This paper introduces a time-variant reverberation algorithm as an extension of the feedback delay network (FDN). By modulating the feedback matrix nearly continuously over time, a complex pattern of concurrent amplitude modulations of the feedback paths evolves. Due to its complexity, the modulation produces less likely perceivable artifacts and the time-variation helps to increase the liveliness of the reverberation tail. A listening test, which has been conducted, confirms that the perceived quality of the reverberation tail can be enhanced by the feedback matrix modulation. In contrast to the prior art time-varying allpass FDNs, it is shown that unitary feedback matrix modulation is guaranteed to be stable. Analytical constraints on the pole locations of the FDN help to describe the modulation effect in depth. Further, techniques and conditions for continuous feedback matrix modulation are presented.

1.
V.
Valimaki
,
J.
Parker
,
L.
Savioja
,
J.
Smith
, and
J.
Abel
, “
Fifty years of artificial reverberation
,”
IEEE Trans. Audio Speech Lang Process.
20
(
5
),
1421
1448
(
2012
).
2.
J. B.
Allen
and
D. A.
Berkley
, “
Image method for efficiently simulating small-room acoustics
,”
J. Acoust. Soc. Am.
65
(
4
),
943
950
(
1979
).
3.
M. R.
Schroeder
and
B. F.
Logan
, “ 
‘Colorless’ artificial reverberation
,”
J. Acoust. Soc. Am.
32
(
11
),
1520
1520
(
1960
).
4.
M.
Vorländer
, “
Simulation of the transient and steady-state sound propagation in rooms using a new combined ray-tracing/image-source algorithm
,”
J. Acoust. Soc. Am.
86
(
1
),
172
178
(
1989
).
5.
D.
Botteldooren
, “
Finite-difference time-domain simulation of low-frequency room acoustic problems
,”
J. Acoust. Soc. Am.
98
(
6
),
3302
3308
(
1995
).
6.
W. G.
Gardner
, “
Reveberation algorithms
,” in
Applications of Digital Signal Processing to Audio and Acoustics
, edited by
K.
Brandenburg
and
M.
Kahrs
(
Kluwer
,
New York
,
2002
), Chap. 3, pp.
85
132
.
7.
J. O.
Smith
, “
A new approach to digital reverberation using closed waveguide networks
,” in
International Computer Music Conference
,
Burnaby, British Columbia, Canada
(
1985
), pp.
47
53
.
8.
H.
Karjalainen
and
M.
Jarvelainen
, “
More about this reverberation science: Perceptually good late reverberation
,”
AES 111th Convention
,
New York
(
2001
).
9.
J. L.
Nielsen
and
U. P.
Svensson
, “
Performance of some linear time-varying systems in control of acoustic feedback
,”
J. Acoust. Soc. Am.
106
(
1
),
240
254
(
1999
).
10.
M.
Poletti
, “
The stability of multichannel sound systems with frequency shifting
,”
J. Acoust. Soc. Am.
116
,
853
871
(
2004
).
11.
D.
Griesinger
, “
Improving room acoustics through time-variant synthetic reverberation
,” in
Audio Engineering Society Convention 90
,
Paris, France
(
1991
), pp.
1
10
.
12.
T.
Lokki
and
J.
Hiipakka
, “
A time-variant reverberation algorithm for reverberation enhancement systems
,” in
Proceedings of COST G-6 Conference on Digital Audio Effects (DAFX-01)
,
Limerick, Ireland
(
2001
), pp.
28
32
.
13.
S. J.
Schlecht
and
E. A.
Habets
, “
Reverberation enhancement from a feedback delay network perspective
,” in
Electrical and Electronics Engineers in Israel (IEEEI), 2012 IEEE 27th Convention
(
2012
).
14.
T.
Laakso
,
V.
Valimaki
,
M.
Karjalainen
, and
U.
Laine
, “
Splitting the unit delay—Tools for fractional delay filter design
,”
IEEE Sign. Process. Mag.
13
(
1
),
30
60
(
1996
).
15.
J.
Dattorro
, “
Effect design, part 1: Reverberator and other filters
,”
J. Audio Eng. Soc.
45
(
9
),
660
684
(
1997
).
16.
R.
Väänänen
,
V.
