Reverberation is a well known effect particularly important for music listening especially for recorded and live music. Generally, there are two approaches for artificial reverberation: the desired signal can be obtained by convolving the input signal with a measured impulse response (IR) or a synthetic one. Taking into account the advantages of both approaches, a hybrid artificial reverberation algorithm is presented. The early reflections are derived from a real IR, truncated considering the calculated mixing time, and the reverberation tail is obtained considering the Moorer's structure. The parameters defining this structure are derived from the analyzed IR, using a minimization criteria based on Simultaneous Perturbation Stochastic Approximation (SPSA). The obtained results showed a high-quality reverberator with a low computational load.

1. Paper ID 8055
A Hybrid Approach for Real-Time Room Acoustic
Response Simulation
A. Primavera1
, L. Palestini1
, S. Cecchi1
, F. Piazza1
and M. Moschetti2
1
3MediaLabs - Universit`a Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy
2
Korg Italy, Via Cagiata, 60027 Osimo, Italy
www.a3lab.dibet.univpm.it
1. Introduction
Reverberation is a well known effect that has an important role in our lis-
tening experience: it is composed of a series of delayed reflections from
many different directions of a reproduced sound.
Artificial Reverberation: State of the Art
• Measured IR: the desired signal can be obtained by convolving the in-
put signal with a measured impulse response → Accurate reproduction
of a space and computational complexity bounded to the IR length.
• Synthetic IR: the reverberation effect can be obtained using an IIR
structure (e.g. comb and/or allpass). → Great flexibility, high compu-
tational efficiency, low accuracy.
Objective of this work
We propose a Hybrid Reverberator (HR) based on both approaches: this
solution attempts to create a parametric and realistic reverberation, with
a low computational cost.
2. Proposed Algorithm
The overall common scheme of the proposed Hybrid Reverberator is de-
rived from the Moorer’s Reverberator [1].
Figure 1: Block diagram of proposed Hybrid Reverberator for the single channel case.
• Early reflections device: based on the convolution with an acoustic IR
for the reproduction of the early echoes.
• Late reflections device: based on the Freeverb structure [2], an IIR
filter network composed of four all-pass filters in series and eight par-
allel low-pass feedback comb filters (for each audio channel), for the
simulation of the reverberation tail.
Figure 2: Block diagram of Freeverb (single channel).
An offline procedure allows to determine all the parameters of the Hybrid
Reverberator starting from an IR of a real environment:
1. Evaluation of the mixing time [3, 4, 5] to set the early reflection device
(Early Reflection Partitioning).
2. Use of a minimization criteria, based on Simultaneous Perturbation
Stochastic Approximation (SPSA) [6, 7] to set the late reflections de-
vice (Late Reflection Analysis).
3. Early Reflection Partitioning
Two main approaches used simultaneously to evaluate the mixing time:
• Gaussianity Estimator, Kurtosis (k) and MAD/SD ratio (r).
k =
E (x − µ)4
σ4
− 3 → 0 r =
E (|x − µ|)
σ
→
2
π
(1)
• Evaluation of the phase distortion based on eXtensive Fourier Trans-
form.
Figure 3: Estimation of the mixing time on Medium and Large Room IRs.
4. Late Reflection Analysis
An adaptation procedure, based on SPSA, has been used to iteratively
find the parameters set of the IIR structure.
Figure 4: General scheme of the adaption proce-
dure.
3 loss functions (It, If, Iff) and
hysteresis system in [8, 9].
Our Approach
4 loss functions (Itmodified, If, Iff,
Itω60) and threshold system.
1. The index It allows to recreate envelope and echo density. Subdividing
the temporal axis in N windows of length Ncam it is possible to define:
It = max(Pi) 1 ≤ i ≤ N (2)
Pi =



Pri
−Pai
Pri
Pri
> Pai
Pai
−Pri
Pai
Pai
> Pri
Pri
= 1
Ncam
Ncam
k=1 h2
r(k + (i − 1)Ncam);
Pai
= 1
Ncam
Ncam
k=1 h2
a(k + (i − 1)Ncam);
In order to reduce the jagged effect due to the normalization a new index
Itmodified based on an extensive window has been introduced:
Ncami
= Ncam0
∗ ρi
1 ≤ ρ ≤ 1.1 (3)

