Direct-diffuse decomposition
View Patent ↗There is disclosed methods and apparatus for decomposing a signal having a plurality of channels into direct and diffuse components. The correlation coefficient between each pair of signals from the plurality of signals may be estimated. A linear system of equations relating the estimated correlation coefficients and direct energy fractions of each of the plurality of channels may be constructed. The linear system may be solved to estimate the direct energy fractions. A direct component output signal and a diffuse component output signal may be generated based in part on the direct energy fractions.
1. A method for direct-diffuse decomposition of an input signal having three or more channels, comprising:
estimating correlation coefficients between each pair of channels from three or more channels;
constructing a linear system of equations relating the estimated correlation coefficients and direct energy fractions of each of the three or more channels;
solving the linear system to estimate the direct energy fractions; and
generating a direct component output signal and a diffuse component output signal based in part on the direct energy fractions.
2. The apparatus of claim 1 further comprising:
separating each of the three or more channels into a plurality of frequency bands; and
performing the estimating, constructing, solving, and generating independently for each of the plurality of frequency bands.
3. The method of claim 1 , wherein each equation in the linear system has the form
log
(
ρ
X
i
,
X
j
)
=
log
(
φ
i
)
+
log
(
φ
j
)
2
wherein:
ρ x i ,x j is the correlation coefficient between channels i and j of the plurality of channels, and
φ i and φ j are the direct energy fractions of channels i and j.
4. The method of claim 1 , wherein estimating the correlation coefficient between each pair of channels is performed using a recursive formula.
5. The method of claim 4 , further comprising:
compensating the recursive correlation coefficient estimates by
setting correlation coefficient estimates below a predetermined value to zero, and
linearly expanding the range of correlation coefficient estimates greater than or equal to the predetermined value to the range [0, 1].
6. The method of claim 1 , wherein generating a direct component output signal and a diffuse component output signal further comprises:
generating direct and diffuse masks based on the direct energy fractions of each of the three or more channels; and
multiplying the input signal by the direct and diffuse masks to provide the direct component output signal and the diffuse component output signal.
7. The method of claim 1 , wherein generating a direct component output signal and a diffuse component output signal further comprises:
estimating a magnitude and phase angle of a direct basis based on, in part, the direct energy fractions of the three or more channels;
estimating a direct component energy and phase shift for each of the three or more channels based, in part, on the respective direct energy fraction; and
generating a direct component output signal for each of the three or more channels from the respective direct component energy and phase shift and the magnitude and phase angle of the direct basis.
8. The method of claim 7 , further comprising:
estimating a diffuse component output signal for each of the three or more channels by subtracting the respective estimated direct component from a respective channel.
9. The method of claim 1 , wherein solving the linear system further comprises:
using one of a linear least square method and a weighted least squares method to solve an overdetermined system of equations.
10. A method for direct-diffuse decomposition of an input signal having three or more input signal channels, comprising:
separating each of the three or more input signal channels into a plurality of frequency bands,
estimating correlation coefficients between each pair of input signal channels from the three or more input signal channels for each of the plurality of frequency bands;
constructing linear systems of equations relating the estimated correlation coefficients and direct energy fractions for each of the plurality of frequency bands;
solving the linear systems to estimate the direct energy fractions for each of the of three or more input signal channels for each of the plurality of frequency bands; and
generating a direct component output signal and a diffuse component output signal for each of the plurality of frequency bands based in part on the direct energy fractions.
11. The method of claim 10 , wherein each equation in the linear system for each of the plurality of frequency bands has the form
log
(
ρ
X
i
,
X
j
)
=
log
(
φ
i
)
+
log
(
φ
j
)
2
wherein:
ρ x i ,x j is the correlation coefficient between input signal channels i and j of the plurality of input signal channels, and
φ i and φ j are the direct energy fractions of input signal channels i and j.
12. The method of claim 11 , wherein estimating the correlation coefficient between each pair of input signal channels is performed using a recursive formula.
13. The method of claim 12 , further comprising:
compensating the recursive correlation coefficient estimates by
setting correlation coefficient estimates below a predetermined value to zero, and
linearly expanding the range of correlation coefficient estimates greater than or equal to the predetermined value to the range [0, 1].
14. The method of claim 10 , wherein generating a direct component output signal and a diffuse component output signal further comprises:
generating direct and diffuse masks for each of the plurality of frequency bands based on the direct energy fractions of each of the three or more input signal channels; and
for each of the plurality of frequency bands, multiplying the input signal by the direct and diffuse masks to provide the direct component output signal and the diffuse component output signal.
15. The method of claim 14 , further comprising:
smoothing the direct and diffuse masks across time and/or frequency.
16. The method of claim 15 , wherein smoothing the direct and diffuse masks further comprises:
smoothing the direct and diffuse mask based, in part, on an estimate of the variance of the correlation coefficient estimates for the three or more input signal channels and plurality of frequency bands.
17. The method of claim 10 , wherein estimating the correlation coefficient between a pair of input signal channels from the three or more input signal channels in one of the plurality of frequency bands further comprises:
if a difference between the pair of input signal channels exceeds a predetermined threshold, overestimating the correlation coefficient between the pair of input signal channels.
18. The method of claim 10 , wherein estimating the correlation coefficient between a pair of signals from the three or more input signal channels in one of the plurality of frequency bands further comprises:
if one of the pair of input signal channels includes a transient, overestimating the correlation coefficient between the pair of input signal channels.
19. The method of claim 10 , wherein solving the linear systems further comprises:
using one of a linear least square method and a weighted least squares method to solve an overdetermined system of equations.
20. An apparatus for direct-diffuse decomposition of an input signal having three or more channels, comprising:
a processor;
a memory coupled to the processor; and
a storage device coupled to the processor, the storage device storing instructions that, when executed by the processor, cause the computing device to perform actions including:
estimating the correlation coefficient between each pair of channels from the three or more channels;
constructing a linear system of equations relating the estimated correlation coefficients and direct energy fractions of each of the three or more channels;
solving the linear system to estimate the direct energy fractions; and
generating a direct component output signal and a diffuse component output signal based in part on the direct energy fractions.