Välimäki
,
J.
Huopaniem
, and
M.
Karjalainen
, “
Efficient and parametric reverberator for room acoustics modeling
,” in
Proceedings of the International Computer Music Conference
,
The International Computer Music Association
(
1997
), pp.
200
203
.
17.
L.
Dahl
and
J.-M.
Jot
, “
A reverberator based on absorbent all-pass filters
,” in
Proceedings of the International Computer Music Conference COST G-6 on Digital Audio Effects (DAFX-00)
,
Verona, Italy
(December, 2000), pp.
1
6
.
18.
J.
Dattorro
, “
Effect design, part 2: Delay line modulation and chorus
,”
J. Audio Eng. Soc.
45
(
10
),
764
788
(
1997
).
19.
J.
Stautner
and
M.
Puckette
, “
Designing multi-channel reverberators
,”
Comput. Music J.
6
(
1
),
52
65
(
1982
).
20.
J.-M.
Jot
and
A.
Chaigne
, “
Digital delay networks for designing artificial reverberators
,” in
Audio Engineering Society Convention 90
,
Paris, France
(February,
1991
), pp.
1
12
.
21.
D.
Rocchesso
and
J. O.
Smith
, “
Circulant and elliptic feedback delay networks for artificial reverberation
,”
IEEE Trans. Audio Speech Lang Process.
5
(
1
),
51
63
(
1997
).
22.
M.
Gerzon
, “
Unitary (energy-preserving) multichannel networks with feedback
,”
Electron. Lett.
12
(
11
),
278
279
(
1976
).
23.
M.
Schroeder
and
B.
Logan
, “
Colorless artificial reverberation
,”
J. Audio Eng. Soc.
9
(
3
),
192
197
(
1961
).
24.
S. J.
Schlecht
and
E. A.
Habets
, “
Connections between parallel and serial combinations of comb filters and feedback delay networks
,” in
International Workshop on Acoustic Signal Enhancement; Proceedings of IWAENC 2012
,
VDE
(
2012
), pp.
1
4
.
25.
C. D.
Meyer
, “
Determinants
,” in
Matrix Analysis and Applied Linear Algebra
(
SIAM
,
Philadelphia
,
2000
), Chap. 6, pp.
459
488
.
26.
J.
Laroche
, “
On the stability of time-varying recursive filters
,”
J. Audio Eng. Soc.
55
(
6
),
460
471
(
2007
).
27.
C. D.
Meyer
, “
Norms, inner products, and orthogonality
,” in
Matrix Analysis and Applied Linear Algebra
(
SIAM
,
Philadelphia
,
2000
), Chap. 5, pp.
269
458
.
28.
J. O.
Smith
, “
Artificial reverberation
,” in
Physical Audio Signal Processing—For Virtual Musical Instruments And Audio Effects
(
W3K
,
2010
).
29.
W.
Hayman
, “
Angular value distribution of power series with gaps
,”
Proc. London Math. Soc.
s3-24
(
4
),
590
624
(
1972
).
30.
P.
Hrubeš
, “
A note on the real τ-conjecture and the distribution of roots
,”
Electron. Colloq. Comput. Complex. (ECCC)
19
(
121
),
1
9
(
2012
).
31.
J.-M.
Jot
, “
An analysis/synthesis approach to real-time artificial reverberation
,” in
International Conference on Acoustics, Speech, and Signal Processing, ICASSP-92
,
IEEE
(
1992
), Vol.
2
, pp.
221
224
.
32.
G.
Waters
, “
Sound quality assessment material—Recordings for subjective tests: User's handbook for the EBU—SQAM compact disk
,” European Broadcasting Union (EBU), technical report (
1988
), pp.
1
13
.
33.
F.
Nagel
,
T.
Sporer
, and
P.
Sedlmeier
, “
Toward a statistically well-grounded evaluation of listening tests—Avoiding pitfalls, misuse, and misconceptions
,” in
Audio Engineering Society Convention 128
,
Audio Engineering Society
(May,
2010
), pp.
1
10
.
34.
J. D.
Gibbons
and
S.
Chakraborti
,
Nonparametric Statistical Inference
(
Dekker
,
New York
,
2003
), Chap.8, pp.
296
318
.
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