,233,552 B1
• Filed: 03/12/1999
• Issued: 05/15/2001
• Est. Priority Date: 03/12/1999
• Status: Expired due to Fees

• Current Assignee: COMSAT Corporation (Reorganized ISA SA)
• Original Assignee: COMSAT Corporation (Reorganized ISA SA)
• Inventors: Mustapha, Azhar, Yeldener, Suat
• Primary Examiner(s): Dorvil, Richemond
• Application Number:
  US09/266,770
• Time in Patent Office: 795 Days
• Field of Search: 704/209, 704/219, 704/205, 704/207, 704/226, 704/227, 704/228
• US Class Current: 704/209
• CPC Class Codes: G10L 19/06 Determination or coding of the spectral characteristics, e.g. of the short-term prediction coefficients

Abstract

An adaptive time-domain post-filtering technique is based on the modified Yule-Walker filter. This technique eliminates the problem of spectral tilt in speech spectrum that can be applied to various speech coders. The new post-filter has a flat frequency response at the formant peaks of speech spectrum. Information is gathered about the relation between poles and formants and then the formants and their bandwidths are estimated. The information about the formants and their bandwidths is then used to design the modified Yule-Walker filter based on a least squares fit in time domain.

Claims

1. A method of designing a filter for filtering a speech signal, said method comprising the steps of:

determining pole information comprising the locations of poles of an LPC spectrum of said speech signal;

estimating the location and bandwidth of formants of said speech signal based on said pole information;

estimating filter coefficients;

comparing a desired filter response characteristic to a filter response characteristic resulting from said estimated filter coefficients to obtain a difference value; and

adjusting said filter coefficients to minimize said difference value.

2. A method according to claim 1, wherein said adjusting step comprises minimizing said difference value according to a least squares method.

3. A method according to claim 1, wherein said step of estimating the location and bandwidth of formants comprises:

arranging at least some of said poles in a predetermined order;

calculating a magnitude of said LPC spectrum at at least some of said arranged poles;

calculating first and second slopes m₁ and m₂, respectively, of said LPC spectrum on either side of at least some of said arranged poles; and

estimating said location and bandwidth of formants based on the location, magnitude and neighboring slopes of said LPC spectrum poles.

4. A method according to claim 3, wherein said step of estimating said location and bandwidth of formants comprises:

(i) estimating first and second adjacent poles to represent different formants if the slope at said first pole is negative in a first direction toward said second pole and if the slope at said second pole is positive in said first direction coming from said first pole.

5. A method according to claim 4, wherein said step of estimating said location and bandwidth of formants further comprises:

(ii) estimating first and second adjacent poles to represent a common formant if the criteria of step (i) are not met and if a difference in magnitudes of said LPC spectrum is less than a threshold value.

6. A method according to claim 5, wherein said threshold value is approximately 3 dB.

7. A method according to claim 5, wherein said step of estimating said location and bandwidth of formants further comprises:

(iii) estimating the larger of said first and second poles to represent a formant if the criteria of steps (i) and (ii) are not met.

8. A method according to claim 7, wherein said step of estimating the location and bandwidth of formants further comprises:

assigning a bandwidth to each formant; and

combining two formants into a signal estimated formant if their assigned bandwidths overlap one another.

9. A method according to claim 1, wherein said filter is a modified Yule Walker filter having an impulse response of the form $\begin{array}{c}\frac{B}{}\end{array}$

(z)A

(z)=b

(1)+b

(2)

z-1+⋯

+b

(N)

z-(N-1)1+a

(1)

z-1+⋯

+a

(N)

z-(N-1)(3)

where N is the order of the filter, and (a(1), a(2), . . . , a(N)) and (b(1), b(2), . . . , b(N)) are filter coefficients.

10. A method according to claim 9, wherein said step of estimating said filter coefficients comprises estimating said coefficients (a(1), a(2), . . . , a(N)) according to Modified Yule-Walker equations using non-recursive correlation coefficients computed by inverse Fourier transformation of the desired filter frequency response.

11. A method according to claim 9, wherein said step of estimating said filter coefficients comprises estimating said coefficients (b(1), b(2), . . . , b(N)) according to the steps of:

computing a numerator polynomial corresponding to an additive decomposition of the power frequency response;

evaluating a complete frequency response of said filter;

estimating an impulse response of said filter; and

adjusting said numerator polynomial in accordance with a least squares fit to said impulse response.

12. A method according to claim 11, wherein said impulse response of said filter is estimated according to a spectral factorization technique.

13. A method according to claim 1, wherein said step of estimating said filter coefficients comprises assigning a unity gain factor to said filter in the region of each formant.

14. A method according to claim 13, wherein said step of estimating said filter coefficients further comprises assigning an attenuation factor τ

to said filter outside of a region of each formant.

15. A method according to claim 14, wherein said attenuation factor τ

is approximately 0.6.

16. A method according to claim 14, wherein said attenuation factor τ

can change from one frame to another of said speech signal.

17. A filter for filtering a speech signal in accordance with filter coefficients, said having a filter employing filter coefficients determined by a method comprising the steps of:

determining pole information comprising the locations of poles of an LPC spectrum of said speech signal;

estimating the location and bandwidth of formants of said speech signal based on said pole information;

estimating filter coefficients;

comparing a desired filter response characteristic to a filter response characteristic resulting from said estimated filter coefficients to obtain a difference value; and

adjusting said filter coefficients to minimize said difference value.

18. A filter according to claim 17, wherein said adjusting step comprises minimizing said difference value according to a least squares method.

19. A filter according to claim 17, wherein said step of estimating the location and bandwidth of formants comprises:

arranging at least some of said poles in a predetermined order;

calculating a magnitude of said LPC spectrum at at least some of said arranged poles;

calculating first and second slopes m₁ and m₂, respectively, of said LPC spectrum on either side of at least some of said arranged poles; and

estimating said location and bandwidth of formants based on the location, magnitude and neighboring slopes of said LPC spectrum poles.

20. A filter according to claim 19, wherein said step of estimating said location and bandwidth of formants comprises:

(i) estimating first and second adjacent poles to represent different formants if the slope at said first pole is negative in a first direction toward said second pole and if the slope at said second pole is positive in said first direction coming from said first pole.

21. A method according to claim 20, wherein said step of estimating said location and bandwidth of formants further comprises:

(ii) estimating first and second adjacent poles to represent a common formant if the criteria of step (i) are not met and if a difference in magnitudes of said LPC spectrum is less than a threshold value.

22. A method according to claim 21, wherein said threshold value is approximately 3 dB.