2. 2. The index If is used to obtain a similar frequency coloration. It is defined
as:
If =
L
k=1
(Hr(f) − Ha(f))2
(4)
where L is the FFT length.
3. The index Iff is used to minimize the maximum shifting. It is defined as
Iff = max (|Fai
− Fri
|) 1 ≤ i ≤ M (5)
where
Fri
= max(Hr(k + (i − 1)Mcam)) 0 < k < Mcam − 1 (6)
Fai
= max(Ha(k + (i − 1)Mcam)) 0 < k < Mcam − 1 (7)
They are obtained subdividing the frequencies axis in M window of
length Mcam, for the i−th window.
4. The index Itω60 allows to recreate the same reverberation time for all the
frequencies.
Itω60 = max (|T60r(ω) − T60a(ω)|) (8)
Figure 5: Evolution of the four indices (It, Itmodified, If and Iff ) against to the iterations numbers.
Taking into account a minimization problem, where L(θ) is the loss func-
tion and θ is the p-dimensional vector of parameters, steepest descent
method can be used to find the set of parameters θ∗
that minimize L(θ):
∂L(θ)
∂θ θ=θ∗
= 0 → characterized by a large number of parameters
Starting from the general recursive form of a classic minimization problem:
θk+1 = θk − ak
∂L(θk)
∂θk
→ SPSA → θk+1 = θk − akgk(θk)
where ak is an arbitrary gain sequence and gk is the gradient estimation
∂L(θk)
∂θk
on the k−th iteration. Considering a simultaneous perturbation, the
value of gk can be computed as
gk(θk) =
y (θk + ck∆k) − y (θk − ck∆k)
2ck


∆k1
...
∆kp


−1
(9)
where y(·) denotes a measure of the loss function, ck is a gain sequence
and ∆(k) is a p-dimensional random vector.
5. Real-Time Implementation
A real time implementation of the Hybrid Reverberator has been real-
ized on DIOPSIS940HF a dual-core processing platform composed of an
ARM926 at 160MHz and a mAgicV VLIW floating-point DSP at 80MHz.
• Early Reflection Device: FIR filtering implemented using the parti-
tioned overlap and save technique [10, 11, 12] to obtain low input/output
delay.
• Late Reflection Device: High performance have been obtained paral-
lelizing DMA transfer and signal processing operations.
Design constraints impose an implementation of the Hybrid Reverberator
using a frame-size (FS) of 64 samples.
6. Experimental Results
The automatic procedure for the parameters setting has been tested
with 2 different real IRs, relative to a Medium and a Large Room.
Figure 6: EDR of natural (top) and artficial (bottom) IRs using Hybrid Reverberator.
The artificial effect generated to reproduce the Medium Room environ-
ment sounds really similar to the natural one, while the effect generated
to reproduce the Large Room environment sounds slightly unnatural.
Maximum length of the IR using Partitioned Overlap-Save (P-OLS) → 64
samples → 160ms.
Workload results as the sum of
two contributes:
• Early Reflections Device → it de-
pends on the mixing time value.
• Late Reflections Device → it is
equal to 11%.
P-OLS HR
(2048 samples) (64 samples)
Medium Room 14% 53%
Large Room 18% 45%
Table 4: Workload obtained using P-OLS and
HR with different values of the FS.
7. Conclusion
• A Hybrid Reverberator with an automatic procedure for the parameters
setting has been proposed.
• The automatic procedure is based on the evaluation of the mixing time
and the minimization of four different loss function using SPSA criteria.
• A real time implementation of the proposed algorithm has been realized
on a DSP platform.
• Different tests have been carried out in order to evaluate reverberation
quality, in terms of subjective evaluation and objective measures.
• The generated artificial effect sounds really similar to the natural one
when T60 is relatively short (T60<1.5s).
• Future works will be oriented toward the refinement of the IIR filters net-
work.
References
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