Paper ID 8333

An Advanced Implementation of aDigital Artificial Reveberator

A. Primavera1, S. Cecchi1, L. Romoli1, P. Peretti1 and F. Piazza1

1A3Lab - DIBET - Universita Politecnica delle MarcheVia Brecce Bianche 1, 60131 Ancona Italy

www.a3lab.dibet.univpm.it

Abstract

Reverberation is a well known effect particularly important for listening of recordedand live music. In this paper we propose a real implementation of an enhancedapproach for digital artificial reverberator. Starting from a preliminary analysis ofthe mixing time, the selected impulse response is decomposed in time domain con-sidering the early and the late reflections. Therefore, a short FIR filter is used tosynthesize the first part of the impulse response, and a generalized recursive struc-ture based on IIR filters is used to synthesize the late reflections, exploiting a min-imization criterion in the cepstral domain. Several results are reported taking intoconsideration different real impulse responses and comparing the results with thoseobtained with a previous proposed technique in terms of computational complexityand reverberation quality.

Introduction

Reverberation is probably the most used audio effect employed by musician during live performancesand recording session.

•MEASURED IR: the desired signal can be obtained by convolving the input signal with a mea-sured impulse response.Pros: accurate reproduction of the acoustic environment.Cons: 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).Pros: Great flexibility and high computational efficiency.Cons: Low accuracy.

State of the Art

We propose a Hybrid Reverberator (HR) based on both approaches: this solution attempts tocreate a parametric and realistic reverberation, with a low computational cost.Pros: Great flexibility, low computational cost and audio quality comparable to the convolutionapproach.Cons: None.

Objective of this work

Proposed Hybrid Reverberator (1)

As previously discussed in [1] [2], the proposed Hybrid Reverberator is mainly composed of two partsas the Moorer’s Reverberator [3].

Fig.1 Hybrid Reverberator block diagram for the single channel case.

Based on the convolution with a real IR forthe reproduction of the early echoes.

Early reflections device

Based on IIR filters network (e.g., comband/or all-pass) and a FDN matrix [4] forthe simulation of the reverberation tail.

Late reflections device

Fig.2 Late reflections device block diagram for the singlechannel case.

Proposed Hybrid Reverberator (2)

Set the parameters of the Hybrid Reverberator in order to emulate a real environment starting fromits impulse response.

Aim of the work

An offline procedure has been developed in order to determine all the parameters of the HybridReverberator starting from the IR of a real environment.

Idea

Evaluation of the mixing time to set theEarly reflection device.

Early Reflections Partitioning Use of a minimization criterium, based onSimultaneous Perturbation Stochastic Ap-proximation (SPSA) to set all the para-maters value of the Late reflections device.

Late Reflections Analysis

Proposed Hybrid Reverberator (3) - Early reflections partitioning

Two main approaches are used simultaneously to evaluate the mixing time:

Similarities between IR behavior and gaussian noise can be found in late reflections. Kurtosis (k)and MAD/SD ratio (r) have been used [5].

k =E (x− µ)4

σ4− 3→ 0 r =

E (|x− µ|)σ

→√

2

π(1)

Gaussianity Estimator

The unwrapped phase of the IR tends to become not linear with late reflections evolution [6].Phase Distortion Evaluation

Fig.3 Mixing time evolution for medium room. Fig.4 Mixing time evolution for large room.

Proposed Hybrid Reverberator (4) - Late Reflection Analysis

An offline adaptation procedure, based on SPSA [7], has been used to iteratively find the parametersset of the IIR structure (81 parameters for each audio channel).

Fig.5 General scheme of the adaption procedure usingSPSA procedure.

Fig.6 Evolution of the loss function L.

4 loss functions (It, If , Iff , IT60ω) and a thresholdsystem in [2].

New Approach

A single loss function L computed in cepstraldomain [8].

L = max

max

√√√√√ K∑

i=1

M∑j=1

[Tr(i, j)− Ta(i, j)]2

where:

• Tr is a matrix representing the Mel-Frequency Cep-stral Coefficients (MFCC) derived from the real IR.

• Ta is the MFCC obtained by the artificial IR.

Loss Function

Experimental Results - EDR

The automatic procedure for the parameters setting has been tested with 2 different real IRs, relativeto a Medium and a Large room.

Fig.7 Energy Decay Relief of the analyzed impulse responses for medium and large room.

Fig.8 Energy Decay Relief of the artificial impulse responses for medium and large room.

Experimental Results - Comparison with a previous method

The proposed method has been compared with a previous one proposed by the same authors [2].

A real-time implementation of the proposed algorithm has been realized on a DSP board (Omap-L137 TI).

The Workload results as the sum of two contributes:

• Early reflections device: it depends on the mixingtime value.

• Late reflections device: it is always equal to 13%.

WORKLOADRoom Proposed approach Previous approach

medium 26% 21%large 24% 19%

Computational Cost

The artificial reverberator has been compared with the approach proposed in [2] and with the real reverberation effect.

Listening Tests

Fig.9 Listening tests results.

As confirmed by the listening tests a low increaseof the required workload produces an evident im-provement of the perceived reverberation effect.

Consideration

Conclusions

• 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 a single loss functioncomputed in the cepestral domain using the SPSA criterium.

• 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 andobjective measures.

• Listening test have been executed in order to compare the proposed algorithm with the performance obtained usinganother approach proposed by the same authors.

• As confirmed by the listening tests the artificial effect generated sounds really similar to the natural one validatingthe proposed approach.

• Future works will be oriented toward the refinement of the minimization criterium (Particle Swarm or Genetic algo-rithms can be used in order to obtain better performance).

References

[1] R. Stewart and D. Murphy, “A Hybrid Artificial Reverberation Algorithm,” in Proc. 122nd Audio Engineering Society Convention (AES’07), Vienna, Austria, May 2007.

[2] A. Primavera, L. Palestini, S. Cecchi, F. Piazza, and M. Moschetti, “A Hybrid Approach for Real-Time Room Acoustic Response Simulation,” in Proc. 128th Audio Engineering Society Convention (AES’10),London, UK, May 2010.

[3] J.A. Moorer, “About This Reverberation Business,” Computer Music Journal, vol. 3, no. 2, pp. 13–28, 1979.

[4] J. Jot, “Digital Delay Networks for designing artificial reverberators,” in Proc. 90th Audio Engineering Society Convention (AES’91), Paris, Feb 1991.

[5] R. Stewart and M. Sandler, “Statisical measures of early reections of room impulse responses,” in in DAFX 07), Bordeaux, France, Sep. 2007.

[6] G. Defrance and J.D. Polack, “Measuring the mixing time in auditoria,” in Proc. 155th Meeting of the Acoustical Society of America), Jun 2001, vol. 49, pp. 867–903.

[7] J.C. Spall, “Implementation of the Simultaneous Perturbation Algorithm for Stochastic Optimization,” in IEEE Transactions on Aerospace and Electronic Systems, 1998, vol. 34, pp. 817–823.

[8] S. Heise, M. Hlatky, and J. Loviscach, “Automatic Adjustment of Off-the-Shelf Reverberation Effects,” in Proc. 126th Audio Engineering Society Convention (AES’09), Munich, Germany, May 2009.